Research Article Multiangle Social Network Recommendation Algorithms and Similarity ... · 2019. 7....

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013 Article ID 248084 8 pageshttpdxdoiorg1011552013248084

Research ArticleMultiangle Social Network Recommendation Algorithms andSimilarity Network Evaluation

Jinyu Hu1 Zhiwei Gao2 and Weisen Pan1

1 Department of Biostatistics and Computational Biology University of Rochester Rochester NY 14642 USA2 Faculty of Engineering and Environment Northumbria University Newcastle upon Tyne NE1 8ST UK

Correspondence should be addressed to Zhiwei Gao zhiweigaonorthumbriaacuk

Received 14 June 2013 Accepted 22 June 2013

Academic Editor Dexing Kong

Copyright copy 2013 Jinyu Hu 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

Multiangle social network recommendation algorithms (MSN) and a new assessment method called similarity network evaluation(SNE) are both proposed From the viewpoint of six dimensions the MSN are classified into six algorithms including user-basedalgorithm from resource point (UBR) user-based algorithm from tag point (UBT) resource-based algorithm from tag point (RBT)resource-based algorithm from user point (RBU) tag-based algorithm from resource point (TBR) and tag-based algorithm fromuser point (TBU) Compared with the traditional recallprecision (RP) method the SNE is more simple effective and visualizedThe simulation results show that TBR and UBR are the best algorithms RBU and TBU are the worst ones and UBT and RBT arein the medium levels

1 Introduction

In recent years social tagging systems have become increas-ingly popular as a means to classify large sets of resources onthe web These systems allow users to add metadata in theform of keywords to share resources [1] Nevertheless therapidly growing data in these systems present new technicalchallenges involved with recommended resources Collabo-rative filtering [2] approach provides a solution to overcomethis challenge which makes recommendations solely base onthe preferred database The Top-N recommendation method[3] tries to recommend the top-n ranked resources that usersmay be interested in

Computation of the similarity plays a key role in thecollaborative filtering and there are many different waysto compute the similarities such as the Pearson correla-tion [4] constrained Pearson correlation [5] cosine-basedsimilarity [6] adjusted cosine similarity [7] and Spearmanrank correlation [8] Currently the user-based collaborativefiltering algorithm mainly considers user similarity from theresource perspective [9] Some papers did not discuss theresource similarity from the user perspective [10] Mostly thetag-based recommendation only takes into account the tagsimilarity based on the resource tag [11] Some papers also

comprehensively consider the user similarity and resourcesimilarity but do not consider the tag similarity [12] Based onthe pursuit of a recommendation system the assessment indi-cators are employed to evaluate an algorithm for instancerecallprecision mean absolute error (MAE) mean averageprecision (MAP) and area under curve (AUC) [13] Forrecommended results there are some auxiliary assessmentindicators [14] such as coverage (COV) diversity (DIV) andaverage popularity (AP)

In this paper the concepts of the 1-mode network and 2-mode network in social network [15] are addressed for collab-orative filtering For movies this paper gives recommendedexplanations of the six algorithms as follows

UBR ldquoUsers who watched your favorite movies alsowatch rdquoUBT ldquoUsers who used your favorite tags alsowatch rdquoRBU ldquoUsers who watch this movie also watch rdquoRBT ldquoTags which annotate this movie also anno-tate rdquoTBR ldquoOther Tags of this movie also annotate rdquoTBU ldquoOther Tags which you used also annotate rdquo

2 Journal of Applied Mathematics

URT

1

11

1

11 1

1 1

1

1

1 1

UR

RU

RT

TR T

U

UT

1

1

111

r1

r2

r3

r4

r5

u1

u2

u3

t1

t2

t3

t4

u1 u2 u3 u1 u2 u3

r1 r2 r3 r4 r5

r1 r2 r3 r4 r5

u1

u2 u3

r1

r2

r3

r4r5 u1

u2 u3

t1 t2 t3 t4

r1r2

r3

r4r5

t1t2

t3t4

UR UTRT

t1 t2 t3 t4

t1t2

t3t4

Figure 1 A process to obtain 2-mode networks and 1-mode networks

On the basis of the similarity network evaluation (SNE)and comparison with the recallprecision it is indicated thatthe results from the two assessment methods are consistentbut the SNE is more simple visualized and effective with lesssteps

2 Multiangle Social NetworkRecommendation Algorithm (MSN)

21 Pretreatment of Social Network The triple (119880 119877 119879) rep-resents the raw data which means the user 119880 is given the tag119879 on the resource 119877 From this triple one can deduce three2-mode networks such as 119880119877 119879119877 and 119880119879 Each 2-modenetwork can deduce two 1-mode networks For instance 119880119877can infer two 1-mode networks119880119877 and 119877119880 119877119879 infers 1-modenetworks 119877119879 and 119879119877 and 119880119879 infers 1-mode networks 119880119879and 119879119880 (see Figure 1) In the present paper the symbol of 1198601015840denotes the transpose of 119860

The matrix 119880119877 shows the membership of each pair ofusers who like the common resources described by 119880119877 =119880119877lowast119880119877

1015840 The matrix 119877119880 represents the membership of eachpair of resources which have the common users described

by 119877119880 = 1198801198771015840 lowast 119880119877 The matrix 119877119879 is the membership ofeach pair of resources which have the same tags describedby 119877119879 = 119877119879 lowast 1198771198791015840 The matrix 119879119877 indicates the membershipof each pair of tags which have the common resources with119879

119877= 119877119879

1015840lowast 119877119879 The matrix 119880119879 means the membership of

each pair of users who annotate the common tags with119880119879 =119880119879lowast119880119879

1015840Thematrix119879119880 shows themembership of each pairof tags which have the common users with 119879119880 = 1198801198791015840 lowast 119880119879

22 User-Based Social Network Algorithm (USN) There aretwo steps of theUSN algorithm firstly to find other users whoare similar to the target user and then recommend the otherusersrsquo favorite resources to the target user The algorithm canbe divided into the two algorithms UBR and UBT

(1) User-Based Algorithm from Resource Perspective (User-Based Resources UBR) The user similarity from resource(USR) perspective means that if two users like the sameresources they are similar The element of the USR denotedby usr

119894119895is defined as

usr119894119895=

119906

119894119895

119906

119894119894+ 119906

119895119895minus 119906

119894119895

119906

119894119895isin 119880

119877 (1)

Journal of Applied Mathematics 3

Based on the above similarity the user-resource interestmatrix UBR is described by

UBR = 1198801198771015840 lowast USR (2)

(2) User-Based Algorithm from Tag Perspective (User-BasedTag UBT) The user similarity from tag (UST) perspectiveindicates two users are similar if they prefer to use the sametagsThe element of the UST denoted by ust

119894119895is computed by

ust119894119895=

119906

119894119895

119906

119894119894+ 119906

119895119895minus 119906

119894119895

119906

119894119895isin 119880

119879 (3)

Based on the similarity the interest matrix UBT is defined as

UBT = 1198801198771015840 lowast UST (4)

23 Resource-Based Social Network Algorithm (RSN) TheRSN algorithm also has two steps firstly to find out theresources that the target user likes and then recommendothersimilar ones to the user It is divided into two algorithms RBUand RBT

(1)Resource-Based Algorithm from User Perspective (Resour-ces-Based User RBU) The resource similarity from user(RSU) perspective means that if two resources are enjoyed bythe same user they are similar where rsu

119894119895is defined by

rsu119894119895=

119903

119894119895

119903

119894119894+ 119903

119895119895minus 119903

119894119895

119903

119894119895isin 119877

119880 (5)

The interest matrix RBU is written as

RBU = RSU lowast 1198801198771015840 (6)

(2)Resource-Based Algorithm from Tag Perspective (Resour-ces-Based Tag RBT) The resource similarity from tag (RST)perspective implies that if two resources are enjoyed by thesame user they are similarThe element of the RST is definedas

rst119894119895=

119903

119894119895

119903

119894119894+ 119903

119895119895minus 119903

119894119895

119903

119894119895isin 119877

119879 (7)

The interest matrix RBT is described by

RBT = RST lowast 1198801198771015840 (8)

24 Tag-Based Social Network Algorithm (TSN) The TSNalgorithm consists of three parts the first step is to look forthe frequently used tags of the target user next to find othersimilar tags and merge both of them into a tag set finallyto recommend these tag-set corresponding resources to thetarget user

(1)Tag-Based Algorithm fromResource Perspective (Tag-BasedResources TBR) The tag similarity from resource (TSR)

perspective means that if two resources are enjoyed by thesame user they are similar The element of the TSR iscomputed as

tsr119894119895=

119905

119894119895

119905

119894119894+ 119905

119895119895minus 119905

119894119895

119905

119894119895isin 119879

119877 (9)

The tag similarity matrix TSR which is viewed from theresources show that if two tags annotate the same resourcesthey are similar One can have

TBR = 119877119879 lowast TSR lowast 1198801198791015840 (10)

(2)Tag-Based Algorithm from User Perspective (Tag-BasedUser TBU) The tag similarity from user perspective (TSU)implies that if two resources are enjoyed by the same userthey are similar The element of the TSU is defined as

tsu119894119895=

119905

119894119895

119905

119894119894+ 119905

119895119895minus 119905

119894119895

119905

119894119895isin 119879

119880 (11)

The interest matrix TBU can be written as

TBU = 119877119879 lowast TSU lowast 1198801198791015840 (12)

3 Similarity Network Evaluation (SNE)

31 Basic Concepts

Definition 1 (similarity network (SN)) A connection matrix119862 is used to store similarity network (SN) whose element is119888

119894119895 defined by

119888

119894119895=

119904

119894119895 119894 gt 119895 119904

119894119895ge 119879 0 le 119879 le 1

0 119894 le 119895

(13)

where 119904119894119895is the similarity between the nodes 119894 and 119895 and 119904

119894119895isin

[0 1] When 119888119894119895= 0 there is no edge between nodes 119894 and 119895

119879 is a threshold

The definition of the similarity of the SN is actually bor-rowed from the definition of the gene community network(GCN) proposed by [16]

Definition 2 (types of the network) The similarity networkscan be divided into six categories in terms of the intensity ofsimilarities

(1) Perfect correlation network (PCN) when 119879 = 1remove the edges whose weights are lower than 1 andthe weights of all edges are 1

(2) Very strong correlation network (VSN) when 119879 =08 delete the edges with the weights lower than 08

(3) Strong correlation network (SCN) when 119879 = 06remove the edges with the weights lower than 06 toform a new network

(4) Moderate correlation network (MCN) when119879 = 04delete the edges whose weights are lower than 04 toform a similarity Network


Preprocess the interest matrices

Recommended inverted list

TOP-N recommendation matrix

Preprocess the training setTest set

Training set

Similarity matrices

Interest matrices

Recallprecision

Preprocess the

recommended inverted list

(1) (2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Datasets

Figure 2 The computing steps of RecallPrecision

Similarity matricesSimilarity network

Evaluation(1)

(2)

Datasets

Figure 3 The computing steps of similarity networks evaluation

(5) Weak correlation network (WCN) when 119879 = 02the values of all the edges are lower than 02 in thenetwork

(6) Uncorrelated network (UCN) when 119879 = 0 all nodesare isolated nodes

32 Algorithm Principle The core of the collaborative fil-tering algorithm is to calculate the similarity The SNEmethod can better evaluate the algorithm if under a certainthreshold value there are fewer isolated nodes but moresmall communities in its similarity networks It includes thefollowing requirements

(1) A Certain Threshold Value Relative to the entire resourcethese recommended resources are quite fewTherefore whenwe evaluate an algorithm the PCN network (119879 = 1)only needs to be considered However in order to have acomprehensive analysis the VSN network (119879 = 08) and theSCN network (119879 = 06) should be considered together

(2) Fewer Isolated Nodes Recommendation algorithm isbased on the similarity The isolated node is not similar toany other nodes In this case the algorithm can not givea recommendation about these isolated nodes Therefore agood algorithmmay produce a similarity network with fewerisolated nodes and more nonisolated ones

(3) More Communities Each community (nodes gt 2) repre-sents a different interest of users The more the communities

the more detailed features can they reflect which makes therecommended results more in line with the userrsquos taste

(4) Fewer Nodes in the Largest Community In the largestcommunity there are toomanynodes to reflect the userrsquos tastein detailThenodes in the largest community should be as fewas possible

Taking into account the previous points and also con-sidering these different networks with different number ofnodes the score of the similarity network evaluation (SNE)is described by

SS (119879) = NC lowastNINA lowastNL

NA ge 1 NL ge 1 (14)

where SS is the score function of similarity network 119879 is thethreshold NA is the number of all nodes in the network NIis the number of nonisolated nodes in the network NC is thenumber of communities and NL is the number of nodes inthe largest community

33 Steps of SNE The recallprecision rate of an algorithmhas nine calculation steps (see Figure 2)

The SNE method only needs to calculate similaritymatrices thus one can directly evaluate the algorithms afterconstructing similarity networks It is a simplemethodwhichonly has one intermediate step (see Figure 3)


(a) Similarity network USR (b) Similarity network UST

(c) Similarity network RSU (d) Similarity network RST

(e) Similarity network TSR (f) Similarity network TSU

Figure 4 The PCN networks of six algorithms

Table 1 The score of the PCN

SN NA NC NL NI SS(119879)USR 2007 137 6 343 39UST 2007 115 10 319 183RSU 5640 315 201 2253 063RST 5640 255 74 1081 066TSR 8390 1146 23 4005 2378TSU 8390 544 611 5656 06SS the score function of similarity network 119879 the threshold of similaritynetwork NA the number of all nodes in the network NI the number ofnonisolated nodes in the network NC the number of communities NL thenumber of nodes in the largest community

4 Results and Discussions

The dataset is ldquohetrec2011-movielens-2krdquo from HetRec 2011[17] which is an extension of MovieLens 10M dataset with2113 users 10197 movies 13222 tags and 855598 ratings Inthis paper we focus on the users resources and tags andignore the ratings

Table 2 The score of the VSN


41 Visual Analysis of the SNE Visual similarity networkanalysis can be more intuitive to roughly evaluate variouskinds of recommendation algorithms We use the Pajek [18]to show the six PCN networks To see more clearly we justintercept 116 of the original screen in the upper-left corner(see Figure 4)


10 20 30 40 50 60 70 80 90 100

Recall

UBR UBTRBU RBTTBR TBU

N

()

5

10

15

20

25

(a) Recall

10 20 30 40 50 60 70 80 90 100

Precision


N

05

10

15

20

25

30

()

(b) Precision

Figure 5 Recallprecision of the six algorithms

Table 3 The score of the SCN


Table 4 Recall of the six algorithms

Top-N UBR UBT RBU RBT TBR TBU10 727 565 395 618 705 51820 1149 755 636 971 1167 85730 1444 980 863 1134 1514 104440 1708 1161 979 1295 1723 116550 1924 1296 1061 1439 1952 132960 2055 1395 1176 1543 2125 153570 2257 1520 1239 1639 2348 165680 2370 1677 1354 1721 2454 175190 2517 1794 1411 1807 2517 1821100 2598 1854 1510 1951 2585 1935

In the SNE evaluation an algorithm with more smallcommunities is better than the one with more large commu-nities In Figure 4 we can see the following

Table 5 Precision of the six algorithms


(1) TheUSTrsquos big communities aremore obvious than theUSRrsquos therefore UBR is better than UBT denoted byUBR gt UBT

(2) The RSU has more big communities than the RSTthus RBT gt RBU indicating RBT is better than RBU

(3) There are very big communities in TSU ConverselyTSR has fewer ones Therefore TBR gt TBU meaningTBR is better than TBU

(4) Obviously the TSU andRSUhave the largest commu-nities thus the algorithmsTBUandRBUare relativelypoor

(5) In the same way the better algorithms are UBR andTBR and the medium ones are UBT and RBT

42 Quantitative Analysis of SNE Based on score function ofSNE the scores of different algorithms under the threshold


Table 6 Comparison analysis of RP and SNE

Recallprecision (RP) Similarity network evaluation (SNE)

Results of evaluation

RecallUBR gt TBR gt RBT gt UBT gt TBU gt RBUPrecisionTBR gt UBR gt RBT gt UBT gt TBU gt RBUConclude from aboveTBR gt UBR gt RBT gt UBT gt TBU gt RBU

119879 = 1

TBR gt UBR gt UBT gt RBT gt RBU gt TBU119879 = 08


TBR gt UBR gt UBT gt RBT gt TBU gt RBUConclude from aboveTBR gt UBR gt UBT gt RBT gt TBU gt RBU

Complexity 9 middle steps high complexity 1 middle step very simpleVisualization No Yes

values of 1 08 and 06 are respectively displayed in Tables1ndash3

According to the similarity scores shown by Tables 1 and2 one can give the order of the algorithms from best to worstas follows TBR gt UBR gt UBT gt RBT gt RBU gt TBU AndfromTable 3 in order of the best algorithm it goes as followsTBR gt UBR gt UBT gt RBT gt TBU gt RBU Overall RBU andTBU are the worst algorithms

43 Comparison with RecallPrecision The recallprecisionrates can evaluate the accuracy of algorithms Based on thetraining set we recommend the top-N resources to usersby using the six algorithms Corresponding to the test setone can obtain the RecallPrecision rates under different 119873values respectively (see Tables 4 and 5)

The Recall and Precision rates of different algorithms anddifferent119873 values are shown in Figure 5

The comparative analysis of two evaluation indicators isgiven in Table 6

From the comparison one can see that the results of twoevaluation algorithms are very agreeable where the sameresults are UBR gt UBT RBT gt RBU and TBR gt TBU Thesimilarity network visualizationmethod can roughly evaluatealgorithms From the perspective of the complexity andvisualization the similarity network assessment algorithm isin an advantageous position

5 Conclusion and Future Work

In the paper not only the collaborative filtering algorithmsare proposed based on social network but also a new assess-ment method of similarity network evaluation is addressedFor these six algorithms TBR and UBR are the best algo-rithms RBU and TBU are the worst ones and UBT and RBTare in the medium levels From the recommended effects wecan conclude that UBR gtUBT RBT gt RBU and TBR gt TBUIt is noted that in the actual use of algorithms the accuracyof the algorithm is not the unique factor to be considered thecomplexity of the algorithm and the maintenance cost of thealgorithm have to be taken into account as well

Future work is encouraged for the three aspects (1)recommended algorithm based on the current similaritycalculationmethod is of interest (2) hybrid algorithms basedon two recommendation algorithms are of significance (3)

the SNE assessment would be extended to evaluate otheralgorithms rather than the collaborative recommended algo-rithms

References

[1] A K Milicevic A Nanopoulos and M Ivanovic ldquoSocialtagging in recommender systems a survey of the state-of-the-art and possible extensionsrdquo Artificial Intelligence Review vol33 no 3 pp 187ndash209 2010

[2] A K Menon K Chitrapura S Garg D Agarwal and N KotaldquoResponse prediction using collaborative filtering with hierar-chies and side-informationrdquo in Proceedings of the 17th ACMSIGKDD International Conference on Knowledge Discovery andData Mining (KDD rsquo11) pp 141ndash149 San Diego Calif USAAugust 2011

[3] X Ning and G Karypis ldquoSLIM sparse linear methods fortop-n recommender systemsrdquo in Proceedings of the 11th IEEEInternational Conference on Data Mining (ICDM rsquo11) pp 497ndash506 Vancouver Canada December 2011

[4] J Bobadilla F Serradilla and A Hernando ldquoCollaborativefiltering adapted to recommender systems of e-learningrdquoKnowledge-Based Systems vol 22 no 4 pp 261ndash265 2009

[5] G Chen F Wang and C Zhang ldquoCollaborative filtering usingorthogonal nonnegative matrix tri-factorizationrdquo InformationProcessing and Management vol 45 no 3 pp 368ndash379 2009

[6] L Candillier F Meyer and M Boulle ldquoComparing state-of-the-art collaborative filtering systemsrdquo in Proceedings of theInternational Conference onMachine Learning andDataMiningpp 548ndash562 Leipzig Germany July 2007

[7] K Choi and Y Suh ldquoA new similarity function for select-ing neighbors for each target item in collaborative filteringrdquoKnowledge-Based Systems vol 37 no 1 pp 146ndash153 2013

[8] D Helic ldquoManaging collaborative learning processes in e-learning applicationsrdquo in Proceedings of the 29th IEEE Interna-tional Conference on Information Technology Interfaces pp 345ndash350 Dubrovnik Croatia June 2007

[9] C Cechinela M Siciliab and S Sanchez-Alonsob ldquoEvaluatingcollaborative filtering recommendations inside large learningobject repositoriesrdquo Information Processing and Managementvol 49 no 1 pp 34ndash50 2013

[10] A Rajput M Dubey S Thakur and M Gondgly ldquoImproveditem based collaboration filtering using recommendation sys-temrdquo Binary Journal of Data Mining and Networking vol 1 no1 pp 6ndash13 2011


[11] R Jaschke A Hotho F Mitzlaff and G Stumme ldquoChallengesin tag recommendations for collaborative tagging systemsrecommender systems for the social webrdquo Intelligent SystemsReference Library vol 32 pp 65ndash87 2012

[12] D Zhang and C Xu ldquoA collaborative filtering recommendationsystem by unifying user similarity and item similarityrdquo inWeb-Age Information Management vol 7142 of Lecture Notes inComputer Science pp 175ndash184 Springer Berlin Germany 2012

[13] Y Shi M Larson and A Hanjalic ldquoMining contextual moviesimilarity with matrix factorization for context-aware rec-ommendationrdquo ACM Transactions on Intelligent Systems andTechnology vol 4 no 1 article 16 2013

[14] L Lu M Medob C Yeungb Y Zhang Z Zhang and T ZhouldquoRecommender systemsrdquo Physics Report vol 519 no 1 pp 1ndash492012

[15] A Mislove B Viswanath K P Gummadi and P DruschelldquoYou are who you know inferring user profiles in onlinesocial networksrdquo in Proceedings of the ACM 3rd InternationalConference on Web Search and Data Mining (WSDM rsquo10) pp251ndash260 New York NY USA February 2010

[16] J Hu and Z Gao ldquoModules identification in gene positive net-works of hepatocellular carcinoma using Pearson agglomerativemethod and Pearson cohesion coupling modularityrdquo Journal ofApplied Mathematics vol 2012 Article ID 248658 21 pages2012

[17] I Cantador P Brusilovsky and T Kuflik ldquoSecond Workshopon Information Heterogeneity and Fusion in RecommenderSystemsrdquo in Proceedings of the 5th ACM conference on Recom-mender Systems (RecSys rsquo11) pp 387ndash388 Chicago Ill USAOctober 2011

[18] W Nooy A Mrva and V Batagelj Exploratory Social NetworkAnalysis with Pajek Cambridge University Press CambridgeUK 2005

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


URT

1

11

1

11 1

1 1

1

1

1 1

UR

RU

RT

TR T

U

UT

1

1

111

r1

r2

r3

r4

r5

u1

u2

u3

t1

t2

t3

t4

u1 u2 u3 u1 u2 u3

r1 r2 r3 r4 r5

r1 r2 r3 r4 r5

u1

u2 u3

r1

r2

r3

r4r5 u1

u2 u3

t1 t2 t3 t4

r1r2

r3

r4r5

t1t2

t3t4

UR UTRT

t1 t2 t3 t4

t1t2

t3t4

Figure 1 A process to obtain 2-mode networks and 1-mode networks

On the basis of the similarity network evaluation (SNE)and comparison with the recallprecision it is indicated thatthe results from the two assessment methods are consistentbut the SNE is more simple visualized and effective with lesssteps

2 Multiangle Social NetworkRecommendation Algorithm (MSN)

21 Pretreatment of Social Network The triple (119880 119877 119879) rep-resents the raw data which means the user 119880 is given the tag119879 on the resource 119877 From this triple one can deduce three2-mode networks such as 119880119877 119879119877 and 119880119879 Each 2-modenetwork can deduce two 1-mode networks For instance 119880119877can infer two 1-mode networks119880119877 and 119877119880 119877119879 infers 1-modenetworks 119877119879 and 119879119877 and 119880119879 infers 1-mode networks 119880119879and 119879119880 (see Figure 1) In the present paper the symbol of 1198601015840denotes the transpose of 119860

The matrix 119880119877 shows the membership of each pair ofusers who like the common resources described by 119880119877 =119880119877lowast119880119877

1015840 The matrix 119877119880 represents the membership of eachpair of resources which have the common users described

by 119877119880 = 1198801198771015840 lowast 119880119877 The matrix 119877119879 is the membership ofeach pair of resources which have the same tags describedby 119877119879 = 119877119879 lowast 1198771198791015840 The matrix 119879119877 indicates the membershipof each pair of tags which have the common resources with119879

119877= 119877119879

1015840lowast 119877119879 The matrix 119880119879 means the membership of

each pair of users who annotate the common tags with119880119879 =119880119879lowast119880119879

1015840Thematrix119879119880 shows themembership of each pairof tags which have the common users with 119879119880 = 1198801198791015840 lowast 119880119879

22 User-Based Social Network Algorithm (USN) There aretwo steps of theUSN algorithm firstly to find other users whoare similar to the target user and then recommend the otherusersrsquo favorite resources to the target user The algorithm canbe divided into the two algorithms UBR and UBT

(1) User-Based Algorithm from Resource Perspective (User-Based Resources UBR) The user similarity from resource(USR) perspective means that if two users like the sameresources they are similar The element of the USR denotedby usr

119894119895is defined as

usr119894119895=

119906

119894119895

119906

119894119894+ 119906

119895119895minus 119906

119894119895

119906

119894119895isin 119880

119877 (1)



UBR = 1198801198771015840 lowast USR (2)



ust119894119895=

119906

119894119895

119906

119894119894+ 119906

119895119895minus 119906

119894119895

119906

119894119895isin 119880

119879 (3)


UBT = 1198801198771015840 lowast UST (4)




rsu119894119895=

119903

119894119895

119903

119894119894+ 119903

119895119895minus 119903

119894119895

119903

119894119895isin 119877

119880 (5)


RBU = RSU lowast 1198801198771015840 (6)


rst119894119895=

119903

119894119895

119903

119894119894+ 119903

119895119895minus 119903

119894119895

119903

119894119895isin 119877

119879 (7)


RBT = RST lowast 1198801198771015840 (8)




tsr119894119895=

119905

119894119895

119905

119894119894+ 119905

119895119895minus 119905

119894119895

119905

119894119895isin 119879

119877 (9)




tsu119894119895=

119905

119894119895

119905

119894119894+ 119905

119895119895minus 119905

119894119895

119905

119894119895isin 119879

119880 (11)




31 Basic Concepts


119894119895 defined by

119888

119894119895=

119904

119894119895 119894 gt 119895 119904

119894119895ge 119879 0 le 119879 le 1

0 119894 le 119895

(13)


119894119895isin














Training set

Similarity matrices

Interest matrices

Recallprecision

Preprocess the


(1) (2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Datasets



Evaluation(1)

(2)

Datasets





























10 20 30 40 50 60 70 80 90 100

Recall


N

()

5

10

15

20

25

(a) Recall

10 20 30 40 50 60 70 80 90 100

Precision


N

05

10

15

20

25

30

()

(b) Precision




















119879 = 1















References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











UBR = 1198801198771015840 lowast USR (2)



ust119894119895=

119906

119894119895

119906

119894119894+ 119906

119895119895minus 119906

119894119895

119906

119894119895isin 119880

119879 (3)


UBT = 1198801198771015840 lowast UST (4)




rsu119894119895=

119903

119894119895

119903

119894119894+ 119903

119895119895minus 119903

119894119895

119903

119894119895isin 119877

119880 (5)


RBU = RSU lowast 1198801198771015840 (6)


rst119894119895=

119903

119894119895

119903

119894119894+ 119903

119895119895minus 119903

119894119895

119903

119894119895isin 119877

119879 (7)


RBT = RST lowast 1198801198771015840 (8)




tsr119894119895=

119905

119894119895

119905

119894119894+ 119905

119895119895minus 119905

119894119895

119905

119894119895isin 119879

119877 (9)




tsu119894119895=

119905

119894119895

119905

119894119894+ 119905

119895119895minus 119905

119894119895

119905

119894119895isin 119879

119880 (11)




31 Basic Concepts


119894119895 defined by

119888

119894119895=

119904

119894119895 119894 gt 119895 119904

119894119895ge 119879 0 le 119879 le 1

0 119894 le 119895

(13)


119894119895isin














Training set

Similarity matrices

Interest matrices

Recallprecision

Preprocess the


(1) (2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Datasets



Evaluation(1)

(2)

Datasets





























10 20 30 40 50 60 70 80 90 100

Recall


N

()

5

10

15

20

25

(a) Recall

10 20 30 40 50 60 70 80 90 100

Precision


N

05

10

15

20

25

30

()

(b) Precision




















119879 = 1















References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Training set

Similarity matrices

Interest matrices

Recallprecision

Preprocess the


(1) (2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Datasets



Evaluation(1)

(2)

Datasets





























10 20 30 40 50 60 70 80 90 100

Recall


N

()

5

10

15

20

25

(a) Recall

10 20 30 40 50 60 70 80 90 100

Precision


N

05

10

15

20

25

30

()

(b) Precision




















119879 = 1















References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















10 20 30 40 50 60 70 80 90 100

Recall


N

()

5

10

15

20

25

(a) Recall

10 20 30 40 50 60 70 80 90 100

Precision


N

05

10

15

20

25

30

()

(b) Precision




















119879 = 1















References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














119879 = 1















References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Multiangle Social Network Recommendation Algorithms and Similarity ... · 2019. 7....

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Transcript of Research Article Multiangle Social Network Recommendation Algorithms and Similarity ... · 2019. 7....