introducción al reconocimiento de patrones en señales...

introducción al reconocimiento de patrones

en señales fisiológicas

Dra Angélica Muñoz MeléndezCoordinación de CienciasComputacionales - [email protected]

Taller sobre Investigación enTecnologías de la Información& EnvejecimientoEnsenada, BC. Octubre 8-9, 2015

“The Future of Robot Caregivers”, Souther Salazar. New York Times Sunday Review, 2014.

mailto:[email protected]

acerca de esta plática …

2

GaitShoe, MIT.

Smartphones, Watch de Apple, Fitbit.

algoritmos programas

aplicacionesam

plifi

caci

ón |

com

pens

ació

n | f

iltra

do |

fusi

ón | …

patrones

patrones (1)

un patrón es una regularidad, una estructura o conjunto de características o condiciones que se repiten en varias o b s e r v a c i o n e s d e u n fenómeno. un patrón define una categoría d e “ o b j e t o s ” f í s i c o s o abstractos.

4

reconocimiento de patrones

el reconocimiento de patrones se puede realizar sobre series de tiempo, conjuntos de observaciones o datos medidos en determinados momentos en el tiempo, espaciados por intervalos uniformes y ordenados de forma cronológica. las observaciones se sintetizan con un conjunto de variables.

7

reconocimiento de patrones (1)

variables v1 v2 v3 … vn ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & #

existen distintos enfoques para reconocer patrones en datos, los más comunes son dos: enfoque estadístico: se calculan distribuciones de probabilidad en las variables observadas y a partir de ellas se buscan correlaciones en los datos. enfoque sintáctico: se estiman relaciones estructurales en los datos y a partir de ello calcular un conjunto de reglas que describan estructuras generales estimadas.

8


9

reconocimiento de patrones (3)variables v1 v2 v3 … vn ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & #

variables relevantes w1 w2 w3 … wn @ ++ % & #* @ ++ % & #* @ ++ % & #* @ ++ % & #*

extracción de características relevantes

variables v1 v2 v3 … vn ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & # ** ** @ ++ % x & #


características modelo

decisión

10



variables relevantes w1 w2 w3 … wn @ ++ % & #* @ ++ % & #* @ ++ % & #* @ ++ % & #*

extracción de características relevantes



características modelo decisión

eval

uaci

ón

fase de entrenamiento

fase de prueba

Usualmente estos modelos se evalúan en pruebas e validación cruzada: los datos se “pliegan” para entrenar un modelo y evaluar su desempeño sobre decisiones de casos con un ground truth conocido.

precision proporción de aciertos del total de respuestas.

recall proporción de aciertos del universo de posibilidades de aciertos.

accuracy proporción de respuestas del universo de posibles respuestas.

ejemplos

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ejemplos (1)análisis de datos de la marcha de adultos mayores. INR, INAOE

Table 1: Number of calls and class associated to them based on psychiatric evaluations. There is alsoadditional data (last column) where there is no class associated.

Severe Moderate Mild Mild AdditionalPatient Depression Depression Depression Normal Manic Total DataP0201 – – 149 149 – 298 435P0302 135 – – 99 – 234 199P0702 – 112 39 – – 151 116P0902 – 142 – 161 – 303 178P1002 – – 35 – 162 197 28

All 135 254 223 409 162 1183 956

information from five patients.Table 1 shows the number of class and class associated to

them based on psychiatric evaluations. It can be seen thatwe have a di↵erent number of calls per patient and per statemoods. The table also shows additional data (last column)indicating the number of phone calls that we have that arenot associated to any state mood as they were performedoutside the 7 days window of the psychiatric assessments.

4. FEATURE SELECTIONFeature selection from smartphone sensory data is proba-

bly the most important factor to consider in order to improvethe recognition performance of machine learning tools. Inthe following subsections, we describe the most representa-tive techniques for extracting time- and frequency domainfeatures from accelerometer raw data and prosodic- and en-ergy features extracted from speech.

Table 2: Features selected for the accelerometer sen-sor signals.Time Domain Frequency Domain(1) Magnitude (1) FFT Energy,(2) Signal magnitude area (2) FFT Mean Energy,(3) Root-Mean-Square (RMS) (3) FFT StdDev Energy,(4) Variance Sum (4) Peak Power,(5) Curve Length, (5) Peak DFT Bin,(6) Non Linear Energy, (6) Peak Magnitude,(7-14) For the 3 axes: (7) Entropy,Variance, Mean, Max, Min, (8) DFTStd. Dev., Absolute, (9) Freq.Dom. Entropy,Median, a dn Range (10)Freq.Dom. Entropy(15-20) Mean and Std. Dev. with DFT,of X, Y and Z axis.For all 20 features, weotained the Min, Max, andMean For all: Min, Max, MeanTotal: 60 Total: 30

4.1 Accelerometer signal features in time-domain(TD)

In order to quantify motor activities from the smartphone,acceleration readings collected during conversation (includ-ing picking up the phone, starting and finishing the call, andreplacing the phone into the holder) were used in our anal-yses. These periods during conversation determine mean-ingful changes of acceleration values. We captured 3-axiallinear acceleration continuously at rates which varied due to

Android system operating conditions, such as system loadand battery levels. In this study, the accelerometer signalswere resampled at a fixed rate of 5 Hz. The accelerometerfeatures proposed in this paper, shown in Table 2, are quitepopular amongst practitioners in the field, and were used asthe basis for identifying periods of activity. To reduce thee↵ect of spikes and noise from accelerometer signal, statis-tical metrics such as mean and median were applied over awindow size of 128 samples.Other features included the root-mean-square (RMS) ac-

celeration for the period of conversation, as an indication ofthe time-averaged power in the signal. The RMS of a signalxi

, yi

and zi

represents a sequence of N=128 discrete valuesobtained using Equation 1 where t1 and t

n

denote the startand the end time of accelerometer readings.

accRMS =

Ptnt1

acc(t)2

t

n

� t1

! 12

(1)

The RMS results demonstrate di↵erences in the motor ac-tivity during the phone conversation. The lower the RMSvalue, the lower the motor response which is manifestedin depressed patients, whereas patients in the manic phaseshow elevated levels, as shown in Figure 1 i).Another suitable measure for phone activities, is the nor-

malized signal magnitude area (SMA) that was used as thebasis for identifying periods of activity during phone conver-satios, where x(t), y(t), and z(t) are the acceleration signalsfrom each axis with respect to time t as denoted by Equa-tion 2.

SMA =1t

Zt

o

x(t)|dt+Z

t

o

y(t)|dt+Z

t

o

x(t)|dt (2)

An example using SMA is presented in Figure 1 ii) wherechanges of motor activity can be compared in two states ofthe disease, transition from mild depressive state to normalstate. The graph inlcudes of number of phone calls in bothstates (n=140).Also, feature like Signal Vector Magnitude (SVM) have

been used to measure the degree of activity intensity andvelocity of phone movement during the phone conversationand was obtained using Equation 3.

SVM =1n

nX

i=1

qx

2i

+ y

2i

+ z

2i

(3)

Furthermore, in order to capture abrupt changes of phoneactivity during the phone conversation we used Averaged

2.2 Relevant variables

BNs and DBNs, being rooted in classical statistics, benefit

from a large number of observations and few variablesfrom those observations to identify significant probabilistic

relationships. A number of methods have been proposed to

alleviate problems with high-dimensional data when only asmall number of instances are available, such as for

instance oversampling and reduction of dimensionality.

Reduction of dimensionality can be achieved by featureselection strategies dropping a subset of variables consid-

ered to be less informative. In this work, we reduce the

dimensionality of our problem in two different ways: first,by keeping only those gait variables picked by an expert,

and second, by applying a well-known feature selection

algorithm, namely forward sequential selection (FSS), to

filter the gait variables with low predictive value from the

set of gait parameters acquired with the GaitRite system.Accordingly, we have built two DBNs for prediction of

fall from two different reduced sets of variables of human

gait. The first model is expert-guided and capitalizes on theset of variables identified by gait analysis experts from the

Human Motion Analysis Laboratory of the INR as perti-

nent for figuring out the risk of falling. These variables areshown in the top half of Table 2.

The second model is strictly computational and isfounded on the set of relevant variables as automatically

selected by the FSS algorithm [21]. The FSS algorithm was

run taking into consideration all the records from the 18patients, that is, all 66 records added up in Table 2. In this

case, the FSS algorithm achieves a reduction of the original

31 variables in Table 1 to 7 relevant variables. Thesevariables are shown in the bottom half of Table 2.

2.2.1 Forward sequential selection

Let X be a matrix whose rows correspond to points (or

observations) and columns correspond to features (or pre-dictor variables). And let Y be a column vector of response

values or class labels for each observation in X. FSS starts

with an empty feature or variable set. It then creates can-didate feature subsets by adding each of the features not yet

selected. For each candidate feature subset, FSS performs a

tenfold cross-validation, by repeatedly calling an evalua-tion function, called FUN, that defines the CRITERIONthat FSS uses to select features and determines when to

stop. See Eq. (1)

Table 1 Spatio-temporal gait parameters obtained with the GaitRitesystem

No. Parameter (unit of measure)

1 Walking distance (cm)

2 Ambulation time (s)

3 Walking velocity (cm/s)

4 Mean normalized velocity

5 Number of steps

6 Cadence

7 Left and right step time differential (s)

8 Left and right step length differential (cm)

9 Left and right cycle time differential (s)

10 Left step time (s)

11 Right step time (s)

12 Mean step time (s)

13 Mean step cycle time (s)

14 Left step length (cm)

15 Right step length (cm)

16 Left stride length (cm)

17 Right stride length (cm)

18 Base of support left step (cm)

19 Base of support right step (cm)

20 Percentage of single support left (%GC)

21 Percentage of single support right (%GC)

22 Percentage of double support left (%GC)

23 Percentage of double support right (%GC)

24 Left swing percentage (%GC)

25 Right swing percentage (%GC)

26 Left stance percentage (%GC)

27 Right stance percentage (%GC)

28 Step length/extremity length ratio left

29 Step Length/extremity length ratio right

30 Left toe in/out angle (!)

31 Right toe in/out angle (!)

Table 2 Relevant variables and their abbreviated names

CAD Cadence

Variables selected by gait analysis experts

LPI Left step length (cm)

LPD Right step length (cm)

BSI Base of support left step(cm)

LPCI Left stride length (cm)

LPCD Right stride length (cm)

BSD Base of support right step(cm)

Variables selected by FSS

TPD Right step time (s)



SDI Left double support (%GC)

RPED Right step/extremity ratio

TIOI Left toe in/out angle (!)

TIOD Right toe in/out angle (!)

Med Biol Eng Comput

123

2.2 Relevant variables

BNs and DBNs, being rooted in classical statistics, benefit

from a large number of observations and few variablesfrom those observations to identify significant probabilistic

relationships. A number of methods have been proposed to

alleviate problems with high-dimensional data when only asmall number of instances are available, such as for

instance oversampling and reduction of dimensionality.

Reduction of dimensionality can be achieved by featureselection strategies dropping a subset of variables consid-

ered to be less informative. In this work, we reduce the

dimensionality of our problem in two different ways: first,by keeping only those gait variables picked by an expert,

and second, by applying a well-known feature selection

algorithm, namely forward sequential selection (FSS), to

filter the gait variables with low predictive value from the

set of gait parameters acquired with the GaitRite system.Accordingly, we have built two DBNs for prediction of

fall from two different reduced sets of variables of human

gait. The first model is expert-guided and capitalizes on theset of variables identified by gait analysis experts from the

Human Motion Analysis Laboratory of the INR as perti-

nent for figuring out the risk of falling. These variables areshown in the top half of Table 2.

The second model is strictly computational and isfounded on the set of relevant variables as automatically

selected by the FSS algorithm [21]. The FSS algorithm was

run taking into consideration all the records from the 18patients, that is, all 66 records added up in Table 2. In this

case, the FSS algorithm achieves a reduction of the original

31 variables in Table 1 to 7 relevant variables. Thesevariables are shown in the bottom half of Table 2.

2.2.1 Forward sequential selection

Let X be a matrix whose rows correspond to points (or

observations) and columns correspond to features (or pre-dictor variables). And let Y be a column vector of response

values or class labels for each observation in X. FSS starts

with an empty feature or variable set. It then creates can-didate feature subsets by adding each of the features not yet

selected. For each candidate feature subset, FSS performs a

tenfold cross-validation, by repeatedly calling an evalua-tion function, called FUN, that defines the CRITERIONthat FSS uses to select features and determines when to

stop. See Eq. (1)

Table 1 Spatio-temporal gait parameters obtained with the GaitRitesystem

No. Parameter (unit of measure)

1 Walking distance (cm)

2 Ambulation time (s)

3 Walking velocity (cm/s)

4 Mean normalized velocity

5 Number of steps

6 Cadence

7 Left and right step time differential (s)

8 Left and right step length differential (cm)

9 Left and right cycle time differential (s)

10 Left step time (s)

11 Right step time (s)

12 Mean step time (s)

13 Mean step cycle time (s)

14 Left step length (cm)

15 Right step length (cm)

16 Left stride length (cm)

17 Right stride length (cm)

18 Base of support left step (cm)

19 Base of support right step (cm)

20 Percentage of single support left (%GC)

21 Percentage of single support right (%GC)

22 Percentage of double support left (%GC)

23 Percentage of double support right (%GC)

24 Left swing percentage (%GC)

25 Right swing percentage (%GC)

26 Left stance percentage (%GC)

27 Right stance percentage (%GC)

28 Step length/extremity length ratio left

29 Step Length/extremity length ratio right

30 Left toe in/out angle (!)

31 Right toe in/out angle (!)

Table 2 Relevant variables and their abbreviated names

CAD Cadence

Variables selected by gait analysis experts

LPI Left step length (cm)

LPD Right step length (cm)


LPCI Left stride length (cm)

LPCD Right stride length (cm)


Variables selected by FSS

TPD Right step time (s)



SDI Left double support (%GC)

RPED Right step/extremity ratio

TIOI Left toe in/out angle (!)

TIOD Right toe in/out angle (!)

Med Biol Eng Comput

123

13


G. Cuaya A. Muñoz Meléndez, L. Nuñez Carrera, E. Morales, I. Quiñones, A.I. Pérez, A. Alessi (2012) “A dynamic Bayesian network for estimating the risk of fall from real gait data”. Med Biol Eng Computing 51(1), pp. 29-47, Springer.



All 135 254 223 409 162 1183 956










, yi

and zi


n


accRMS =

Ptnt1

acc(t)2

t

n

� t1

! 12

(1)



SMA =1t

Zt

o

x(t)|dt+Z

t

o

y(t)|dt+Z

t

o

x(t)|dt (2)



SVM =1n

nX

i=1

qx

2i

+ y

2i

+ z

2i

(3)


precision of 70 % in predicting both imminent falls and 6months risk of falling.

Both models were evaluated using leave-one-out cross

validation (LOOCV). The LOOCV is a technique thatfacilitates estimation of performance of a predictive model

when the available number of samples is low, as it occurs

in this case where data from 18 patients only are available.During LOOCV, observations are left out one at a time and

a model instance is trained with the remaining observations

and tested on the observation left out. This procedure isrepeated for all of the observations and the predictive

power of the model is considered to be the average of all

the model instances.Thereby, for each of the two conceptual models (the

expert selection based and the FSS selection based), 18

different model instances were built using data from 17patients and tested on the remaining patient on the most

probable value of the node fall, 0 = no fall or 1 = fall. Notethat here we exclude all observations corresponding to the

longitudinal assessments for a given subject at a time,

rather than dropping every single observation separately.Figure 4 shows the DBNs built by Hugin using human gait

data.

The effectiveness of the forecasting of imminent fallsand 6 months risk of falling is defined as the ratio of the

number of falls predicted by the model divided by the

number of falls that actually occurred in the correspondingtime interval.

The effectiveness of the forecasting of imminent falls

and 6 months risk of falling were 72.22 % in both cases forthe DBN model built upon the variables selected by the

domain experts, and 72.22 and 66.66 % for the DBN built

upon the variables that were automatically selected withFSS algorithm. These results are summarized in Fig. 5.

The effectiveness of both models is presented without

confidence intervals due to the small number of samples.Tables 3 and 4 detail he confusion matrices for the two

conceptual models at the two time intervals considered;

imminent and 6 months, respectively. The confusionmatrices presented have been built from the agglomerate

results during the LOOCV.

Finally, the sensitivity and specificity of the conceptualmodels have been estimated. Sensitivity (also called recall

rate in some fields) measures the proportion of actual

positives which are correctly identified over the total realpositives (i.e. the percentage of elders who are correctly

(a) DBN based on expert’s variables.

(b) DBN based on automatic selectedvariables.

Fig. 4 a DBN based on gait parameters selected by experts, b DBNbased on gait parameters selected by the FSS algorithm. See Table 2for the definition of abbreviations

Fig. 5 Comparison of the prognosis results of the two models

Med Biol Eng Comput

123















data.




















Med Biol Eng Comput

123

14




All 135 254 223 409 162 1183 956










, yi

and zi


n


accRMS =

Ptnt1

acc(t)2

t

n

� t1

! 12

(1)



SMA =1t

Zt

o

x(t)|dt+Z

t

o

y(t)|dt+Z

t

o

x(t)|dt (2)



SVM =1n

nX

i=1

qx

2i

+ y

2i

+ z

2i

(3)


G. Cuaya A. Muñoz Meléndez, L. Nuñez Carrera, E. Morales, I. Quiñones, A.I. Pérez, A. Alessi (2012) “A dynamic Bayesian network for estimating the risk of fall from real gait data”. Med Biol Eng Computing 51(1), pp. 29-47, Springer.















data.




















Med Biol Eng Comput

123

identified as fallers). Specificity measures the proportion of

negatives which are correctly identified over the total realnegatives (i.e. the percentage of elders who are correctly

identified as not fallers). The sensitivity and specificity of

both conceptual models are presented in Table 5.

4 Discussion

This research aims at generating a model for prediction of

fall in the elderly that capitalizes on quantifying probabi-listic dependencies among gait variables. Our objective has

been to develop an intelligible model for non-experts in

probabilistic reasoning that afford them with complemen-tary information. Distinctly from related work [17, 38], our

model incorporates people’s gait degradation as captured

by assessment instruments and learns the probabilistic

relationships among the variables recorded by such

instruments to forecast the risk of fall of an elder.A strictly computational model based on selected

information extracted from gait assessments was compared

with an analogous model based on information drawn fromthe gait assessments by experts. For estimating the risk of

fall, the computational feature selection method picked out

variables of human gait that were not considered relevantby the experts. Nevertheless, both conceptual models

yielded comparable performances.Although the model based upon automatic feature

selection exhibits lower performance for the 6 monthsprediction, this model emerges from a very limited datasetand still afforded competitive performance. In this sense,

the experts base his/her selection on an experience cer-

tainly spanning more observations than those in the dataset.In general, the larger the training dataset the more reliable

model can be expected.

This work demonstrates the feasibility of employingprobabilistic models such as DBNs to estimate the proba-

bility of a fall. We have presented two probabilistic models

of fall risk assessment that were developed from actualrecords of spatio-temporal gait parameters. To our

knowledge, these are the first probabilistic models of fall

risk assessment that exploit relationships among relevantvariables. Since a gait model is now available, it can be

applied by human gait experts and clinicians to obtain

additional elements to enrich their decisions about treat-ment and therapies to be prescribed to elders with different

degrees of gait impairment.

Note that both, the strictly computational model and theexpert-guided model achieve comparable performances as

measured by sensitivity and specificity outcomes. This can

be indicative that there is a further reduced set of variablesof human gait relevant for predicting falls, perhaps in the

intersection of the subsets of variables considered by both

models.We are currently bettering the models by enlarging the

dataset. Models for predicting falls within 12 and

18 months will be developed as we grow our cohort sizeand expand follow-up times. We will also incorporate

information from people with normal gait to compare their

assessments with those from individuals with pathologicalgait.

Acknowledgments This research was supported by the NationalInstitute for Astrophysics, Optics and Electronics (INAOE), and theMexican National Council for Science and Technology (CONACyT),through the scholarship for doctoral studies 174498. The researchersof the Human Motion Analysis Laboratory of the National Institute ofRehabilitation in Mexico provided the gait data to develop the modelspresented in this work, under the research grant 01-042 of CONA-CyT-Health Sector Fund 2003.

Table 3 Confusion matrix to prognostic of imminent falls

Negative Positive

Predicted using information get with computational techniques

Actual

Negative 31 2

Positive 13 9

Predicted with information get of experts

Actual

Negative 30 3

Positive 12 10

Table 4 Confusion matrix to prognostic of 6 months risk of fall

Negative Positive

Predicted using information get withcomputational techniques

Actual

Negative 34 4

Positive 14 3

Predicted with information get of experts

Actual

Negative 36 2

Positive 13 4

Table 5 Sensitivity and specificity measures

Imminent fall Six months risk of fall

FSS INR FSS INR

Sensitivity 0.952 0.930 0.902 0.952

Specificity 0.704 0.714 0.708 0.734

Med Biol Eng Comput

123

Muchas gracias!

Más información

Angélica Muñoz MeléndezCoordinación de Ciencias Computacionales

Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE

[email protected]

[email protected]

ccc.inaoep.mx/~munoz

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