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Hindawi Publishing CorporationAdvances in Fuzzy SystemsVolume 2013 Article ID 385974 7 pageshttpdxdoiorg1011552013385974
Research ArticleSpatiotemporal Hotspots Analysis for Exploring the Evolution ofDiseases An Application to Oto-Laryngopharyngeal Diseases
Ferdinando Di Martino1 Roberta Mele1 Umberto E S Barillari2 Maria Rosaria Barillari2
Irina Perfilieva3 and Sabrina Senatore4
1 Universita degli Studi di Napoli Federico II Dipartimento di Architettura Via Toledo 402 80134 Napoli Italy2 Seconda Universita degli Studi di Napoli Dipartimento di Psichiatria Neuropsichiatria InfantileAudiofoniatria e Dermatovenereologia Lgo Madonna delle Grazie 80138 Napoli Italy
3 Centre of Excellence IT4 Innovations Institute for Research and Applications of Fuzzy Modelling University of Ostrava30 dubna 22 70103 Ostrava Czech Republic
4Universita degli Studi di Salerno Dipartimento di Informatica Via Ponte don Melillo 80084 Fisciano Salerno Italy
Correspondence should be addressed to Ferdinando Di Martino fdimartiuninait
Received 1 May 2013 Revised 29 July 2013 Accepted 29 July 2013
Academic Editor Salvatore Sessa
Copyright copy 2013 Ferdinando Di Martino et alThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper presents a spatiotemporal analysis of hotspot areas based on the Extended Fuzzy C-Means method implemented in ageographic information system This method has been adapted for detecting spatial areas with high concentrations of events andtested to study their temporal evolution The data consist of georeferenced patterns corresponding to the residence of patients inthe district of Naples (Italy) to whom a surgical intervention to the oto-laryngopharyngeal apparatus was carried out between theyears 2008 and 2012
1 Introduction
In a GIS the impact of phenomena in a specific area due tothe proximity of the event (eg the study of the impact area ofan earthquake or the area constraint around a river basin) isperformed using buffer area geoprocessing functions Given ageospatial event topologically represented as a georeferencedpunctual linear or areal element an atomic buffer area isconstituted by circular areas centered on the element Forexample if the event is the epicenter of an earthquakegeoreferenced by a point a set of buffer areas is formed byconcentric circular areas around that point the radius of eachcircular buffer area is defined a priori
When it is not possible to define statically an area ofimpact and we need to determine what is the area affectedby the presence of a consistent set of events we are facedwith the problem of detecting this area as a cluster on whichthe georeferenced events are thickened as well These clusters
are georeferenced represented as polygons on the map andcalled hotspot areas
The study of hotspot areas is vital in many disciplinessuch as crime analysis [1ndash3] which studies the spread onthe territory of criminal events fire analysis [4] whichanalyzes the phenomenon of spread of fires on forested areasand disease analysis [5ndash7] which studies the localizationof focuses of diseases and their temporal evolution Theclustering methods mainly used for detecting hotspot areasare the algorithms based on density (see [8 9]) they candetect the exact geometry of the hotspots but are highlyexpensive in terms of computational complexity and in thegreatmajority of cases it is not necessary to determine exactlythe shape of the clusters The clustering algorithmmore usedfor its linear computational complexity is the Fuzzy C-Meansalgorithm (FCM) [10] a partitive fuzzy clustering methodthat uses the Euclidean distance to determine prototypescluster as points
2 Advances in Fuzzy Systems
Let X = x1 x
119873 sub 119877
119899 be a dataset composed of119873 pattern x
119895= (119909
1119895 1199092119895 119909
119899119895)
119879 where 119909119896119895
is the 119896thcomponent (feature) of the pattern x
119895 The FCM algorithm
minimizes the following objective function
119869 (XUV) =
119862
sum
119894=1
119873
sum
119895=1
119906
119898
119894119895119889
2
119894119895 (1)
where 119862 is the number of clusters fixed a priori 119906119894119895is the
membership degree of the pattern x119895to the 119894th cluster (119894 =
1 119862) V = v1 v
119862 sub 119877
119899 is the set of points given bythe centers of the 119862 clusters (prototypes) 119898 is the fuzzifierparameter and 119889
119894119895is the distance between the center k
119894=
(V1119894 V2119894 V
119899119895)
119879 of the 119894th cluster and the 119895th vector x119895
calculated as the Euclidean norm
119889119894119895=
10038171003817100381710038171003817
(x119895minus k119894)
10038171003817100381710038171003817
= radic
119899
sum
119896=1
(x119896119895
minus k119896119894)
2
(2)
Using the Lagrange multipliers method for minimizing theobjective function (1) we obtain the following solution for thecenter of each cluster prototype
k119894=
sum
119873
119895=1119906
119898
119894119895x119895
sum
119873
119895=1119906
119898
119894119895
(3)
where 119894 = 1 119862 and for membership degrees 119906119894119895
119906119894119895=
1
(sum
119888
ℎ=1(119889
2
119894119895119889
2
ℎ119895))
2(119898minus1) (4)
subjected to the constraints
119862
sum
119894=1
119906119894119895= 1 forall119895 isin 1 119873
0 lt
119873
sum
119895=1
119906119894119895lt 119873 forall119894 isin 1 119862
(5)
Initially the 119906119894119895rsquos and the v
119894are assigned randomly and
updated in each iteration If 119880
(119897)= (119906
(119897)
119894119895) is the matrix U
calculated at the 119897-th step the iterative process stops when10038171003817100381710038171003817
U(119897) minus U(119897minus1)10038171003817100381710038171003817
= max119894119895
10038161003816100381610038161003816
119906
(119897)
119894119895minus 119906
(119897minus1)
119894119895
10038161003816100381610038161003816
lt 120576 (6)
where 120576 gt 0 is a prefixed parameterThis algorithm has a linear computational complexity
however it is sensitive to the presence of noise and outliersfurthermore the number of cluster 119862 is fixed a priori andneeds to use a validity index for determining an optimal valuefor the parameter 119862
In order to overcome these shortcomings in [11 12] theEFCM algorithm is proposed where the cluster prototypesare hyperspheres in the case of the Euclidean metric LikeFCM the EFCM algorithm is characterized by a linear com-putational complexity furthermore it is robust with respect
A minus (A cap B)
= A minus B
A cap BB minus (A cap B) =
B minus A
Figure 1 Intersections of two hotspots detected for events thathappened in two consecutive periods
to the presence of noise and outliers and the final number ofclusters is determined during the iterative process
In [13 14] the authors propose the use of the EFCMalgorithm for detecting hotspot areas The final hotspots areidentified as the detected cluster prototypes and shown on themap as circular areas In [4] the authors analyze the spatio-temporal evolution of the hotspots in the fire analysis Thepattern event dataset is partitioned according to the timeof the eventrsquos detection so each subset is corresponding toa specific time interval The authors compare the hotspotsobtained in two consecutive years by studying their inter-sections on the map In this way it is possible to follow theevolution of a particular phenomenon
The cluster prototypes detected from EFCM method arecircular areas on themap that can approximate a hotspot areaFigure 1 shows an example of two circular hotspots obtainedas clusters
Figure 1 shows three different regions
(i) An area in which the hotspot 119860 is not intersectedby the hotspot 119861 (corresponding to 119860 minus (119860 cap 119861) =
119860minus119861) this region can be considered as a geographicalarea in which prematurely detected event disappearssuccessively
(ii) The region of intersection of the two hotspots 119860 cap 119861this region can be considered a geographical area inwhich the event continues to persist
(iii) An area in which the hotspot B is not intersected bythe hotspotA (corresponding to 119861minus(119860cap119861) = 119861minus119860)this region can be considered as a geographical area inwhich the prematurely undetected event propagatessuccessively
We can study the spatio-temporal evolution of the hotspotsby analyzing the interactions between the correspondingcircular cluster prototypes obtained for consecutive periods
Advances in Fuzzy Systems 3
and detecting the presence of new hotspots in regions previ-ously not covered by hotspots and the absebce of hotspots inregions previously spatially included in hotspot areas
In this research we present a method for studyingthe spatio-temporal evolution of hotspots areas in diseaseanalysis we apply the EFCM algorithm for comparingin consecutive years event datasets corresponding to oto-laryngopharyngeal diseases diagnosis detected in the districtof Naples (I) Each event corresponds to the residence of thepatient who contracted the disease
We study the spatio-temporal evolution of the hotspotsanalyzing the intersections of hotspots corresponding totwo consecutive years the displacement of the centroidsthe increase or reduction of the hotspots areas and theemergence of new hotspots
In Section 2 we give an overview of the EFCM algo-rithm In Section 3 we present our method for studying thespatio-temporal evolution of hotspots in disease analysis InSection 4 we present the results of the spatio-temporal evolu-tion of hotspots for the otolaryngologist-laryngopharyngealdiseases diagnosis events detected in the district of Naples (I)Our conclusions are in Section 5
2 The EFCM Algorithm
In the EFCM algorithm we consider clustering prototypesgiven by hyperspheres in the 119899-dimensional featurersquos spaceThe 119894th hypersphere is characterized by a centroid v
119894=
(k1119894 k
119899119894) and a radius 119903
119894
Indeed if 119903119894is the radius of 119881
119894 we say that 119909
119895belongs to
119881119894if 119889119894119895le 119903119894
The radius 119903119894is obtained considering the covariance
matrix 119875119894associated with the 119894th cluster defined as
P119894=
sum
119873
119895=1119906
119898
119894119895(x119895minus k119894) (x119895minus k119894)
119879
sum
119873
119895=1119906
119898
119894119895
(7)
whose determinant gives the volume of the 119894th cluster SinceP119894is symmetric and positive it can be decomposed in the
following form
Pi = Q119894Λ119894Q119879119894 (8)
where 119876119894is an orthonormal matrix and Δ
119894= (120582
119894119895) is
a diagonal matrix The radius 119903119894is given by the following
formula (see [12])
119903119894=
1
119899
radic
119899
prod
119896=1
120582
1119899
119894119896=
radicdet (119875119894)
1119899
(9)
The objective function to be minimized is the following
119869 (119883119880 119881) =
119862
sum
119894=1
119873
sum
119895=1
119906
119898
119894119895(119889
2
119894119895minus 119903
2
119894) (10)
where the membership degrees 119906119894119895are updated as
119906119894119895= 1 times (
119862
sum
ℎ=1
((119889
2
119894119895max (0 1 minus 119903
2
119894119889
2
119894119895))
(119889
2
ℎ119895max (0 1 minus 119903
2
ℎ119889
2
ℎ119895)))
1(119898minus1)
)
minus1
=
1
sum
119862
ℎ=1(119889
2
119894119895119908119894119895119889
2
ℎ119895119908ℎ119895)
1(119898minus1)
(11)
We set 11988910158402119896119895
= 119889
2
119896119895119908119896119895
= max(0 1198892119896119895
minus 119903
2
119896) and define the
number 120593119895
= card119896 isin 1 119862 119889
1015840
119896119895= 0 for any 119895 =
1 119873 thus we obtain
119906119894119895=
1
sum
119862
ℎ=1(119889
1015840
119894119895119889
1015840
ℎ119895)
2(119898minus1)if 120593119895= 0
119906119894119895=
0 if 1198891015840119894119895gt 0
if 120593119895gt 0
1
120593119895
if 1198891015840119894119895= 0
(12)
However the usage of (12) produces the negative effect ofdiminishing the objective function (10) when a meaningfulnumber of features are placed in a cluster and this fact canprevent the separation of the clusters Then a solution to thisproblem consists in the assumption of a small starting valueof 119903119894and then it is increased gradually with the factor120573(119897)119862(119897)
where119862(119897) is the number of clusters at the 119897th iteration and120573
(119897)
is defined recursively as 120573(0) = 1 120573
(119897)= min(119862(119897minus1) 120573(119897minus1)) by
setting
119868119894119896
=
sum
119873
119895=1min (119906
119894119895 119906119896119894)
sum
119873
119895=1119906119894119895
(13)
and the symmetric matrix 119878 = (119878119894119896) where 119878
119894119896= max119868
119894119896 119868119896119894
is defined as well If 119878(119897) is the matrix 119878 at the 119897th iteration (119897 gt
1) and the threshold 120572
(119897)= 1(119862
(119897)minus 1) is introduced as limit
then two indexes 119894lowast and 119896
lowast are determined such that 119878(119897)119894lowast119896lowast
ge
120572
(119897) and thus 119894lowast and 119896
lowast are merged by setting
119906
(119897)
119894lowast119895= 119906
(119897)
119894lowast119895+ 119906
(119897)
119896lowast119895 forall119895 isin 1 119873
119862
(119897)= 119862
(119897minus1)+ 1
(14)
The 119896
lowastth row can be removed from the matrix 119880
(119897) Inother words the EFCM algorithm can be summarized in thefollowing steps
(1) The user assigns the initial number of clusters 119862
(0)
119898 gt 1 (usually119898 = 2) 120576 gt 0 the initial value 119878(0)119894119896
= 0and 120573
(0)= 1
(2) The membership degrees 119906
(0)
119894119895(119895 = 1 119873 and 119894 =
1 119862(0)) are assigned randomly
4 Advances in Fuzzy Systems
Figure 2 Example of events georeferenced on a road network
(3) The centers of the clusters V119894are calculated by using
(3)(4) The radii of the clusters are calculated by using (9)(5) 119906119894119895is calculated by using (12)
(6) The indexes 119894lowast and 119896
lowast are determined in such a waythat 119878(119897)119894lowast119896lowast assumes the possible greatest value at the 119897th
iteration(7) If |119878(119897)
119894lowast119896lowast minus 119878
(119897minus1)
119894lowast119896lowast | lt 120576 and 119878
(119897)
119894lowast119896lowast gt 120572(119897) = 1(119862
(119897minus1)minus 1)
then the 119894lowastth and 119896
lowastth clusters aremerged via (14) andthe 119896lowastth row is deleted from 119880
(119897)(8) If (6) is satisfied then the process stops otherwise go
to the step (3) for the (119897 + 1)th iteration
3 Hotspots Detection and Evolution inDisease Analysis
Each pattern is given by the event corresponding to theresidence of the patient to whom a specific disease has beendetected The two features of the pattern are the geographiccoordinates of the residence
The first step of our process is a geocoding activitynecessary for obtaining the event dataset starting by the streetaddress of the patients
To ensure an accurate matching for the geopositioning ofthe event we need the topologically correct road network andthe corresponding complete toponymic data
The starting data include the name of the street and thehouse number of the patientrsquos residence After the matchingprocess each data is converted in an event point georefer-enced on the map
In Figure 2 the road network of the district of Naples isshown the name of the street is labeled on themap the eventsare georeferenced as points on the map
Figure 3 shows the data corresponding to an eventselected on the map
After geo-referencing each event the event dataset canbe split partitioning them by time interval For example theevent in Figure 3 can be split by the field ldquoYearrdquo
For each subset of events we apply the EFCM algorithmto detect the final cluster prototypes
Figure 3 Data associated to an event on the map
Figure 4 A form created in theGIS Tool ESRIArcGIS formanagingthe EFCM process
In this research we point out the analysis of the temporalevolution and spread of oto-laryngo-pharyngeal diseasesdetected within the district of Naples The datasets dividedby time sequences corresponding to periods of one yearare made up of patterns for different events georeferencedcorresponding to ailments encountered in patients for whichan intervention and the subsequent histological examinationwere pointed out as well The event refers to the geoposition-ing of the location of the patient
The data have been further divided by the type of thedisease for analyzing the distribution and evolution of eachspecific disease on the area of the study
The EFCM algorithm has been encapsulated in the GISplatform ESRI ArcGIS Figure 4 shows the mask created forsetting the parameters and running the EFCM algorithm
We can set other numerical fields for adding otherfeatures to the geographical coordinates
Initially we set the initial number of clusters the fuzzifierm and the error threshold for stopping the iterations Afterrunning EFCM the number of iterations the final numberof clusters and the error calculated at the last iteration arereported The resultant clusters are shown as circular areason the map and can be saved in a new geographic layer
The final process concerns the comparative analysis ofthe hotspots obtained by the clusters corresponding to eachsubsets of events
Advances in Fuzzy Systems 5
Figure 5 Analysis of the spatio-temporal evolution of hotspotsdetected in two consecutive periods
Figure 6 Edema of bilateral Reinke diseasemdashyear 2011 display ofthe hotspots on the map
Figure 5 shows an example of display on the map ofhotspots obtained as final clusters for two consecutive subsetof events
In order to assess the expansion and the displacementof a hotspot we measure the radius of the hotspot and thedistance between the centroids of two intersecting hotspots
In the next section we present the results obtained byapplying this method for the data corresponding to surgicalinterventions to the oto-laryngo-pharyngeal apparatus inpatients residents in the district of Naples between the years2008 and 2012
We divide the dataset per year and analyze various typesof diseases
Among the types of the most frequent diseases thefollowing were analyzed
(i) carcinoma(ii) edema of bilateral Reinke(iii) hypertrophy of the inferior turbinate(iv) nasal polyposis(v) bilateral vocal fold prolapse
In the next section we show the most significant resultsobtained by applying this method to the each partitioneddataset of events
Figure 7 Edema of bilateral Reinke diseasemdashyear 2012 display ofthe hotspots on the map
Table 1 Endema of bilateral Reinke diseasemdashfinal number ofclusters and final error for year
Year Initial numberof clusters
Final numberof clusters |119880
(119897)minus 119880
(119897minus1)| 120576
2008 15 4 048 times 10
minus21 times 10
minus2
2009 15 4 055 times 10
minus21 times 10
minus2
2010 15 4 071 times 10
minus21 times 10
minus2
2011 15 4 067 times 10
minus21 times 10
minus2
2012 15 3 053 times 10
minus21 times 10
minus2
4 Test Results
Wepresent the results obtained on the event dataset describedabove in the period between the years 2008 and 2012
We consider first the subset of data corresponding to theedema of bilateral Reinke disease
We fix the fuzzifier parameter to 01 the initial number ofclusters to 15 and the final iteration error to 1 times 10minus2
Table 1 shows the results obtained for each yearWe present the details relating to the comparison of the
hotspots obtained by considering the event data for the years2011 and 2012
Figures 6 and 7 show respectively the hotspots obtainedby using the pattern subset of events that occurred in the years2011 and 2012
Figure 8 shows the overlap of the hotspots obtained forthe two years in red the hotspots corresponding to the year2011 in blue the ones corresponding to the year 2012
Table 2 shows in the first two columns the labels of thehotspots in 2011 and 2012 in third (resp fourth) column theradius obtained in 2011 (resp 2012) and the distance betweenthe centroids is given in the fifth column
The results show that only hotspot 3 obtained for the year2011 remains almost unchanged in the year 2012 Insteadhotspots 1 and 2 seem to merge into a single larger hotspot(the hotspot 1 obtained for the year 2012) and hotspot 4 thatshifts about 1 km is expanded the radius of this hotspot in2012 is about 65 km (hotspot 3 obtained for the year 2012 inFigure 8)
6 Advances in Fuzzy Systems
Figure 8 Edema of bilateral Reinke diseasemdashyears 2011 and 2012display of the two hotspotsrsquo series
Table 2 Endema of bilateral Reinke diseasemdashcomparison results ofthe hotspots obtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 1724 3848 17592 1 1943 3848 15073 2 3434 3453 00744 3 3591 6519 1115
Table 3 Nasal polyposismdashcomparison results of the hotspotsobtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 3087 4951 26562 2 4915 7103 1052
Now we show the results obtained for the disease nasalpolyposis
Figure 9 shows the overlap of the hotspots obtained forthe two years 2011 and 2012
In Table 3 the comparisonrsquos results are reportedThe results in Figure 9 show that in 2011 and 2012 there
are two hotspots the one covering an area of the city ofNaples and the other coveringmanyVesuvian townsThe twohotspots which in 2011 covered a circular area with a radii ofabout 3 and 5 km respectively in 2012 cover a circular areawith radii of about 5 and 7 km respectively
The histogram in Figure 10 shows the trend of the radii ofthe two hotspots in the course of time
It is relevant the spread in recent years of the hotspot thatsurrounds the Vesuvian towns (the radius of this hotspotfrom about 2 km in the year 2008 is about 7 km in the year2012)
Another significant trend concerns the hotspots obtainedfor the carcinoma disease
Also in this case the two main hotsposts cover the cityof Naples and many Vesuvian towns In in this case we havea very high spread of the hotspot covering the city of Naples
Figure 9 Nasal polyposis diseasemdashyears 2011 and 2012 display ofthe two hotspotsrsquo series
8
7
6
5
4
3
2
1
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 10 Nasal polyposis diseasemdashhistogram showing the varia-tion of the radius of the two hotspots over time
(cfr Figure 11) in recent years the radius of this hotspot isincreased up to 95 km
5 Conclusions
The hyperspheres obtained as clusters (circles in case oftwo dimensions) by using EFCM can represent hotspots inhotspot analysis this method has a linear computationalcomplexity and is robust to noises and outliers In hotspotsanalysis the patterns are bidimensional and the features areformed by geographic coordinates the cluster prototypes arecircles that can represent a good approximation of hotspotareas and can be displayed as circular areas on the map
In this paper we present a new method that uses theEFCM algorithm for studying the spatio-temporal evolutionof hotspots in disease analysis
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
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2 Advances in Fuzzy Systems
Let X = x1 x
119873 sub 119877
119899 be a dataset composed of119873 pattern x
119895= (119909
1119895 1199092119895 119909
119899119895)
119879 where 119909119896119895
is the 119896thcomponent (feature) of the pattern x
119895 The FCM algorithm
minimizes the following objective function
119869 (XUV) =
119862
sum
119894=1
119873
sum
119895=1
119906
119898
119894119895119889
2
119894119895 (1)
where 119862 is the number of clusters fixed a priori 119906119894119895is the
membership degree of the pattern x119895to the 119894th cluster (119894 =
1 119862) V = v1 v
119862 sub 119877
119899 is the set of points given bythe centers of the 119862 clusters (prototypes) 119898 is the fuzzifierparameter and 119889
119894119895is the distance between the center k
119894=
(V1119894 V2119894 V
119899119895)
119879 of the 119894th cluster and the 119895th vector x119895
calculated as the Euclidean norm
119889119894119895=
10038171003817100381710038171003817
(x119895minus k119894)
10038171003817100381710038171003817
= radic
119899
sum
119896=1
(x119896119895
minus k119896119894)
2
(2)
Using the Lagrange multipliers method for minimizing theobjective function (1) we obtain the following solution for thecenter of each cluster prototype
k119894=
sum
119873
119895=1119906
119898
119894119895x119895
sum
119873
119895=1119906
119898
119894119895
(3)
where 119894 = 1 119862 and for membership degrees 119906119894119895
119906119894119895=
1
(sum
119888
ℎ=1(119889
2
119894119895119889
2
ℎ119895))
2(119898minus1) (4)
subjected to the constraints
119862
sum
119894=1
119906119894119895= 1 forall119895 isin 1 119873
0 lt
119873
sum
119895=1
119906119894119895lt 119873 forall119894 isin 1 119862
(5)
Initially the 119906119894119895rsquos and the v
119894are assigned randomly and
updated in each iteration If 119880
(119897)= (119906
(119897)
119894119895) is the matrix U
calculated at the 119897-th step the iterative process stops when10038171003817100381710038171003817
U(119897) minus U(119897minus1)10038171003817100381710038171003817
= max119894119895
10038161003816100381610038161003816
119906
(119897)
119894119895minus 119906
(119897minus1)
119894119895
10038161003816100381610038161003816
lt 120576 (6)
where 120576 gt 0 is a prefixed parameterThis algorithm has a linear computational complexity
however it is sensitive to the presence of noise and outliersfurthermore the number of cluster 119862 is fixed a priori andneeds to use a validity index for determining an optimal valuefor the parameter 119862
In order to overcome these shortcomings in [11 12] theEFCM algorithm is proposed where the cluster prototypesare hyperspheres in the case of the Euclidean metric LikeFCM the EFCM algorithm is characterized by a linear com-putational complexity furthermore it is robust with respect
A minus (A cap B)
= A minus B
A cap BB minus (A cap B) =
B minus A
Figure 1 Intersections of two hotspots detected for events thathappened in two consecutive periods
to the presence of noise and outliers and the final number ofclusters is determined during the iterative process
In [13 14] the authors propose the use of the EFCMalgorithm for detecting hotspot areas The final hotspots areidentified as the detected cluster prototypes and shown on themap as circular areas In [4] the authors analyze the spatio-temporal evolution of the hotspots in the fire analysis Thepattern event dataset is partitioned according to the timeof the eventrsquos detection so each subset is corresponding toa specific time interval The authors compare the hotspotsobtained in two consecutive years by studying their inter-sections on the map In this way it is possible to follow theevolution of a particular phenomenon
The cluster prototypes detected from EFCM method arecircular areas on themap that can approximate a hotspot areaFigure 1 shows an example of two circular hotspots obtainedas clusters
Figure 1 shows three different regions
(i) An area in which the hotspot 119860 is not intersectedby the hotspot 119861 (corresponding to 119860 minus (119860 cap 119861) =
119860minus119861) this region can be considered as a geographicalarea in which prematurely detected event disappearssuccessively
(ii) The region of intersection of the two hotspots 119860 cap 119861this region can be considered a geographical area inwhich the event continues to persist
(iii) An area in which the hotspot B is not intersected bythe hotspotA (corresponding to 119861minus(119860cap119861) = 119861minus119860)this region can be considered as a geographical area inwhich the prematurely undetected event propagatessuccessively
We can study the spatio-temporal evolution of the hotspotsby analyzing the interactions between the correspondingcircular cluster prototypes obtained for consecutive periods
Advances in Fuzzy Systems 3
and detecting the presence of new hotspots in regions previ-ously not covered by hotspots and the absebce of hotspots inregions previously spatially included in hotspot areas
In this research we present a method for studyingthe spatio-temporal evolution of hotspots areas in diseaseanalysis we apply the EFCM algorithm for comparingin consecutive years event datasets corresponding to oto-laryngopharyngeal diseases diagnosis detected in the districtof Naples (I) Each event corresponds to the residence of thepatient who contracted the disease
We study the spatio-temporal evolution of the hotspotsanalyzing the intersections of hotspots corresponding totwo consecutive years the displacement of the centroidsthe increase or reduction of the hotspots areas and theemergence of new hotspots
In Section 2 we give an overview of the EFCM algo-rithm In Section 3 we present our method for studying thespatio-temporal evolution of hotspots in disease analysis InSection 4 we present the results of the spatio-temporal evolu-tion of hotspots for the otolaryngologist-laryngopharyngealdiseases diagnosis events detected in the district of Naples (I)Our conclusions are in Section 5
2 The EFCM Algorithm
In the EFCM algorithm we consider clustering prototypesgiven by hyperspheres in the 119899-dimensional featurersquos spaceThe 119894th hypersphere is characterized by a centroid v
119894=
(k1119894 k
119899119894) and a radius 119903
119894
Indeed if 119903119894is the radius of 119881
119894 we say that 119909
119895belongs to
119881119894if 119889119894119895le 119903119894
The radius 119903119894is obtained considering the covariance
matrix 119875119894associated with the 119894th cluster defined as
P119894=
sum
119873
119895=1119906
119898
119894119895(x119895minus k119894) (x119895minus k119894)
119879
sum
119873
119895=1119906
119898
119894119895
(7)
whose determinant gives the volume of the 119894th cluster SinceP119894is symmetric and positive it can be decomposed in the
following form
Pi = Q119894Λ119894Q119879119894 (8)
where 119876119894is an orthonormal matrix and Δ
119894= (120582
119894119895) is
a diagonal matrix The radius 119903119894is given by the following
formula (see [12])
119903119894=
1
119899
radic
119899
prod
119896=1
120582
1119899
119894119896=
radicdet (119875119894)
1119899
(9)
The objective function to be minimized is the following
119869 (119883119880 119881) =
119862
sum
119894=1
119873
sum
119895=1
119906
119898
119894119895(119889
2
119894119895minus 119903
2
119894) (10)
where the membership degrees 119906119894119895are updated as
119906119894119895= 1 times (
119862
sum
ℎ=1
((119889
2
119894119895max (0 1 minus 119903
2
119894119889
2
119894119895))
(119889
2
ℎ119895max (0 1 minus 119903
2
ℎ119889
2
ℎ119895)))
1(119898minus1)
)
minus1
=
1
sum
119862
ℎ=1(119889
2
119894119895119908119894119895119889
2
ℎ119895119908ℎ119895)
1(119898minus1)
(11)
We set 11988910158402119896119895
= 119889
2
119896119895119908119896119895
= max(0 1198892119896119895
minus 119903
2
119896) and define the
number 120593119895
= card119896 isin 1 119862 119889
1015840
119896119895= 0 for any 119895 =
1 119873 thus we obtain
119906119894119895=
1
sum
119862
ℎ=1(119889
1015840
119894119895119889
1015840
ℎ119895)
2(119898minus1)if 120593119895= 0
119906119894119895=
0 if 1198891015840119894119895gt 0
if 120593119895gt 0
1
120593119895
if 1198891015840119894119895= 0
(12)
However the usage of (12) produces the negative effect ofdiminishing the objective function (10) when a meaningfulnumber of features are placed in a cluster and this fact canprevent the separation of the clusters Then a solution to thisproblem consists in the assumption of a small starting valueof 119903119894and then it is increased gradually with the factor120573(119897)119862(119897)
where119862(119897) is the number of clusters at the 119897th iteration and120573
(119897)
is defined recursively as 120573(0) = 1 120573
(119897)= min(119862(119897minus1) 120573(119897minus1)) by
setting
119868119894119896
=
sum
119873
119895=1min (119906
119894119895 119906119896119894)
sum
119873
119895=1119906119894119895
(13)
and the symmetric matrix 119878 = (119878119894119896) where 119878
119894119896= max119868
119894119896 119868119896119894
is defined as well If 119878(119897) is the matrix 119878 at the 119897th iteration (119897 gt
1) and the threshold 120572
(119897)= 1(119862
(119897)minus 1) is introduced as limit
then two indexes 119894lowast and 119896
lowast are determined such that 119878(119897)119894lowast119896lowast
ge
120572
(119897) and thus 119894lowast and 119896
lowast are merged by setting
119906
(119897)
119894lowast119895= 119906
(119897)
119894lowast119895+ 119906
(119897)
119896lowast119895 forall119895 isin 1 119873
119862
(119897)= 119862
(119897minus1)+ 1
(14)
The 119896
lowastth row can be removed from the matrix 119880
(119897) Inother words the EFCM algorithm can be summarized in thefollowing steps
(1) The user assigns the initial number of clusters 119862
(0)
119898 gt 1 (usually119898 = 2) 120576 gt 0 the initial value 119878(0)119894119896
= 0and 120573
(0)= 1
(2) The membership degrees 119906
(0)
119894119895(119895 = 1 119873 and 119894 =
1 119862(0)) are assigned randomly
4 Advances in Fuzzy Systems
Figure 2 Example of events georeferenced on a road network
(3) The centers of the clusters V119894are calculated by using
(3)(4) The radii of the clusters are calculated by using (9)(5) 119906119894119895is calculated by using (12)
(6) The indexes 119894lowast and 119896
lowast are determined in such a waythat 119878(119897)119894lowast119896lowast assumes the possible greatest value at the 119897th
iteration(7) If |119878(119897)
119894lowast119896lowast minus 119878
(119897minus1)
119894lowast119896lowast | lt 120576 and 119878
(119897)
119894lowast119896lowast gt 120572(119897) = 1(119862
(119897minus1)minus 1)
then the 119894lowastth and 119896
lowastth clusters aremerged via (14) andthe 119896lowastth row is deleted from 119880
(119897)(8) If (6) is satisfied then the process stops otherwise go
to the step (3) for the (119897 + 1)th iteration
3 Hotspots Detection and Evolution inDisease Analysis
Each pattern is given by the event corresponding to theresidence of the patient to whom a specific disease has beendetected The two features of the pattern are the geographiccoordinates of the residence
The first step of our process is a geocoding activitynecessary for obtaining the event dataset starting by the streetaddress of the patients
To ensure an accurate matching for the geopositioning ofthe event we need the topologically correct road network andthe corresponding complete toponymic data
The starting data include the name of the street and thehouse number of the patientrsquos residence After the matchingprocess each data is converted in an event point georefer-enced on the map
In Figure 2 the road network of the district of Naples isshown the name of the street is labeled on themap the eventsare georeferenced as points on the map
Figure 3 shows the data corresponding to an eventselected on the map
After geo-referencing each event the event dataset canbe split partitioning them by time interval For example theevent in Figure 3 can be split by the field ldquoYearrdquo
For each subset of events we apply the EFCM algorithmto detect the final cluster prototypes
Figure 3 Data associated to an event on the map
Figure 4 A form created in theGIS Tool ESRIArcGIS formanagingthe EFCM process
In this research we point out the analysis of the temporalevolution and spread of oto-laryngo-pharyngeal diseasesdetected within the district of Naples The datasets dividedby time sequences corresponding to periods of one yearare made up of patterns for different events georeferencedcorresponding to ailments encountered in patients for whichan intervention and the subsequent histological examinationwere pointed out as well The event refers to the geoposition-ing of the location of the patient
The data have been further divided by the type of thedisease for analyzing the distribution and evolution of eachspecific disease on the area of the study
The EFCM algorithm has been encapsulated in the GISplatform ESRI ArcGIS Figure 4 shows the mask created forsetting the parameters and running the EFCM algorithm
We can set other numerical fields for adding otherfeatures to the geographical coordinates
Initially we set the initial number of clusters the fuzzifierm and the error threshold for stopping the iterations Afterrunning EFCM the number of iterations the final numberof clusters and the error calculated at the last iteration arereported The resultant clusters are shown as circular areason the map and can be saved in a new geographic layer
The final process concerns the comparative analysis ofthe hotspots obtained by the clusters corresponding to eachsubsets of events
Advances in Fuzzy Systems 5
Figure 5 Analysis of the spatio-temporal evolution of hotspotsdetected in two consecutive periods
Figure 6 Edema of bilateral Reinke diseasemdashyear 2011 display ofthe hotspots on the map
Figure 5 shows an example of display on the map ofhotspots obtained as final clusters for two consecutive subsetof events
In order to assess the expansion and the displacementof a hotspot we measure the radius of the hotspot and thedistance between the centroids of two intersecting hotspots
In the next section we present the results obtained byapplying this method for the data corresponding to surgicalinterventions to the oto-laryngo-pharyngeal apparatus inpatients residents in the district of Naples between the years2008 and 2012
We divide the dataset per year and analyze various typesof diseases
Among the types of the most frequent diseases thefollowing were analyzed
(i) carcinoma(ii) edema of bilateral Reinke(iii) hypertrophy of the inferior turbinate(iv) nasal polyposis(v) bilateral vocal fold prolapse
In the next section we show the most significant resultsobtained by applying this method to the each partitioneddataset of events
Figure 7 Edema of bilateral Reinke diseasemdashyear 2012 display ofthe hotspots on the map
Table 1 Endema of bilateral Reinke diseasemdashfinal number ofclusters and final error for year
Year Initial numberof clusters
Final numberof clusters |119880
(119897)minus 119880
(119897minus1)| 120576
2008 15 4 048 times 10
minus21 times 10
minus2
2009 15 4 055 times 10
minus21 times 10
minus2
2010 15 4 071 times 10
minus21 times 10
minus2
2011 15 4 067 times 10
minus21 times 10
minus2
2012 15 3 053 times 10
minus21 times 10
minus2
4 Test Results
Wepresent the results obtained on the event dataset describedabove in the period between the years 2008 and 2012
We consider first the subset of data corresponding to theedema of bilateral Reinke disease
We fix the fuzzifier parameter to 01 the initial number ofclusters to 15 and the final iteration error to 1 times 10minus2
Table 1 shows the results obtained for each yearWe present the details relating to the comparison of the
hotspots obtained by considering the event data for the years2011 and 2012
Figures 6 and 7 show respectively the hotspots obtainedby using the pattern subset of events that occurred in the years2011 and 2012
Figure 8 shows the overlap of the hotspots obtained forthe two years in red the hotspots corresponding to the year2011 in blue the ones corresponding to the year 2012
Table 2 shows in the first two columns the labels of thehotspots in 2011 and 2012 in third (resp fourth) column theradius obtained in 2011 (resp 2012) and the distance betweenthe centroids is given in the fifth column
The results show that only hotspot 3 obtained for the year2011 remains almost unchanged in the year 2012 Insteadhotspots 1 and 2 seem to merge into a single larger hotspot(the hotspot 1 obtained for the year 2012) and hotspot 4 thatshifts about 1 km is expanded the radius of this hotspot in2012 is about 65 km (hotspot 3 obtained for the year 2012 inFigure 8)
6 Advances in Fuzzy Systems
Figure 8 Edema of bilateral Reinke diseasemdashyears 2011 and 2012display of the two hotspotsrsquo series
Table 2 Endema of bilateral Reinke diseasemdashcomparison results ofthe hotspots obtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 1724 3848 17592 1 1943 3848 15073 2 3434 3453 00744 3 3591 6519 1115
Table 3 Nasal polyposismdashcomparison results of the hotspotsobtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 3087 4951 26562 2 4915 7103 1052
Now we show the results obtained for the disease nasalpolyposis
Figure 9 shows the overlap of the hotspots obtained forthe two years 2011 and 2012
In Table 3 the comparisonrsquos results are reportedThe results in Figure 9 show that in 2011 and 2012 there
are two hotspots the one covering an area of the city ofNaples and the other coveringmanyVesuvian townsThe twohotspots which in 2011 covered a circular area with a radii ofabout 3 and 5 km respectively in 2012 cover a circular areawith radii of about 5 and 7 km respectively
The histogram in Figure 10 shows the trend of the radii ofthe two hotspots in the course of time
It is relevant the spread in recent years of the hotspot thatsurrounds the Vesuvian towns (the radius of this hotspotfrom about 2 km in the year 2008 is about 7 km in the year2012)
Another significant trend concerns the hotspots obtainedfor the carcinoma disease
Also in this case the two main hotsposts cover the cityof Naples and many Vesuvian towns In in this case we havea very high spread of the hotspot covering the city of Naples
Figure 9 Nasal polyposis diseasemdashyears 2011 and 2012 display ofthe two hotspotsrsquo series
8
7
6
5
4
3
2
1
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 10 Nasal polyposis diseasemdashhistogram showing the varia-tion of the radius of the two hotspots over time
(cfr Figure 11) in recent years the radius of this hotspot isincreased up to 95 km
5 Conclusions
The hyperspheres obtained as clusters (circles in case oftwo dimensions) by using EFCM can represent hotspots inhotspot analysis this method has a linear computationalcomplexity and is robust to noises and outliers In hotspotsanalysis the patterns are bidimensional and the features areformed by geographic coordinates the cluster prototypes arecircles that can represent a good approximation of hotspotareas and can be displayed as circular areas on the map
In this paper we present a new method that uses theEFCM algorithm for studying the spatio-temporal evolutionof hotspots in disease analysis
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
Submit your manuscripts athttpwwwhindawicom
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Distributed Sensor Networks
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Advances in
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Human-ComputerInteraction
Advances in
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Advances in Fuzzy Systems 3
and detecting the presence of new hotspots in regions previ-ously not covered by hotspots and the absebce of hotspots inregions previously spatially included in hotspot areas
In this research we present a method for studyingthe spatio-temporal evolution of hotspots areas in diseaseanalysis we apply the EFCM algorithm for comparingin consecutive years event datasets corresponding to oto-laryngopharyngeal diseases diagnosis detected in the districtof Naples (I) Each event corresponds to the residence of thepatient who contracted the disease
We study the spatio-temporal evolution of the hotspotsanalyzing the intersections of hotspots corresponding totwo consecutive years the displacement of the centroidsthe increase or reduction of the hotspots areas and theemergence of new hotspots
In Section 2 we give an overview of the EFCM algo-rithm In Section 3 we present our method for studying thespatio-temporal evolution of hotspots in disease analysis InSection 4 we present the results of the spatio-temporal evolu-tion of hotspots for the otolaryngologist-laryngopharyngealdiseases diagnosis events detected in the district of Naples (I)Our conclusions are in Section 5
2 The EFCM Algorithm
In the EFCM algorithm we consider clustering prototypesgiven by hyperspheres in the 119899-dimensional featurersquos spaceThe 119894th hypersphere is characterized by a centroid v
119894=
(k1119894 k
119899119894) and a radius 119903
119894
Indeed if 119903119894is the radius of 119881
119894 we say that 119909
119895belongs to
119881119894if 119889119894119895le 119903119894
The radius 119903119894is obtained considering the covariance
matrix 119875119894associated with the 119894th cluster defined as
P119894=
sum
119873
119895=1119906
119898
119894119895(x119895minus k119894) (x119895minus k119894)
119879
sum
119873
119895=1119906
119898
119894119895
(7)
whose determinant gives the volume of the 119894th cluster SinceP119894is symmetric and positive it can be decomposed in the
following form
Pi = Q119894Λ119894Q119879119894 (8)
where 119876119894is an orthonormal matrix and Δ
119894= (120582
119894119895) is
a diagonal matrix The radius 119903119894is given by the following
formula (see [12])
119903119894=
1
119899
radic
119899
prod
119896=1
120582
1119899
119894119896=
radicdet (119875119894)
1119899
(9)
The objective function to be minimized is the following
119869 (119883119880 119881) =
119862
sum
119894=1
119873
sum
119895=1
119906
119898
119894119895(119889
2
119894119895minus 119903
2
119894) (10)
where the membership degrees 119906119894119895are updated as
119906119894119895= 1 times (
119862
sum
ℎ=1
((119889
2
119894119895max (0 1 minus 119903
2
119894119889
2
119894119895))
(119889
2
ℎ119895max (0 1 minus 119903
2
ℎ119889
2
ℎ119895)))
1(119898minus1)
)
minus1
=
1
sum
119862
ℎ=1(119889
2
119894119895119908119894119895119889
2
ℎ119895119908ℎ119895)
1(119898minus1)
(11)
We set 11988910158402119896119895
= 119889
2
119896119895119908119896119895
= max(0 1198892119896119895
minus 119903
2
119896) and define the
number 120593119895
= card119896 isin 1 119862 119889
1015840
119896119895= 0 for any 119895 =
1 119873 thus we obtain
119906119894119895=
1
sum
119862
ℎ=1(119889
1015840
119894119895119889
1015840
ℎ119895)
2(119898minus1)if 120593119895= 0
119906119894119895=
0 if 1198891015840119894119895gt 0
if 120593119895gt 0
1
120593119895
if 1198891015840119894119895= 0
(12)
However the usage of (12) produces the negative effect ofdiminishing the objective function (10) when a meaningfulnumber of features are placed in a cluster and this fact canprevent the separation of the clusters Then a solution to thisproblem consists in the assumption of a small starting valueof 119903119894and then it is increased gradually with the factor120573(119897)119862(119897)
where119862(119897) is the number of clusters at the 119897th iteration and120573
(119897)
is defined recursively as 120573(0) = 1 120573
(119897)= min(119862(119897minus1) 120573(119897minus1)) by
setting
119868119894119896
=
sum
119873
119895=1min (119906
119894119895 119906119896119894)
sum
119873
119895=1119906119894119895
(13)
and the symmetric matrix 119878 = (119878119894119896) where 119878
119894119896= max119868
119894119896 119868119896119894
is defined as well If 119878(119897) is the matrix 119878 at the 119897th iteration (119897 gt
1) and the threshold 120572
(119897)= 1(119862
(119897)minus 1) is introduced as limit
then two indexes 119894lowast and 119896
lowast are determined such that 119878(119897)119894lowast119896lowast
ge
120572
(119897) and thus 119894lowast and 119896
lowast are merged by setting
119906
(119897)
119894lowast119895= 119906
(119897)
119894lowast119895+ 119906
(119897)
119896lowast119895 forall119895 isin 1 119873
119862
(119897)= 119862
(119897minus1)+ 1
(14)
The 119896
lowastth row can be removed from the matrix 119880
(119897) Inother words the EFCM algorithm can be summarized in thefollowing steps
(1) The user assigns the initial number of clusters 119862
(0)
119898 gt 1 (usually119898 = 2) 120576 gt 0 the initial value 119878(0)119894119896
= 0and 120573
(0)= 1
(2) The membership degrees 119906
(0)
119894119895(119895 = 1 119873 and 119894 =
1 119862(0)) are assigned randomly
4 Advances in Fuzzy Systems
Figure 2 Example of events georeferenced on a road network
(3) The centers of the clusters V119894are calculated by using
(3)(4) The radii of the clusters are calculated by using (9)(5) 119906119894119895is calculated by using (12)
(6) The indexes 119894lowast and 119896
lowast are determined in such a waythat 119878(119897)119894lowast119896lowast assumes the possible greatest value at the 119897th
iteration(7) If |119878(119897)
119894lowast119896lowast minus 119878
(119897minus1)
119894lowast119896lowast | lt 120576 and 119878
(119897)
119894lowast119896lowast gt 120572(119897) = 1(119862
(119897minus1)minus 1)
then the 119894lowastth and 119896
lowastth clusters aremerged via (14) andthe 119896lowastth row is deleted from 119880
(119897)(8) If (6) is satisfied then the process stops otherwise go
to the step (3) for the (119897 + 1)th iteration
3 Hotspots Detection and Evolution inDisease Analysis
Each pattern is given by the event corresponding to theresidence of the patient to whom a specific disease has beendetected The two features of the pattern are the geographiccoordinates of the residence
The first step of our process is a geocoding activitynecessary for obtaining the event dataset starting by the streetaddress of the patients
To ensure an accurate matching for the geopositioning ofthe event we need the topologically correct road network andthe corresponding complete toponymic data
The starting data include the name of the street and thehouse number of the patientrsquos residence After the matchingprocess each data is converted in an event point georefer-enced on the map
In Figure 2 the road network of the district of Naples isshown the name of the street is labeled on themap the eventsare georeferenced as points on the map
Figure 3 shows the data corresponding to an eventselected on the map
After geo-referencing each event the event dataset canbe split partitioning them by time interval For example theevent in Figure 3 can be split by the field ldquoYearrdquo
For each subset of events we apply the EFCM algorithmto detect the final cluster prototypes
Figure 3 Data associated to an event on the map
Figure 4 A form created in theGIS Tool ESRIArcGIS formanagingthe EFCM process
In this research we point out the analysis of the temporalevolution and spread of oto-laryngo-pharyngeal diseasesdetected within the district of Naples The datasets dividedby time sequences corresponding to periods of one yearare made up of patterns for different events georeferencedcorresponding to ailments encountered in patients for whichan intervention and the subsequent histological examinationwere pointed out as well The event refers to the geoposition-ing of the location of the patient
The data have been further divided by the type of thedisease for analyzing the distribution and evolution of eachspecific disease on the area of the study
The EFCM algorithm has been encapsulated in the GISplatform ESRI ArcGIS Figure 4 shows the mask created forsetting the parameters and running the EFCM algorithm
We can set other numerical fields for adding otherfeatures to the geographical coordinates
Initially we set the initial number of clusters the fuzzifierm and the error threshold for stopping the iterations Afterrunning EFCM the number of iterations the final numberof clusters and the error calculated at the last iteration arereported The resultant clusters are shown as circular areason the map and can be saved in a new geographic layer
The final process concerns the comparative analysis ofthe hotspots obtained by the clusters corresponding to eachsubsets of events
Advances in Fuzzy Systems 5
Figure 5 Analysis of the spatio-temporal evolution of hotspotsdetected in two consecutive periods
Figure 6 Edema of bilateral Reinke diseasemdashyear 2011 display ofthe hotspots on the map
Figure 5 shows an example of display on the map ofhotspots obtained as final clusters for two consecutive subsetof events
In order to assess the expansion and the displacementof a hotspot we measure the radius of the hotspot and thedistance between the centroids of two intersecting hotspots
In the next section we present the results obtained byapplying this method for the data corresponding to surgicalinterventions to the oto-laryngo-pharyngeal apparatus inpatients residents in the district of Naples between the years2008 and 2012
We divide the dataset per year and analyze various typesof diseases
Among the types of the most frequent diseases thefollowing were analyzed
(i) carcinoma(ii) edema of bilateral Reinke(iii) hypertrophy of the inferior turbinate(iv) nasal polyposis(v) bilateral vocal fold prolapse
In the next section we show the most significant resultsobtained by applying this method to the each partitioneddataset of events
Figure 7 Edema of bilateral Reinke diseasemdashyear 2012 display ofthe hotspots on the map
Table 1 Endema of bilateral Reinke diseasemdashfinal number ofclusters and final error for year
Year Initial numberof clusters
Final numberof clusters |119880
(119897)minus 119880
(119897minus1)| 120576
2008 15 4 048 times 10
minus21 times 10
minus2
2009 15 4 055 times 10
minus21 times 10
minus2
2010 15 4 071 times 10
minus21 times 10
minus2
2011 15 4 067 times 10
minus21 times 10
minus2
2012 15 3 053 times 10
minus21 times 10
minus2
4 Test Results
Wepresent the results obtained on the event dataset describedabove in the period between the years 2008 and 2012
We consider first the subset of data corresponding to theedema of bilateral Reinke disease
We fix the fuzzifier parameter to 01 the initial number ofclusters to 15 and the final iteration error to 1 times 10minus2
Table 1 shows the results obtained for each yearWe present the details relating to the comparison of the
hotspots obtained by considering the event data for the years2011 and 2012
Figures 6 and 7 show respectively the hotspots obtainedby using the pattern subset of events that occurred in the years2011 and 2012
Figure 8 shows the overlap of the hotspots obtained forthe two years in red the hotspots corresponding to the year2011 in blue the ones corresponding to the year 2012
Table 2 shows in the first two columns the labels of thehotspots in 2011 and 2012 in third (resp fourth) column theradius obtained in 2011 (resp 2012) and the distance betweenthe centroids is given in the fifth column
The results show that only hotspot 3 obtained for the year2011 remains almost unchanged in the year 2012 Insteadhotspots 1 and 2 seem to merge into a single larger hotspot(the hotspot 1 obtained for the year 2012) and hotspot 4 thatshifts about 1 km is expanded the radius of this hotspot in2012 is about 65 km (hotspot 3 obtained for the year 2012 inFigure 8)
6 Advances in Fuzzy Systems
Figure 8 Edema of bilateral Reinke diseasemdashyears 2011 and 2012display of the two hotspotsrsquo series
Table 2 Endema of bilateral Reinke diseasemdashcomparison results ofthe hotspots obtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 1724 3848 17592 1 1943 3848 15073 2 3434 3453 00744 3 3591 6519 1115
Table 3 Nasal polyposismdashcomparison results of the hotspotsobtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 3087 4951 26562 2 4915 7103 1052
Now we show the results obtained for the disease nasalpolyposis
Figure 9 shows the overlap of the hotspots obtained forthe two years 2011 and 2012
In Table 3 the comparisonrsquos results are reportedThe results in Figure 9 show that in 2011 and 2012 there
are two hotspots the one covering an area of the city ofNaples and the other coveringmanyVesuvian townsThe twohotspots which in 2011 covered a circular area with a radii ofabout 3 and 5 km respectively in 2012 cover a circular areawith radii of about 5 and 7 km respectively
The histogram in Figure 10 shows the trend of the radii ofthe two hotspots in the course of time
It is relevant the spread in recent years of the hotspot thatsurrounds the Vesuvian towns (the radius of this hotspotfrom about 2 km in the year 2008 is about 7 km in the year2012)
Another significant trend concerns the hotspots obtainedfor the carcinoma disease
Also in this case the two main hotsposts cover the cityof Naples and many Vesuvian towns In in this case we havea very high spread of the hotspot covering the city of Naples
Figure 9 Nasal polyposis diseasemdashyears 2011 and 2012 display ofthe two hotspotsrsquo series
8
7
6
5
4
3
2
1
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 10 Nasal polyposis diseasemdashhistogram showing the varia-tion of the radius of the two hotspots over time
(cfr Figure 11) in recent years the radius of this hotspot isincreased up to 95 km
5 Conclusions
The hyperspheres obtained as clusters (circles in case oftwo dimensions) by using EFCM can represent hotspots inhotspot analysis this method has a linear computationalcomplexity and is robust to noises and outliers In hotspotsanalysis the patterns are bidimensional and the features areformed by geographic coordinates the cluster prototypes arecircles that can represent a good approximation of hotspotareas and can be displayed as circular areas on the map
In this paper we present a new method that uses theEFCM algorithm for studying the spatio-temporal evolutionof hotspots in disease analysis
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
4 Advances in Fuzzy Systems
Figure 2 Example of events georeferenced on a road network
(3) The centers of the clusters V119894are calculated by using
(3)(4) The radii of the clusters are calculated by using (9)(5) 119906119894119895is calculated by using (12)
(6) The indexes 119894lowast and 119896
lowast are determined in such a waythat 119878(119897)119894lowast119896lowast assumes the possible greatest value at the 119897th
iteration(7) If |119878(119897)
119894lowast119896lowast minus 119878
(119897minus1)
119894lowast119896lowast | lt 120576 and 119878
(119897)
119894lowast119896lowast gt 120572(119897) = 1(119862
(119897minus1)minus 1)
then the 119894lowastth and 119896
lowastth clusters aremerged via (14) andthe 119896lowastth row is deleted from 119880
(119897)(8) If (6) is satisfied then the process stops otherwise go
to the step (3) for the (119897 + 1)th iteration
3 Hotspots Detection and Evolution inDisease Analysis
Each pattern is given by the event corresponding to theresidence of the patient to whom a specific disease has beendetected The two features of the pattern are the geographiccoordinates of the residence
The first step of our process is a geocoding activitynecessary for obtaining the event dataset starting by the streetaddress of the patients
To ensure an accurate matching for the geopositioning ofthe event we need the topologically correct road network andthe corresponding complete toponymic data
The starting data include the name of the street and thehouse number of the patientrsquos residence After the matchingprocess each data is converted in an event point georefer-enced on the map
In Figure 2 the road network of the district of Naples isshown the name of the street is labeled on themap the eventsare georeferenced as points on the map
Figure 3 shows the data corresponding to an eventselected on the map
After geo-referencing each event the event dataset canbe split partitioning them by time interval For example theevent in Figure 3 can be split by the field ldquoYearrdquo
For each subset of events we apply the EFCM algorithmto detect the final cluster prototypes
Figure 3 Data associated to an event on the map
Figure 4 A form created in theGIS Tool ESRIArcGIS formanagingthe EFCM process
In this research we point out the analysis of the temporalevolution and spread of oto-laryngo-pharyngeal diseasesdetected within the district of Naples The datasets dividedby time sequences corresponding to periods of one yearare made up of patterns for different events georeferencedcorresponding to ailments encountered in patients for whichan intervention and the subsequent histological examinationwere pointed out as well The event refers to the geoposition-ing of the location of the patient
The data have been further divided by the type of thedisease for analyzing the distribution and evolution of eachspecific disease on the area of the study
The EFCM algorithm has been encapsulated in the GISplatform ESRI ArcGIS Figure 4 shows the mask created forsetting the parameters and running the EFCM algorithm
We can set other numerical fields for adding otherfeatures to the geographical coordinates
Initially we set the initial number of clusters the fuzzifierm and the error threshold for stopping the iterations Afterrunning EFCM the number of iterations the final numberof clusters and the error calculated at the last iteration arereported The resultant clusters are shown as circular areason the map and can be saved in a new geographic layer
The final process concerns the comparative analysis ofthe hotspots obtained by the clusters corresponding to eachsubsets of events
Advances in Fuzzy Systems 5
Figure 5 Analysis of the spatio-temporal evolution of hotspotsdetected in two consecutive periods
Figure 6 Edema of bilateral Reinke diseasemdashyear 2011 display ofthe hotspots on the map
Figure 5 shows an example of display on the map ofhotspots obtained as final clusters for two consecutive subsetof events
In order to assess the expansion and the displacementof a hotspot we measure the radius of the hotspot and thedistance between the centroids of two intersecting hotspots
In the next section we present the results obtained byapplying this method for the data corresponding to surgicalinterventions to the oto-laryngo-pharyngeal apparatus inpatients residents in the district of Naples between the years2008 and 2012
We divide the dataset per year and analyze various typesof diseases
Among the types of the most frequent diseases thefollowing were analyzed
(i) carcinoma(ii) edema of bilateral Reinke(iii) hypertrophy of the inferior turbinate(iv) nasal polyposis(v) bilateral vocal fold prolapse
In the next section we show the most significant resultsobtained by applying this method to the each partitioneddataset of events
Figure 7 Edema of bilateral Reinke diseasemdashyear 2012 display ofthe hotspots on the map
Table 1 Endema of bilateral Reinke diseasemdashfinal number ofclusters and final error for year
Year Initial numberof clusters
Final numberof clusters |119880
(119897)minus 119880
(119897minus1)| 120576
2008 15 4 048 times 10
minus21 times 10
minus2
2009 15 4 055 times 10
minus21 times 10
minus2
2010 15 4 071 times 10
minus21 times 10
minus2
2011 15 4 067 times 10
minus21 times 10
minus2
2012 15 3 053 times 10
minus21 times 10
minus2
4 Test Results
Wepresent the results obtained on the event dataset describedabove in the period between the years 2008 and 2012
We consider first the subset of data corresponding to theedema of bilateral Reinke disease
We fix the fuzzifier parameter to 01 the initial number ofclusters to 15 and the final iteration error to 1 times 10minus2
Table 1 shows the results obtained for each yearWe present the details relating to the comparison of the
hotspots obtained by considering the event data for the years2011 and 2012
Figures 6 and 7 show respectively the hotspots obtainedby using the pattern subset of events that occurred in the years2011 and 2012
Figure 8 shows the overlap of the hotspots obtained forthe two years in red the hotspots corresponding to the year2011 in blue the ones corresponding to the year 2012
Table 2 shows in the first two columns the labels of thehotspots in 2011 and 2012 in third (resp fourth) column theradius obtained in 2011 (resp 2012) and the distance betweenthe centroids is given in the fifth column
The results show that only hotspot 3 obtained for the year2011 remains almost unchanged in the year 2012 Insteadhotspots 1 and 2 seem to merge into a single larger hotspot(the hotspot 1 obtained for the year 2012) and hotspot 4 thatshifts about 1 km is expanded the radius of this hotspot in2012 is about 65 km (hotspot 3 obtained for the year 2012 inFigure 8)
6 Advances in Fuzzy Systems
Figure 8 Edema of bilateral Reinke diseasemdashyears 2011 and 2012display of the two hotspotsrsquo series
Table 2 Endema of bilateral Reinke diseasemdashcomparison results ofthe hotspots obtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 1724 3848 17592 1 1943 3848 15073 2 3434 3453 00744 3 3591 6519 1115
Table 3 Nasal polyposismdashcomparison results of the hotspotsobtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 3087 4951 26562 2 4915 7103 1052
Now we show the results obtained for the disease nasalpolyposis
Figure 9 shows the overlap of the hotspots obtained forthe two years 2011 and 2012
In Table 3 the comparisonrsquos results are reportedThe results in Figure 9 show that in 2011 and 2012 there
are two hotspots the one covering an area of the city ofNaples and the other coveringmanyVesuvian townsThe twohotspots which in 2011 covered a circular area with a radii ofabout 3 and 5 km respectively in 2012 cover a circular areawith radii of about 5 and 7 km respectively
The histogram in Figure 10 shows the trend of the radii ofthe two hotspots in the course of time
It is relevant the spread in recent years of the hotspot thatsurrounds the Vesuvian towns (the radius of this hotspotfrom about 2 km in the year 2008 is about 7 km in the year2012)
Another significant trend concerns the hotspots obtainedfor the carcinoma disease
Also in this case the two main hotsposts cover the cityof Naples and many Vesuvian towns In in this case we havea very high spread of the hotspot covering the city of Naples
Figure 9 Nasal polyposis diseasemdashyears 2011 and 2012 display ofthe two hotspotsrsquo series
8
7
6
5
4
3
2
1
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 10 Nasal polyposis diseasemdashhistogram showing the varia-tion of the radius of the two hotspots over time
(cfr Figure 11) in recent years the radius of this hotspot isincreased up to 95 km
5 Conclusions
The hyperspheres obtained as clusters (circles in case oftwo dimensions) by using EFCM can represent hotspots inhotspot analysis this method has a linear computationalcomplexity and is robust to noises and outliers In hotspotsanalysis the patterns are bidimensional and the features areformed by geographic coordinates the cluster prototypes arecircles that can represent a good approximation of hotspotareas and can be displayed as circular areas on the map
In this paper we present a new method that uses theEFCM algorithm for studying the spatio-temporal evolutionof hotspots in disease analysis
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 5
Figure 5 Analysis of the spatio-temporal evolution of hotspotsdetected in two consecutive periods
Figure 6 Edema of bilateral Reinke diseasemdashyear 2011 display ofthe hotspots on the map
Figure 5 shows an example of display on the map ofhotspots obtained as final clusters for two consecutive subsetof events
In order to assess the expansion and the displacementof a hotspot we measure the radius of the hotspot and thedistance between the centroids of two intersecting hotspots
In the next section we present the results obtained byapplying this method for the data corresponding to surgicalinterventions to the oto-laryngo-pharyngeal apparatus inpatients residents in the district of Naples between the years2008 and 2012
We divide the dataset per year and analyze various typesof diseases
Among the types of the most frequent diseases thefollowing were analyzed
(i) carcinoma(ii) edema of bilateral Reinke(iii) hypertrophy of the inferior turbinate(iv) nasal polyposis(v) bilateral vocal fold prolapse
In the next section we show the most significant resultsobtained by applying this method to the each partitioneddataset of events
Figure 7 Edema of bilateral Reinke diseasemdashyear 2012 display ofthe hotspots on the map
Table 1 Endema of bilateral Reinke diseasemdashfinal number ofclusters and final error for year
Year Initial numberof clusters
Final numberof clusters |119880
(119897)minus 119880
(119897minus1)| 120576
2008 15 4 048 times 10
minus21 times 10
minus2
2009 15 4 055 times 10
minus21 times 10
minus2
2010 15 4 071 times 10
minus21 times 10
minus2
2011 15 4 067 times 10
minus21 times 10
minus2
2012 15 3 053 times 10
minus21 times 10
minus2
4 Test Results
Wepresent the results obtained on the event dataset describedabove in the period between the years 2008 and 2012
We consider first the subset of data corresponding to theedema of bilateral Reinke disease
We fix the fuzzifier parameter to 01 the initial number ofclusters to 15 and the final iteration error to 1 times 10minus2
Table 1 shows the results obtained for each yearWe present the details relating to the comparison of the
hotspots obtained by considering the event data for the years2011 and 2012
Figures 6 and 7 show respectively the hotspots obtainedby using the pattern subset of events that occurred in the years2011 and 2012
Figure 8 shows the overlap of the hotspots obtained forthe two years in red the hotspots corresponding to the year2011 in blue the ones corresponding to the year 2012
Table 2 shows in the first two columns the labels of thehotspots in 2011 and 2012 in third (resp fourth) column theradius obtained in 2011 (resp 2012) and the distance betweenthe centroids is given in the fifth column
The results show that only hotspot 3 obtained for the year2011 remains almost unchanged in the year 2012 Insteadhotspots 1 and 2 seem to merge into a single larger hotspot(the hotspot 1 obtained for the year 2012) and hotspot 4 thatshifts about 1 km is expanded the radius of this hotspot in2012 is about 65 km (hotspot 3 obtained for the year 2012 inFigure 8)
6 Advances in Fuzzy Systems
Figure 8 Edema of bilateral Reinke diseasemdashyears 2011 and 2012display of the two hotspotsrsquo series
Table 2 Endema of bilateral Reinke diseasemdashcomparison results ofthe hotspots obtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 1724 3848 17592 1 1943 3848 15073 2 3434 3453 00744 3 3591 6519 1115
Table 3 Nasal polyposismdashcomparison results of the hotspotsobtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 3087 4951 26562 2 4915 7103 1052
Now we show the results obtained for the disease nasalpolyposis
Figure 9 shows the overlap of the hotspots obtained forthe two years 2011 and 2012
In Table 3 the comparisonrsquos results are reportedThe results in Figure 9 show that in 2011 and 2012 there
are two hotspots the one covering an area of the city ofNaples and the other coveringmanyVesuvian townsThe twohotspots which in 2011 covered a circular area with a radii ofabout 3 and 5 km respectively in 2012 cover a circular areawith radii of about 5 and 7 km respectively
The histogram in Figure 10 shows the trend of the radii ofthe two hotspots in the course of time
It is relevant the spread in recent years of the hotspot thatsurrounds the Vesuvian towns (the radius of this hotspotfrom about 2 km in the year 2008 is about 7 km in the year2012)
Another significant trend concerns the hotspots obtainedfor the carcinoma disease
Also in this case the two main hotsposts cover the cityof Naples and many Vesuvian towns In in this case we havea very high spread of the hotspot covering the city of Naples
Figure 9 Nasal polyposis diseasemdashyears 2011 and 2012 display ofthe two hotspotsrsquo series
8
7
6
5
4
3
2
1
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 10 Nasal polyposis diseasemdashhistogram showing the varia-tion of the radius of the two hotspots over time
(cfr Figure 11) in recent years the radius of this hotspot isincreased up to 95 km
5 Conclusions
The hyperspheres obtained as clusters (circles in case oftwo dimensions) by using EFCM can represent hotspots inhotspot analysis this method has a linear computationalcomplexity and is robust to noises and outliers In hotspotsanalysis the patterns are bidimensional and the features areformed by geographic coordinates the cluster prototypes arecircles that can represent a good approximation of hotspotareas and can be displayed as circular areas on the map
In this paper we present a new method that uses theEFCM algorithm for studying the spatio-temporal evolutionof hotspots in disease analysis
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
6 Advances in Fuzzy Systems
Figure 8 Edema of bilateral Reinke diseasemdashyears 2011 and 2012display of the two hotspotsrsquo series
Table 2 Endema of bilateral Reinke diseasemdashcomparison results ofthe hotspots obtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 1724 3848 17592 1 1943 3848 15073 2 3434 3453 00744 3 3591 6519 1115
Table 3 Nasal polyposismdashcomparison results of the hotspotsobtained for the years 2011 and 2012
2011hotspot
Intersecting2012 hotspot
Radius 2011hotspot (km)
Radius 2012hotspot (km)
Centroidrsquosdistance (km)
1 1 3087 4951 26562 2 4915 7103 1052
Now we show the results obtained for the disease nasalpolyposis
Figure 9 shows the overlap of the hotspots obtained forthe two years 2011 and 2012
In Table 3 the comparisonrsquos results are reportedThe results in Figure 9 show that in 2011 and 2012 there
are two hotspots the one covering an area of the city ofNaples and the other coveringmanyVesuvian townsThe twohotspots which in 2011 covered a circular area with a radii ofabout 3 and 5 km respectively in 2012 cover a circular areawith radii of about 5 and 7 km respectively
The histogram in Figure 10 shows the trend of the radii ofthe two hotspots in the course of time
It is relevant the spread in recent years of the hotspot thatsurrounds the Vesuvian towns (the radius of this hotspotfrom about 2 km in the year 2008 is about 7 km in the year2012)
Another significant trend concerns the hotspots obtainedfor the carcinoma disease
Also in this case the two main hotsposts cover the cityof Naples and many Vesuvian towns In in this case we havea very high spread of the hotspot covering the city of Naples
Figure 9 Nasal polyposis diseasemdashyears 2011 and 2012 display ofthe two hotspotsrsquo series
8
7
6
5
4
3
2
1
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 10 Nasal polyposis diseasemdashhistogram showing the varia-tion of the radius of the two hotspots over time
(cfr Figure 11) in recent years the radius of this hotspot isincreased up to 95 km
5 Conclusions
The hyperspheres obtained as clusters (circles in case oftwo dimensions) by using EFCM can represent hotspots inhotspot analysis this method has a linear computationalcomplexity and is robust to noises and outliers In hotspotsanalysis the patterns are bidimensional and the features areformed by geographic coordinates the cluster prototypes arecircles that can represent a good approximation of hotspotareas and can be displayed as circular areas on the map
In this paper we present a new method that uses theEFCM algorithm for studying the spatio-temporal evolutionof hotspots in disease analysis
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 7
12
10
8
6
4
2
0
(km
)
2008 2009 2010 2011 2012Year
NaplesVesuvian towns
Figure 11 Carcinoma diseasemdashhistogram showing the variation ofthe radius of the two hotspots over time
We consider the residencersquos information of patients inthe district of Naples (Italy) to whom a surgical interventionto the oto-laryngo-pharyngeal apparatus was carried outbetween the years 2008 and 2012 A geocoding process isused for geo-referencing the data then the georeferenceddataset is partitionedper year and type of disease we comparethe hotspots obtained for each pair of consecutive years andanalyze the trend of each hotspot over time measuring thevariation of the radius and the distance between intersectingcluster centroids concerning two consecutive years
The results show a consistent spread in the last years ofthe nasal polyposis disease hotspot covering some Vesuviantowns and of the carcinoma disease hotspot covering the cityof Naples
References
[1] S P Chainey S Reid and N Stuart ldquoWhen is a hotspot ahotspot A procedure for creating statistically robust hotspotgeo-graphic maps of crimerdquo in Innovations in GIS 9 Socioe-conomic Applications of Geographic Information Science DKidner G Higgs and S White Eds Taylor and FrancisLondon UK 2002
[2] K Harries Geographic Mapping Crime Principle and PracticeNational Institute of Justice Washington DC USA 1999
[3] A T Murray I McGuffog J S Western and P MullinsldquoExploratory spatial data analysis techniques for examiningurban crimerdquo British Journal of Criminology vol 41 no 2 pp309ndash329 2001
[4] F Di Martino and S Sessa ldquoThe extended fuzzy c-meansalgorithm for hotspots in spatio-temporal GISrdquo Expert Systemswith Applications vol 38 no 9 pp 11829ndash11836 2011
[5] R M Mullner K Chung K G Croke and E K MensahldquoIntroduction geographic information systems in public healthandmedicinerdquo Journal ofMedical Systems vol 28 no 3 pp 215ndash221 2004
[6] K Polat ldquoApplication of attribute weighting method based onclustering centers to discrimination of linearly non-separablemedical datasetsrdquo Journal of Medical Systems vol 36 no 4 pp2657ndash2673 2012
[7] C K Wei S Su and M C Yang ldquoApplication of data miningon the develoment of a disease distribution map of screenedcommunity residents of Taipei County in Taiwanrdquo Journal ofMedical Systems vol 36 no 3 pp 2021ndash2027 2012
[8] I Gath and A B Geva ldquoUnsupervised optimal fuzzy clus-teringrdquo IEEE Transactions on Pattern Analysis and MachineIntelligence vol 11 no 7 pp 773ndash780 1989
[9] R Krishnapuram and J Kim ldquoClustering algorithms based onvolume criteriardquo IEEE Transactions on Fuzzy Systems vol 8 no2 pp 228ndash236 2000
[10] J C Bezdek Pattern Recognition with Fuzzy Objective FunctionAlgorithms Plenum Press New York NY USA 1981
[11] U Kaymak R BabuskaM Setnes H B Verbruggen andHMvanNauta Lemke ldquoMethods for simplification of fuzzymodelsrdquoin Intelligent Hybrid Systems D Ruan Ed pp 91ndash108 KluwerAcademic Publishers Dordrecht The Netherlands 1997
[12] U Kaymak and M Setnes ldquoFuzzy clustering with volumeprototypes and adaptive cluster mergingrdquo IEEE Transactions onFuzzy Systems vol 10 no 6 pp 705ndash712 2002
[13] F Di Martino V Loia and S Sessa ldquoExtended fuzzy c-meansclustering algorithm for hotspot events in spatial analysisrdquoInternational Journal of Hybrid Intelligent Systems vol 4 pp 1ndash14 2007
[14] F Di Martino and S Sessa ldquoImplementation of the extendedfuzzy c-means algorithm in geographic information systemsrdquoJournal of Uncertain Systems vol 3 no 4 pp 298ndash306 2009
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
top related