research article context-aware recommendation via graph...

Research ArticleContext-Aware Recommendation via Graph-Based ContextualModeling and Postfiltering

Hao Wu Kun Yue Xiaoxin Liu Yijian Pei and Bo Li

School of Information Science and Engineering Yunnan University Kunming 650091 China

Correspondence should be addressed to Hao Wu haowuynueducn

Received 18 December 2014 Revised 17 February 2015 Accepted 27 February 2015

Academic Editor Houbing Song

Copyright copy 2015 Hao Wu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Context-aware recommender systems generate more relevant recommendations by adapting them to the specific contextualsituation of the user and have become one of the most active research areas in the recommender systems However there remains akey issue as howcontextual information can be used to create intelligent anduseful recommender systems To assist the developmentand use of context-aware recommendation capabilities we propose a graph-based framework to model and incorporate contextualinformation into the recommendation process in an advantageous way A contextual graph-based relevance measure (CGR)is specifically designed to assess the potential relevance between the target user and the items further used to make an itemrecommendation We also propose a probabilistic-based postfiltering strategy to refine the recommendation results as contextualconditions are explicitly given in a query Depending on the experimental results on the two datasets the CGR-based methodis much superior to the traditional collaborative filtering methods and the proposed postfiltering method is much effective incontext-aware recommendation scenario

1 Introduction

Recommender systems [1] are popular tools for assisting cus-tomers in navigating through huge archives and alleviatingthe side effects of information overload in big data era Mostof the recommender systems focus on mining associationsbetween users and items (movies music Web informationgoods etc) and a few works consider the context which theitems are associated with [2] However in ubiquitous com-puting scenario users can access and exchange informationat anytime anyplace and in any way and context-awarenessis the fundamental objective of ubiquitous computing [3]User preferencesmay be changed by switching contexts (suchas time location surrounding people emotion devicesnetwork conditions etc) and solely relying on the user-itemassociation does not lead to a valid recommendation Forinstance some users prefer the morning instead of noonto be recommended appropriate news some users in thetourist are likely to be recommended suitable surroundingrestaurants or shopping malls and some users prefer towatch romantic movies at a theater if they are togetherwith boyfriendsgirlfriends Consequently the effectiveness

of recommendations will be affected if these contextualfactors are not considered into the recommender systemsContext-aware recommender systems (CARS) generatemorerelevant recommendations by adapting them to the specificcontextual situation of the user and have gradually becomeone of the most active research areas in the recommendedsystems [2]

Nowadays there are three recognized paradigms forincorporating contextual information into the recommenda-tion process contextual prefiltering contextual postfilteringand contextual modeling [2 4ndash6] Among them prefilteringis particularly attractive due to a straightforward justificationwhen context matters use in the recommendation processonly the data acquired in the same contextual situation of thetarget user because only this data is relevant for predictinguser preferences However prefiltering has not always beenthe best choice Its major limitation is the difficulty toobtain enough ratings in all possible contextual conditionsto build a strong and applicable prediction model [2 7ndash9] On the contrary postfiltering modeling and contextualmodeling can directly exploit available contextual factorsto enrich data used for prediction increasing in turn the

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015 Article ID 613612 10 pageshttpdxdoiorg1011552015613612

2 International Journal of Distributed Sensor Networks

effectiveness of the recommendations Nevertheless how tomodel contextual factors into a recommendation processand how to combine different strategies of CARS are stillchallenging tasks and many issues are yet to be taken upTo cope with this issue we propose a unified graph-basedcontextual modeling framework to incorporate contextualinformation in an advantageous way A contextual graph-based relevance measure and a probabilistic postfilteringstrategy are designed to facilitate the development and useof context-aware recommendation capabilities Experimentalresults against two real-world datasets show the merits of allthe proposed approaches in context-aware recommendation

The rest of the paper is structured as follows Section 2introduces our models and the corresponding recommenda-tion approaches for CARS In Section 3 experiments againsttwo datasets from different domains are conducted to watchthe effectiveness of the proposed methods Section 4 reviewsrelated works and makes some discussions Finally we con-clude the works and point to future directions

2 The Proposed Methods

21 Graph-Based Contextual Modeling CARS address mod-eling and predicting user tastes and preferences by incorpo-rating existing contextual information into the recommenda-tion process as explicit additional categories of data Theselong-term preferences and tastes are generally expressed asratings and are modeled as the function of not only items andusers but also the context Adomavicius et al [2] formallydefine the recommending process in CARS as 119877 119880119904119890119903 times

119868119905119890119898 times 119862119900119899119905119890119909119905 rarr 119877119886119905119894119899119892 where User Item and Ratingare the domains of users items and ratings respectively andContext specifies the contextual information associated withthe application Once the function 119877 is estimated for thewhole User times Item times Context space a recommender systemcan suggest the highest-rated item for users Note that contextfactors indicate the upper-level contextual concepts (egdaytype and location) while context conditions represent thecombination of contextual concept instances for exampleMonday Office Room

Distinct from building a prediction model we examinethe context-aware recommendation as a searching problemto find interesting items for a user given a context graphFormally suppose119866 = 119881 119864 is a context graphThevertex set119881 are divided into several distinct sets including a set of users119880 a set of items 119868 a set of attributes119860 and a set of contexts119862In particular we distinguish the contextual information of 119862from the static information of119860 of users or items consideringthat the attributes basically do not change while the contextfactors often change over different ratings The edge set 119864

consists of the existing connections of the Cartesian product119881 times 119881 Edges with diverse types have distinct semantics Forexample 119880 times 119860 connects users and their attributes 119880 times 119868

means the users have accessed items 119880 times 119862 represents thatthe users have activities given the contextual condition Thesituation for items is equal to that of users The context graph119866 can be represented as an adjacent matrix 119872 (as shown in

Table 1 A matrix representation of contextual user-item interac-tion

Users Items Contexts AttributesUsers 119880119880 119880119868 119880119862 119880119860

Items 119880119868T 0 119868119862 119868119860

Contexts 119880119862T

119868119862T 0 0

Attributes 119880119860T

119868119860T 0 0

Table 1) where submatrixes are all configured as symmetric(eg 119880119868

T is the transport matrix of 119880119868)Considering a random search that starts fromnode 119894 in119866

the search iteratively transmits to its neighborhood 119895with theprobability that is proportional to the edge weights 119878

119894119895 Also

at each step it has some probability 1 minus 119889 (the default settingis 119889 = 085) to return to the node 119894 The relevance score ofnode 119895 with respect to node 119894 is described as the steady-stateprobability the search will finally stay at node 119895 The steadyprobability can be gotten using the power method as in thefollowing equation until convergence

P(119899) = 119889119878TP(119899minus1) + (1 minus 119889) e (1)

where the row-normalized matrix 119878 is the transitivity matrixof random walks and vector e is a personalized vector thatmay represent the interests of a particular user Such a theoryis called the random walks with restarts (also known asPersonalized PageRank) and has attractedmany attentions invarious recommendation scenes [10ndash12]

A contextualized data graph adheres to the schema of 119866In the data graph given the source node 119894 the target node 119895

and the relationship type 119871 of an edge the transitivity matrixis initialized as follows

119878119894119895

=

119908 (119871)119908 (119894 119895 119871)

sum119896119908 (119894 119896 119871)

if 119908 (119894 119895 119871) gt 0

0 otherwise(2)

119908(119871) is the weight of the relationship typed 119871 in the schemaof 119866 and 119908(119894 119896 119871) represents the weights of out-edges typed119871 of 119894 in the data graph Since the graph 119866 is symmetric119908(119895 119894 119871) = 119908(119894 119895 119871) Here we examine the weights of edgesin two aspects (I) edge with different types has unusualsemantics thus it may affect the selection of nodes duringrandomwalks For instance when searching items of interesta usermaywish to consult hisher friends other than viewingthe ratings of the itemsWe use119908(119871) to impose this influencein the process of the userrsquos random walks (II) edges mustbe assigned weights to reflect users usage data For instancea user may have contacted an item several times or accessseparate items under the same context condition Thus wefurther assign a weight of 119908(119894 119895 119871) to the edges

With respect to the types of edges 119871 and the weights119908(119871)they can be defined at different levels of concepts We firstdefine 119871 at the highest level according to Table 1 resulting in11 types of119871 Tomake a difference among numerous attributesor context factors we further extend the definition of 119871 and119908(119871) to a fine-grained level of concept For instance givena set of item attributes 119860 = 119860

1 119860

119894 119860

119899 we can

International Journal of Distributed Sensor Networks 3

Input 119880 119868 119860 119862 119889 119906 119868119906 the empty 119866 the index of vertex 119894119899119889(sdot)

Output The CGR vector of 119866(1) Add all elements in 119880 119868 119860 and 119862 as graph nodes to 119866 and assign an unique index for each node(2) Add edges to 119866 and assign an type label 119871 for each edge(3) for all 119894 isin 119881 do(4) for all 119895 isin 119881 do(5) if There exists an edge from 119894 to 119895 then(6) Get the edge type 119871 and the weight 119908(119871)

(7) 119878119894119895= 119908(119871)

119908(119894 119895 119871)

sum119896119908(119894 119896 119871)

(8) else(9) 119878

119894119895= 0

(10) end if(11) end for(12) for all 119895 isin 119881 do

(13) 119878119894119895=

119878119894119895

sum119896119878119894119896

(14) end for(15) end for(16) for all 119895 isin 119881 do(17) if 119895 == 119894119899119889(119906) then(18) e1015840

119895= 1

(19) else(20) e1015840

119895= 0

(21) end if(22) end for(23) Compute P1

(119899)= 119889119878

TP1(119899minus1)

+ (1 minus 119889)e1015840(24) for all 119895 isin 119881 do(25) if 119895 isin 119868

119906then

(26) e10158401015840119895

=1

|119868119906|

(27) else(28) e10158401015840

119895= 0


(119899)= 119889119878

TP2(119899minus1)

+ (1 minus 119889)e10158401015840(32) return (P1 + P2)2

Algorithm 1 Contextual graph-based relevance

partition 119868119860 = ⋃119899

119894119868119860119894and define 119908(119868119860) = sum

119899

119894119908(119868119860119894)

where 119908(119868119860119894) is the weight of the 119894th attribute By this we

can provide a more scalable framework for the contextualmodeling

In the scenario of recommendation to estimate thelikelihood of an unseen item 119894 isin 119868 to be accessed by 119906 isin 119880119875(119894 | 119906) we suggest combining two ranking values of 119894 bybiasing different personalized vectors shown as follows

119875 (119894 | 119906) =P1 (119894) + P2 (119894)

2 (3)

where P1(119894) and P2(119894) is the ranking values of 119894 with respectto e1015840 and e10158401015840 respectively For the calculation of P1 we lete1015840119895

= 1 if 119895 is the index of 119906 For the calculation of P2 welet e10158401015840119895

= 1|119868119906| where 119895 isin 119868

119906and 119868119906is the set of items has

been accessed by 119906 In both cases the remaining elements of eare all settled at zero Given the contextual graph119866 P1 biasesthe items interested in the neighborhood of the current user

119906 while P2 prefers to the items similar to the set 119868119906 Such a

facile combination has the advantages of both worlds since itresembles the recommendation combination of a user-basedCF and an item-based CF which have been proved as a betterway to increase the accuracy of recommendations We calledthe user-item relevance achieved by newly proposed methodas CGR (contextual graph-based relevance) to distinguishit from our former work [13] Details of CGR method arepresented as Algorithm 1

22 Context-Aware Postfiltering With respect to the CGRall contextual information and attributes of users or itemscan be taken into account in estimating user-item relevanceHowever there remain some significant issues not consid-ered On one hand the rating information which explicitlyrepresents usersrsquo preferences to items is not exploited On theother hand it is very difficult for the CGRmodel to deal withthe query in which context factors are explicitly specified


To cope with these problems in CARS we further submit apostfitering strategy Given an instance of the context factors119862 = 119888

1 119888

119894 119888

119899 the likelihood of an unseen item 119894 isin 119868

to be accessed by 119906 isin 119880 can be estimated as follows

119875 (119894 | 119906 119862) = 119875 (119894 | 119862) 119875 (119894 | 119906) (4)

if the random variables 119906 and 119862 are assumed to be inde-pendent For the estimation of 119875(119894 | 119906) we can use CGR-based method or collaborative filtering approaches or theircombinations Let 119875CGR(119894 | 119906) and 119875CF(119894 | 119906) be theCGR-based and CF-based relevance of 119906 and 119894 respectively119875CGR(119894 | 119906) can be estimated using (3) and 119875CF(119894 | 119906) can begiven in 119903(119906 119894)max 119903(sdot) and max 119903(sdot) is the maximal valueof ratings in a dataset (eg 5) 119903(119906 119894) is the predicted ratingbased a CF algorithm 119875(119894 | 119862) can be estimated as follows

119875 (119894 | 119862) prop sum

119888119896isin119862

119875 (119894 | 119888119896) 119875 (119888119896| 119862) =

1

|119862|sum

119888119896isin119862

freq (119894 119888119896)

sum119895freq (119895 119888

119896)

(5)

where freq(119894 119888119896) is the occurrence frequency of item 119894 given

the context condition 119888119896 and 119875(119888

119896| 119862) takes 1119862 for sim-

plicity This probabilistic-based method reranks a candidatelist of items that has beenmade by a recommendationmodelThus it can be viewed as a postfiltering model of CARS

3 Experiments

31 Datasets We use two datasets from different domains toevaluate the presented methods The first one is the LDOS-CoMoDa which is specially designed for context-awarepersonalization research [14 15] The dataset comprises 2296rating records from 121 users to 1232 items accompanyingcontextual factors Content items are movies while the itemconsumption device is a personal computer with a web-basedapplication to acquire the userrsquos context [14] Each recordcontains 30 variables including a user an item a rating12 context factors 4 attributes of users and 11 attributes ofitems Context factors associated with ratings include timedaytype season location weather social endEmo dominan-tEmo mood physical decision and interaction Also eachcontext factor may have multiple discrete values amountingto 49 context conditions For example there are three values(Working day Weekend and Holiday) as for the daytypeconditions and seven values (Alone My partner FriendsColleagues Parents Public andMy family) with respect to thesocial condition Other variables are general user attributes(age sex city and country) and movie attributes (directormovieCountry movieLanuage movieYear genre1 genre2genre3 actor1 actor2 actor3 and budget)

The second dataset is scripted from httpwwwtripad-visorcom which is a tourism website that advises tripslocations and activities for users and contains a socialcomponent which allows lots of elements to be reviewed [16]The dataset is about hotel reviews and consists of 4669 ratingsfrom 1202 users to 1890 hotels [9] The attributes of usersare state and timezone and the attributes of hotels are citystate and timezone And there is only one context trip type

Table 2 The statistics of datasets

Dataset LDOS-CoMoDa TripAdvisorUsers 121 1202Items 1232 1890Ratings 2296 4669Rating scales 1ndash5 1ndash5Context factors 12 1User attributes 4 2Item attributes 7 3Sparsity 9846 9979

assigned to each rating showing the types of trips that the usersuggests for this hotel For this context the user can selecta subset of five possible values Family Couples BusinessSolo travel and Friends The statistics of both datasets arepresented in Table 2 where we can see that the TripAdvisordataset is considerably sparser than the LDOS-CoMoDadataset

32 Performance Metrics Along with the progress of recom-mendation techniques various metrics have been applied tomeasure the accuracy of recommendations including statis-tical accuracy metrics and decision-support measures Sincewe focus on recommending top-119873 items instead of ratingprediction of items Precision119873 Recall119873 and nDCG119873

are selected to evaluate the recommendation accuracyGiven a rank list of recommended items Precision119873 is

the fraction of recommended items that are relevant in thetop-119873 position as follows

119875119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

119873 (6)

while Recall119873 is the fraction of relevant items returned inthe top-119873 position to the true number of relevant items thatshould have been returned

119877119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

|119903119890119897119890V119886119899119905 119894119905119890119898119904| (7)

Discounted cumulative gain is a measure that gives moreweight to highly ranked resources and incorporates differentrelevance levels through different gain values One popularvariant is described as

DCG119873 =

119873

sum

119894=1

2119903119890119897(119894)

minus 1

log2(119894 + 1)

IDCG119873 =

119870

sum

119894=1

1

log2(119894 + 1)

(8)

Here the relevance level of 119894th item 119903119890119897(119894) depends on just abinary notion of relevance whether the items are relevant ornot to the target user We use 119903119890119897(119894) = 1 for relevant itemsif 119903(119906 119894) ge 3 and 119903119890119897(119894) = 0 for irrelevant items if 119903(119906 119894) lt

3 With the definition of DCG119873 we can find the idealDCG119873 (IDCG119873) as (8) where 119870 is the number of rel-evant items inside the top-119873 recommendations We use thenormalized DCG119873 (119899DCG119873 = DCG119873IDCG119873) toevaluate the recommendation accuracy [13]


Table 3 The statistics of training and test datasets

LDOS-CoMoDa TripAdvisorSplitting ratio 80 20 70 30Ratings for training 1833 2887Ratings for test 228 1339Users for test 60 963Relevant items per query 380 139

33 Evaluated Methods UPCC and IPCC the methodsare the classical user-based collaborative filtering and theitem-based collaborative filtering [1] and adopt the Pearsoncorrelation coefficient (PCC) to define the similarity betweentwo users or two items

SVD++ [17] and CAMF [18] SVD++ is a well-knownlatent factor model that comprises an alternative approach tocollaborative filtering with the more holistic goal to uncoverlatent features that explain observed ratings CAMF is anextension of classical matrix factorization (MF) approachfor taking into account contextual information in the ratingprediction Similar to SVD++ it is also induced by SVD onthe user-item ratings matrix Learning the prediction modelsfor both of them is solved using stochastic gradient descentWe fix dimension of latent factors as 20 other parameters areoptimized to realize the best predicting performance

CGR Candidate items are recommended to the user accord-ing to their CGR-based relevances All available informationin contextual graph 119866 is considered however for simplicitywe let119908(119879) = 1 for all the weights of relationship types in theschema of 119866 Note that for all collaborative filtering basedmodels (UPCC IPCC SVD++ and CAMF) candidates aresorted by their predicted ratings For CGR-based models thecandidates are ranked according to their relevance scores

34 Experimental Results on Contextual Modeling In thissection we conduct experiments to observe the recom-mendation performance of graph-based contextualmodelingapproach Under this case each query has no prescribedcontext conditions to prefilter or postfilter the recommendedcandidatesThe LDOS-CoMoDa dataset is randomly dividedinto the training dataset and the test dataset by a ratio of80 20 and the TripAdvisor dataset is divided into twocorresponding parts by the ratio of 70 30 Since we donot focus on the cold-start problem of recommendation newusers and new items in the test dataset are not consideredduring the recommendation process Statistics of trainingdataset and refined test dataset are presented in Table 3

Firstly we observe the recommendation accuracy of theCGR using five separate schemes of context graph By thiswe can identify which of the components work best forthe task of top-N item recommendation The results arepresented in Figures 1 and 2 ALL simultaneously considerscontextual information attributes of users and items and usedata of users to itemsALL-UC-IC corresponds the casewherecontextual information are not considered namely119908(119880119862) =

0 119908(119880119862T) = 0 119908(119868119862) = 0 and 119908(119868119862

T) = 0 Similarly

ALL-UI ALL-UA and ALL-IA respectively exclude thedirect connections of users-items attributes of users andattributes of items According to Figure 1 ALL-UA performsin a way much better than the other cases it shows that theuser attributes have negative effects on the LDOS-CoMoDadatasetsThe reason lies in that usersrsquo attributes (age sex cityand country) in the LDOS-CoMoDa dataset are not discrim-inative thus the neighborhoods of users found by a randomwalk through the links of usersrsquo attributes are not consistent intheir spectrums of interest As for the TripAdvisor dataset allcontextual information attributes of users and items seem tobe bringing positive effects to recommendations Further bycombining experimental results from both datasets we findthat the connections of users-items are a key factor for findingrelevant recommendations followedby the attributes of itemswhich seem to be more important than the attributes of usersand the contextual information

Next we compare the CGR with other baseline methodsWe are focused on top-10 and top-20 recommendationsas users are more concerned about the candidates being atthe front of the recommendation list Experimental resultson both datsets are presented in Figure 3 For the LDOS-CoMoDa dataset the CGR model significantly outperformsUPCC IPCC SVD++ andCAMF in all accuratemetrics andit improves them by at least 80 in all performance metricsSimilar trends are observed in the TripAdvisor dataset wherethe CGR model obviously beats all the others In particularit outperforms them by at least 200 in all performanceindicators Since the TripAdvisor dataset ismuch sparser thanthe LDOS-CoMoDa dataset we think that CGR-model isstronger than traditional CF-like recommenders and moresuitable to cope with the problem of data sparsity Onone hand CGR-based models perform in a more superiorway when data is sparse On the other hand it offers aneasier way to integrate various contextual factors to improverecommendation performance which is still thought as achallenging task in other ways

35 Experimental Results on Context-Aware Postfiltering Inthis section we did the experiment with the postfilteringmodel for CARS For this we reuse the training and the testdatasets provided in Table 3 Each query in this experimentis linked to a context condition and the context factorsassociated with a pertinent item must match the contextcondition given in the query Context factors considered forthe LDOS-CoMoDa dataset are daytype and social which aretwo important factors affecting a userrsquos choice for watching amovieThe context factor took into account for the TripAdvi-sor dataset is only TripType By splitting items using selectedcontext factors we further obtain 225 queries in the LDOS-CoMoDa test dataset and 1102 queries in the TripAdvisor testdataset The average numbers of relevant items per queryare correspondingly 101 and 122 Obviously every context-aware query only has about one relevant item We studyrecommendation effectiveness of evaluated methods withor without postfiltering strategies The results are presentedin Table 4 where the best values for every indicator areunderlined Since the number of relevant items per query is


0 10 20 30 40 50 600

002

004

006

008

01

012

014

016

018LDOS-CoMoDa

Prec

ision

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025LDOS-CoMoDa

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

005

01

015

02

025

03

035

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

LDOS-CoMoDa

Top-N

(c)

Figure 1 Recommendation accuracy of CGR using different graphic schema on the LDOS-CoMoDa dataset

extremely small we consider the recall to evaluate recoveryability of recommenders

As for the case without using postfiltering (wo) we cansee that the CGR model largely improve all the other modelson both datasets This outcome is very consistent with priorexperimental results (see Figures 1 and 2) UPCC IPCC andSVD++ achieve comparable performances on both datasetsunder this case It is worth emphasizing that CAMF is muchbetter than UPCC IPCC and SVD++ in terms of 11987710 and11987720 on the LDOS-CoMoDa dataset showing its merits incontext-aware recommendations As for using postfiltering(PoF) significant improvements are observed in four CF-based methods against both datasets The gains reach toat least 103 across all indicators on the LDOS-CoMoDa

dataset and at least 16 in terms of 11987720 and 11987730 againstthe TripAdvisor dataset However the case for CGR model isvery unique combining post-filtering in it degrades the recallof recommendations particularly in the TripAdvisor datasetTherefore it is not suitable for the CGR to exploit the PoFstrategy directly

36 Experimental Results on Hybrid Model Since directlycombining the PoF strategy with the CGRmodel reduces thequality of recommendations we suggest a linear combinationof a CGR-based and a CF-based relevance measure between119906 and 119894 aiming at having both worlds It is shown as follows

119875 (119894 | 119862 119906) = 120572119875CGR (119894 | 119862 119906) + (1 minus 120572) 119875CF (119894 | 119862 119906) (9)


0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)

Figure 2 Recommendation accuracy of CGR using different graphic schema on the TripAdvisor dataset

where 120572 is a coefficient to combine the normalized values oftwo terms Both terms are computed using (4)-(5) and scaledusing max-min normalization We perform an experimentagainst the LDOC-CoMoDa dataset to observe the effective-ness of novel hybrid model where we take the IPCC as therating predictor The results are shown in Figure 4 where anotable improvement can be observed as the coefficient 120572

increasesThe gains for R30 andR20 can reach about 24and 60 respectively This confirms our speculation thatCGR-based method is useful to enhance recommendationeffectiveness along with the additional methods Since CGRis dominant and much better than counterparts against theTripAdvisor dataset using a hybrid in this dataset cannot

achieve additional profits we omit the results with respect tothe TripAdvisor dataset

4 Related Works

Context-aware recommender systems represent an increas-ingly active and highly problem-rich research area especiallyfor pervasive computing environments where individualusers consuming various products or services are alwaysassociated with rich contexts A lot of existing researchon CARS addressed different aspects of the problem suchas general-purpose algorithms evaluation protocols and


P10 P20 R10 R20 nDCG10 nDCG200

005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)

Figure 3 Recommendation performance comparison between the CGR and the baseline methods

Table 4 Recall performance of different recommenders in combination with or without postfiltering strategy

LDOS-CoMoDa TripAdvisor11987710 11987720 11987730 11987710 11987720 11987730

UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)

CGRwo 01556 01748 01970 00594 01310 01638PoF 01330 (minus170) 01743 (minus001) 02018 (+24) 00445 (minus335) 00717 (minus827) 00907 (minus806)

domain-specific engineering Instead of providing a detailedsurvey of CARS we only think of the algorithmic principlesmost pertinent to our approaches As for a recent survey onCARS and the discussion of probable directions users canrefer to the work [2] For the comparisons of different CARSusers can refer to works [4ndash6]

From the algorithmic perspective there are currentlythree recognized paradigms for incorporating contextualinformation into the recommendation process (i) contextualprefiltering context is used for selecting the relevant setof rating data before computing predictions For contextualprefiltering many recommendation models such as collab-orative filtering and matrix factorization can be directlyutilized before or after computing predictions [2] Prefiltering

is particularly appealing due to its straight-forward andflexibility of justification Some strategies have been pro-posed such as splitting ways [7] context relaxation [9] andsemantic filtering [8] to acquire more pertinent data forpredicting user preferences in the same contextual situationof the target user (ii) Contextual postfiltering context isused to adjust predictions generated by a context-free 2Dprediction model Distinct from prefiltering the rerankingstrategies are required for the recommendation list alreadyobtained (iii) Contextual modeling contextual informationis directly incorporated in the prediction model usually bygeneralizing the 2D prediction model to an 119899-dimensionalone As for contextual modeling more complex algorithmsare typically explored Tensor decomposition [19] aims to


0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30

Figure 4 Recall of the hybrid model against LDOS-CoMoDa data-set

factorize the tensor over user items and all categoricalcontext variables directly to improve prediction accuracyNonetheless with the increased contextual factors efficiencybecomes the bottleneck of the method [20] In contrastBaltrunas et al present a novel MF-based context-awarerecommendation algorithm [18] which models the inter-action of contextual factors with item ratings introducingadditional model parameters The proposed solution pro-vides comparable results to the tensor decomposition basedapproaches with the merits of smaller computational costHowever incorporating contextual factors into existing CF-based or MF-based algorithms is always a challenging taskdue to the inherent limits of scalability and flexibility of thesealgorithms

Another kind of approach similar to us is graph-based which incorporates contextual information into rec-ommender systems in a flexible and scalable way Graph-based methods can mitigate data sparsity problem utiliz-ing rich contextual information [10 11 21 22] Howeverpresented graph models are not grounding on a unifiedmodeling framework Also these domain-specific modelshave not been tested across different scenarios of applicationsReporting to them our works design a general-purposeframework to facilitate the development and use of context-aware recommendation capabilitiesWe put forward a unifiedgraph-based contextual modeling framework to incorporatecontexts in the prediction model and specially design theCGR measure to estimate the relevance between the targetuser and the items Also we put forward a probabilisticpostfiltering strategy to improve the effectiveness of context-aware recommendation In addition we proved that thenewly proposed methods can work with additional methodsto continue to improve the recommendation performance

5 Conclusions and Future Works

We have proposed a graph-based framework for incor-porating contextual information in the recommendation

process Also we present a probabilistic reranking strategyto filter recommendation consequences given the contextualconditions Experimental results have illustrated that all theproposed approaches are helpful to facilitate the developmentand use of context-aware recommendation capabilities Inaddition our proposed model can be viewed as a componentand entered into a hybrid model to enhance effectiveness ofCARS

Some issues have yet to be investigated in the futureAt first we want to examine proposed methods on addi-tional context-aware datasets and compare them with morepowerful counterparts We currently utilize the contextualgraph in a simplified manner as we do not recognise on theimportance of different contextual factors and relationshipsIn the subsequent phase we propose using machine-learningalgorithms to determine the importance of semantic relations(including contextual factors) in the recommendation andthen automatically assign weights to these relations in thecontextual graph In addition since not all information pro-duces positive effects in context-modeling feature selectionwill be used to get rid of weak features

Disclosure

This work is an extended version of the short paper presentedin [13]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Special Funds for ldquoMiddle-agedand Young Core Instructor Training Programrdquo of YunnanUniversity the Applied Basic Research Project of YunnanProvince (2013FB009 2014FA023) the Program for Innova-tive Research Team inYunnanUniversity (XT412011) and theNational Natural Science Foundation of China (61472345)The authors are grateful to the anonymous reviewers for theirconstructive comments and suggestions which contributesubstantially to the improvement of this paper

References

[1] G Adomavicius and A Tuzhilin ldquoToward the next generationof recommender systems a survey of the state-of-the-art andpossible extensionsrdquo IEEE Transactions on Knowledge and DataEngineering vol 17 no 6 pp 734ndash749 2005

[2] G Adomavicius B Mobasher F Ricci and A TuzhilinldquoContext-aware recommender systemsrdquo AI Magazine vol 32no 3 pp 67ndash80 2011

[3] M Baldauf S Dustdar and F Rosenberg ldquoA survey on context-aware systemsrdquo International Journal of Ad Hoc and UbiquitousComputing vol 2 no 4 pp 263ndash277 2007

[4] P G Campos I Fernndez-Tobas I Cantador and F DezldquoContext-aware movie recommendations an empirical com-parison of pre-filtering post-filtering and contextual modeling


approachesrdquo in E-Commerce andWeb Technologies Proceedingsof the 14th International Conference (EC-Web rsquo13) Prague CzechRepublic August 27-28 2013 vol 152 of Lecture Notes in BusinessInformation Processing pp 137ndash149 Springer Berlin Germany2013

[5] U Panniello and M Gorgoglione ldquoIncorporating context intorecommender systems an empirical comparison of context-based approachesrdquo Electronic Commerce Research vol 12 no1 pp 1ndash30 2012

[6] U Panniello A Tuzhilin and M Gorgoglione ldquoComparingcontext-aware recommender systems in terms of accuracy anddiversityrdquo User Modeling and User-Adapted Interaction vol 24no 1-2 pp 35ndash65 2014

[7] L Baltrunas and F Ricci ldquoExperimental evaluation of context-dependent collaborative filtering using item splittingrdquo UserModeling and User-Adapted Interaction vol 24 no 1-2 pp 7ndash34 2014

[8] V Codina F Ricci and L Ceccaroni ldquoExploiting the semanticsimilarity of contextual situations for pre-filtering recommen-dationrdquo in Proceedings of the 21th International Conference onUser Modeling Adaptation and Personalization pp 165ndash177Springer 2013

[9] Y Zheng R Burke and B Mobasher ldquoDifferential contextrelaxation for context-aware travel recommendationrdquo in Pro-ceedings of the 13th International Conference on ElectronicCommerce andWeb Technologies (EC-WEB rsquo12) pp 88ndash99 2012

[10] I Konstas V Stathopoulos and J M Jose ldquoOn social networksand collaborative recommendationrdquo in Proceedings of the 32ndAnnual International ACM SIGIR Conference on Research andDevelopment in Information Retrieval (SIGIR rsquo09) pp 195ndash202ACM July 2009

[11] HWu XH Cui J He B Li and Y J Pei ldquoOn improving aggre-gate recommendation diversity and novelty in folksonomy-based social systemsrdquo Personal and Ubiquitous Computing vol18 no 8 pp 1855ndash1869 2014

[12] H Wu Y J Pei B Li Z Kang X Liu and H Li ldquoItemrecommendation in collaborative tagging systems via heuristicdata fusionrdquo Knowledge-Based Systems vol 75 pp 124ndash1402015

[13] H Wu X X Liu Y J Pei and B Li ldquoEnhancing contextawarerecommendation via a unified graph modelrdquo in Proceedings ofthe International Conference on Identification Information andKnowledge in the Internet of Things pp 1ndash4 IEEE 2014

[14] A Koir A Odi M Kunaver M Tkali and J F Tasi ldquoDatabasefor contextual personalizationrdquo Elektrotehniki vestnik vol 78no 5 pp 270ndash274 2011

[15] A Odic M Tkalcic J F Tasic and A Kosir ldquoPredictingand detecting the relevant contextual information in a movie-recommender systemrdquo Interacting with Computers vol 25 no1 pp 74ndash90 2013

[16] H A Lee R Law and J Murphy ldquoHelpful reviewers in TripAd-visor an online travel communityrdquo Journal of Travel amp TourismMarketing vol 28 no 7 pp 675ndash688 2011

[17] Y Koren ldquoFactor in the neighbors Scalable and accurate col-laborative filteringrdquoACMTransactions on Knowledge Discoveryfrom Data vol 4 no 1 article 1 2010

[18] L Baltrunas B Ludwig S Peer and F Ricci ldquoContext relevanceassessment and exploitation in mobile recommender systemsrdquoPersonal and Ubiquitous Computing vol 16 no 5 pp 507ndash5262012

[19] AKaratzoglou XAmatriain L Baltrunas andNOliver ldquoMul-tiverse recommendation n-dimensional tensor factorization

for context-aware collaborative filteringrdquo in Proceedings of the4th ACMRecommender Systems Conference (RecSys rsquo10) pp 79ndash86 ACM September 2010

[20] B Zou C Li L Tan and H Chen ldquoGPUTENSOR effi-cient tensor factorization for context-aware recommendationsrdquoInformation Sciences vol 299 pp 159ndash177 2015

[21] H Wu F Luo X M Ning and H Jin ldquoA suggested frameworkfor exploring contextual information to evaluate and recom-mend servicesrdquo in Advances in Grid and Pervasive ComputingProceedings of the 3rd International Conference GPC 2008Kunming China May 25ndash28 2008 vol 5036 of Lecture Notesin Computer Science pp 471ndash482 Springer Berlin Germany2008

[22] S Lee S-I Song M Kahng D Lee and S-G Lee ldquoRandomwalk based entity ranking on graph for multi-dimensionalrecommendationrdquo in Proceedings of the 5th ACMConference onRecommender Systems (RecSys rsquo11) pp 93ndash100 ACM October2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



effectiveness of the recommendations Nevertheless how tomodel contextual factors into a recommendation processand how to combine different strategies of CARS are stillchallenging tasks and many issues are yet to be taken upTo cope with this issue we propose a unified graph-basedcontextual modeling framework to incorporate contextualinformation in an advantageous way A contextual graph-based relevance measure and a probabilistic postfilteringstrategy are designed to facilitate the development and useof context-aware recommendation capabilities Experimentalresults against two real-world datasets show the merits of allthe proposed approaches in context-aware recommendation

The rest of the paper is structured as follows Section 2introduces our models and the corresponding recommenda-tion approaches for CARS In Section 3 experiments againsttwo datasets from different domains are conducted to watchthe effectiveness of the proposed methods Section 4 reviewsrelated works and makes some discussions Finally we con-clude the works and point to future directions

2 The Proposed Methods

21 Graph-Based Contextual Modeling CARS address mod-eling and predicting user tastes and preferences by incorpo-rating existing contextual information into the recommenda-tion process as explicit additional categories of data Theselong-term preferences and tastes are generally expressed asratings and are modeled as the function of not only items andusers but also the context Adomavicius et al [2] formallydefine the recommending process in CARS as 119877 119880119904119890119903 times

119868119905119890119898 times 119862119900119899119905119890119909119905 rarr 119877119886119905119894119899119892 where User Item and Ratingare the domains of users items and ratings respectively andContext specifies the contextual information associated withthe application Once the function 119877 is estimated for thewhole User times Item times Context space a recommender systemcan suggest the highest-rated item for users Note that contextfactors indicate the upper-level contextual concepts (egdaytype and location) while context conditions represent thecombination of contextual concept instances for exampleMonday Office Room

Distinct from building a prediction model we examinethe context-aware recommendation as a searching problemto find interesting items for a user given a context graphFormally suppose119866 = 119881 119864 is a context graphThevertex set119881 are divided into several distinct sets including a set of users119880 a set of items 119868 a set of attributes119860 and a set of contexts119862In particular we distinguish the contextual information of 119862from the static information of119860 of users or items consideringthat the attributes basically do not change while the contextfactors often change over different ratings The edge set 119864

consists of the existing connections of the Cartesian product119881 times 119881 Edges with diverse types have distinct semantics Forexample 119880 times 119860 connects users and their attributes 119880 times 119868

means the users have accessed items 119880 times 119862 represents thatthe users have activities given the contextual condition Thesituation for items is equal to that of users The context graph119866 can be represented as an adjacent matrix 119872 (as shown in

Table 1 A matrix representation of contextual user-item interac-tion

Users Items Contexts AttributesUsers 119880119880 119880119868 119880119862 119880119860

Items 119880119868T 0 119868119862 119868119860

Contexts 119880119862T

119868119862T 0 0

Attributes 119880119860T

119868119860T 0 0

Table 1) where submatrixes are all configured as symmetric(eg 119880119868

T is the transport matrix of 119880119868)Considering a random search that starts fromnode 119894 in119866

the search iteratively transmits to its neighborhood 119895with theprobability that is proportional to the edge weights 119878

119894119895 Also

at each step it has some probability 1 minus 119889 (the default settingis 119889 = 085) to return to the node 119894 The relevance score ofnode 119895 with respect to node 119894 is described as the steady-stateprobability the search will finally stay at node 119895 The steadyprobability can be gotten using the power method as in thefollowing equation until convergence

P(119899) = 119889119878TP(119899minus1) + (1 minus 119889) e (1)

where the row-normalized matrix 119878 is the transitivity matrixof random walks and vector e is a personalized vector thatmay represent the interests of a particular user Such a theoryis called the random walks with restarts (also known asPersonalized PageRank) and has attractedmany attentions invarious recommendation scenes [10ndash12]

A contextualized data graph adheres to the schema of 119866In the data graph given the source node 119894 the target node 119895

and the relationship type 119871 of an edge the transitivity matrixis initialized as follows

119878119894119895

=

119908 (119871)119908 (119894 119895 119871)

sum119896119908 (119894 119896 119871)

if 119908 (119894 119895 119871) gt 0

0 otherwise(2)

119908(119871) is the weight of the relationship typed 119871 in the schemaof 119866 and 119908(119894 119896 119871) represents the weights of out-edges typed119871 of 119894 in the data graph Since the graph 119866 is symmetric119908(119895 119894 119871) = 119908(119894 119895 119871) Here we examine the weights of edgesin two aspects (I) edge with different types has unusualsemantics thus it may affect the selection of nodes duringrandomwalks For instance when searching items of interesta usermaywish to consult hisher friends other than viewingthe ratings of the itemsWe use119908(119871) to impose this influencein the process of the userrsquos random walks (II) edges mustbe assigned weights to reflect users usage data For instancea user may have contacted an item several times or accessseparate items under the same context condition Thus wefurther assign a weight of 119908(119894 119895 119871) to the edges

With respect to the types of edges 119871 and the weights119908(119871)they can be defined at different levels of concepts We firstdefine 119871 at the highest level according to Table 1 resulting in11 types of119871 Tomake a difference among numerous attributesor context factors we further extend the definition of 119871 and119908(119871) to a fine-grained level of concept For instance givena set of item attributes 119860 = 119860

1 119860

119894 119860

119899 we can




(7) 119878119894119895= 119908(119871)

119908(119894 119895 119871)

sum119896119908(119894 119896 119871)

(8) else(9) 119878

119894119895= 0


(13) 119878119894119895=

119878119894119895

sum119896119878119894119896


119895= 1

(19) else(20) e1015840

119895= 0


(119899)= 119889119878

TP1(119899minus1)


119906then

(26) e10158401015840119895

=1

|119868119906|

(27) else(28) e10158401015840

119895= 0


(119899)= 119889119878

TP2(119899minus1)

+ (1 minus 119889)e10158401015840(32) return (P1 + P2)2


partition 119868119860 = ⋃119899

119894119868119860119894and define 119908(119868119860) = sum

119899

119894119908(119868119860119894)




119875 (119894 | 119906) =P1 (119894) + P2 (119894)

2 (3)



= 1|119868119906| where 119895 isin 119868








1 119888

119894 119888



119875 (119894 | 119906 119862) = 119875 (119894 | 119862) 119875 (119894 | 119906) (4)


119875 (119894 | 119862) prop sum

119888119896isin119862

119875 (119894 | 119888119896) 119875 (119888119896| 119862) =

1

|119862|sum

119888119896isin119862

freq (119894 119888119896)

sum119895freq (119895 119888

119896)

(5)



119896| 119862) takes 1119862 for sim-


3 Experiments









119875119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

119873 (6)


119877119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

|119903119890119897119890V119886119899119905 119894119905119890119898119904| (7)


DCG119873 =

119873

sum

119894=1

2119903119890119897(119894)

minus 1

log2(119894 + 1)

IDCG119873 =

119870

sum

119894=1

1

log2(119894 + 1)

(8)











0 119908(119880119862T) = 0 119908(119868119862) = 0 and 119908(119868119862

T) = 0 Similarly





0 10 20 30 40 50 600

002

004

006

008

01

012

014

016

018LDOS-CoMoDa

Prec

ision

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025LDOS-CoMoDa

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

005

01

015

02

025

03

035

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

LDOS-CoMoDa

Top-N

(c)






119875 (119894 | 119862 119906) = 120572119875CGR (119894 | 119862 119906) + (1 minus 120572) 119875CF (119894 | 119862 119906) (9)


0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)





4 Related Works




005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












(7) 119878119894119895= 119908(119871)

119908(119894 119895 119871)

sum119896119908(119894 119896 119871)

(8) else(9) 119878

119894119895= 0


(13) 119878119894119895=

119878119894119895

sum119896119878119894119896


119895= 1

(19) else(20) e1015840

119895= 0


(119899)= 119889119878

TP1(119899minus1)


119906then

(26) e10158401015840119895

=1

|119868119906|

(27) else(28) e10158401015840

119895= 0


(119899)= 119889119878

TP2(119899minus1)

+ (1 minus 119889)e10158401015840(32) return (P1 + P2)2


partition 119868119860 = ⋃119899

119894119868119860119894and define 119908(119868119860) = sum

119899

119894119908(119868119860119894)




119875 (119894 | 119906) =P1 (119894) + P2 (119894)

2 (3)



= 1|119868119906| where 119895 isin 119868








1 119888

119894 119888



119875 (119894 | 119906 119862) = 119875 (119894 | 119862) 119875 (119894 | 119906) (4)


119875 (119894 | 119862) prop sum

119888119896isin119862

119875 (119894 | 119888119896) 119875 (119888119896| 119862) =

1

|119862|sum

119888119896isin119862

freq (119894 119888119896)

sum119895freq (119895 119888

119896)

(5)



119896| 119862) takes 1119862 for sim-


3 Experiments









119875119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

119873 (6)


119877119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

|119903119890119897119890V119886119899119905 119894119905119890119898119904| (7)


DCG119873 =

119873

sum

119894=1

2119903119890119897(119894)

minus 1

log2(119894 + 1)

IDCG119873 =

119870

sum

119894=1

1

log2(119894 + 1)

(8)











0 119908(119880119862T) = 0 119908(119868119862) = 0 and 119908(119868119862

T) = 0 Similarly





0 10 20 30 40 50 600

002

004

006

008

01

012

014

016

018LDOS-CoMoDa

Prec

ision

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025LDOS-CoMoDa

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

005

01

015

02

025

03

035

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

LDOS-CoMoDa

Top-N

(c)






119875 (119894 | 119862 119906) = 120572119875CGR (119894 | 119862 119906) + (1 minus 120572) 119875CF (119894 | 119862 119906) (9)


0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)





4 Related Works




005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1 119888

119894 119888



119875 (119894 | 119906 119862) = 119875 (119894 | 119862) 119875 (119894 | 119906) (4)


119875 (119894 | 119862) prop sum

119888119896isin119862

119875 (119894 | 119888119896) 119875 (119888119896| 119862) =

1

|119862|sum

119888119896isin119862

freq (119894 119888119896)

sum119895freq (119895 119888

119896)

(5)



119896| 119862) takes 1119862 for sim-


3 Experiments









119875119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

119873 (6)


119877119873 =

1003816100381610038161003816119903119890119897119890V119886119899119905 119894119905119890119898119904 cap 119905119900119901-119873 1198941199051198901198981199041003816100381610038161003816

|119903119890119897119890V119886119899119905 119894119905119890119898119904| (7)


DCG119873 =

119873

sum

119894=1

2119903119890119897(119894)

minus 1

log2(119894 + 1)

IDCG119873 =

119870

sum

119894=1

1

log2(119894 + 1)

(8)











0 119908(119880119862T) = 0 119908(119868119862) = 0 and 119908(119868119862

T) = 0 Similarly





0 10 20 30 40 50 600

002

004

006

008

01

012

014

016

018LDOS-CoMoDa

Prec

ision

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025LDOS-CoMoDa

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

005

01

015

02

025

03

035

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

LDOS-CoMoDa

Top-N

(c)






119875 (119894 | 119862 119906) = 120572119875CGR (119894 | 119862 119906) + (1 minus 120572) 119875CF (119894 | 119862 119906) (9)


0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)





4 Related Works




005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















0 119908(119880119862T) = 0 119908(119868119862) = 0 and 119908(119868119862

T) = 0 Similarly





0 10 20 30 40 50 600

002

004

006

008

01

012

014

016

018LDOS-CoMoDa

Prec

ision

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025LDOS-CoMoDa

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

005

01

015

02

025

03

035

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

LDOS-CoMoDa

Top-N

(c)






119875 (119894 | 119862 119906) = 120572119875CGR (119894 | 119862 119906) + (1 minus 120572) 119875CF (119894 | 119862 119906) (9)


0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)





4 Related Works




005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 600

002

004

006

008

01

012

014

016

018LDOS-CoMoDa

Prec

ision

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025LDOS-CoMoDa

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

005

01

015

02

025

03

035

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

LDOS-CoMoDa

Top-N

(c)






119875 (119894 | 119862 119906) = 120572119875CGR (119894 | 119862 119906) + (1 minus 120572) 119875CF (119894 | 119862 119906) (9)


0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)





4 Related Works




005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 600

0002

0004

0006

0008

001

0012

0014

TripAdvisorPr

ecisi

on

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(a)

0 10 20 30 40 50 600

005

01

015

02

025TripAdvisor

Reca

ll

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(b)

0 10 20 30 40 50 600

001

002

003

004

005

006

007

008

009TripAdvisor

nDCG

ALLALL-UC-ICALL-UA

ALL-IAALL-UI

Top-N

(c)





4 Related Works




005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











005

01

015

02

025

03

035LDOS-CoMoDa

UPCCIPCCSVD++

CAMFCGR (ALL-UA)

(a)


UPCCIPCCSVD++

CAMF

0

002

004

006

008

01

012

014TripAdvisor

CGR (ALL)

(b)




UPCCwo 00311 00400 00577 00163 00241 00318PoF 01055 (+239) 01560 (+290) 01789 (+210) 00150 (minus8) 00318 (+320) 00422 (+327)

IPCCwo 00444 00667 00948 00163 00241 00318PoF 01238 (+179) 01606 (+141) 01927 (+103) 00150 (minus8) 00318 (+320) 00422 (+327)

SVD++wo 00444 00637 00908 00133 00252 00350PoF 01174 (+164) 01697 (+166) 01881 (+107) 00177 (+331) 00295 (+171) 00408 (+166)

CAMFwo 00543 00765 00849 00104 00204 00340PoF 01147 (+111) 01651 (+116) 01972 (+132) 00182 (+750) 00295 (+446) 00413 (+215)






0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 02 04 06 08 1004

006

008

01

012

014

016

018

02

LDOS-CoMoDa

120572

R20

R30

nDCG20

nDCG30








Disclosure




Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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