Probability Matrix Decomposition Based Collaborative Filtering Recommendation Algorithm

Transcription

1 Informatca 4 ( Probablty Matrx Decomposton Based Collaboratve Flterng Recommendaton Algorthm Yl Tan and Hujuan Zhao Department of Statstcs, College of Scence, North Chna Unversty of Scence and Technology, Hebe, 06310, Chna E-mal: tangyl_tyl@163.com Yourong Wang Department of Basc, Tangshan College, Hebe, , Chna Mn Qu Publc Mathematcs Department, Hube Unversty of Automotve Technology, Hube, 4400, Chna Techncal Paper Keywords: probablty matrx, collaboratve flterng, recommendaton algorthm Receved: Aprl 8, 018 Wth the development of the socety, the ncreased amount of nformaton has extensvely appeared on the Internet. It ncludes almost all the content we need. But nformaton overload makes people unable to correctly fnd the nformaton they need. Collaboratve flterng recommendaton algorthm can recommend tems for users accordng to ther demands. But tradtonal recommendaton algorthm whch has defects such as data sparsty needs to be mproved. In ths study, the collaboratve flterng recommendaton algorthm was analyzed, an mproved collaboratve flterng recommendaton algorthm based on the probablty matrx was put forward, and the feasblty of the algorthm was verfed. Moreover the tradtonal algorthms ncludng user based collaboratve flterng algorthm, tem based collaboratve flterng algorthm, sngular value based collaboratve flterng algorthm and basc matrx based collaboratve flterng algorthm were tested. The test results demonstrated that the proposed algorthm had a hgher accuracy compared to the tradtonal algorthms, and ts mean absolute error and root-mean-square error were sgnfcantly smaller than those of the tradtonal algorthms. Therefore t can be appled n the daly lfe. Povzetek: V sestavku je predstavljena dekompozcja verjetnostne matrke s prporočlnm algortmom na osnov skupnskega fltrranja. 1 Introducton He ncreased amount of nformaton whch appeared due to the development of Internet technology ncreases the dffculty of fndng the target nformaton. Therefore, many recommendaton algorthms were proposed. Such recommendaton algorthms can flter nformaton accordng to the personal preference; hence they have been unversally appled n felds such as web browsng, flm recommendaton and e-commerce [1]. L [] analyzed the sales records n the current tea leaves sales system by combnng Hadoop dstrbuted system wth the tradtonal collaboratve flterng algorthm to obtan the recommendaton rules whch could satsfy the preference of customer and help users fnd the tea leaves they needed. Yu et al. [3] proposed the weghed cloud model attrbutes based servce cluster algorthm and calculated the user score smlarty usng the weghed Pearson correlaton coeffcent method of servce cluster algorthm and the user servce selecton ndex weght. They found that the algorthm could accurately calculate servce recommendaton credblty, satsfyng the demands of users on servce credblty, and enhance the success rate of the user servce selecton. The collaboratve flterng algorthm has hgh degree of ndvdualzaton and automaton, but t exhbts a few problems such as sparsty and system extensblty. Therefore, n ths study a probablty matrx based collaboratve flterng algorthm was put forward to correct up the defects of the tradtonal collaboratve flterng algorthm and performed smulaton experments. The expermental results suggested that the mean absolute error (MAE, the root-mean-square error (RMSE and the accuracy of the algorthm could reach the expected levels. Ths work provdes a reference for the applcaton of probablty matrx based collaboratve flterng recommendaton algorthm n the searchng of Internet nformaton. Collaboratve flterng recommendaton algorthm.1 Collaboratve flterng algorthms based on dfferent elements

2 66 Informatca 4 ( Y. Tan et al..1.1 Collaboratve flterng algorthm based on users User based collaboratve flterng algorthm focuses on users. It recommends usng user-tem score matrx. It frstly searches for users whch are smlar to the target users and then recommends the selecton of the searched users to the target users. The algorthm has two functons,.e. one for calculatng the smlarty between adjacent users to establsh matrx and one for recommendng the target users usng algorthm evaluaton method..1. Collaboratve flterng algorthm based on tems Item based collaboratve flterng algorthm can provde recommendatons to users based on evaluaton data after establshng user-tem evaluaton data model. In detals, t calculates the smlarty between dfferent tems to determne the preference of target users and then recommends smlar tems to target users. The algorthm has functons for calculatng the smlarty between tems, establshng smlarty matrx and recommendng target users by scorng smlar tems usng algorthm evaluaton method.. Collaboratve recommendaton algorthm based on probablty matrx The probablty matrx can reflect the nformaton of users and tems to low-dmensonal characterstc space n the aspect of probablty and then analyze the concerns of uses about tems usng the lnear combnaton of low-dmensonal vectors [4]. Item score matrx could be expressed as matrx M F j ; a M a whose mean value was 0 and varance was Na j and a random number matrx whose mean N value and varance were 0 and respectvely were produced by MATLAB [5], n whch a refers to the dmenson of, M a refers to a- dmensonal characterstc square matrx of users, and Na j refers to the a-dmensonal characterstc square matrx of tem. Vector M m and n were the correspondng potental characterstc vectors. In general, T T FM a Na j M a Na jf. The matrx was obtaned through the learnng of machne tranng. Suppose the mean value of the error between actual score Fmn and predcted score F mn as 0 and the varable of as Gaussan dstrbuton of F, then T the probablty dstrbuton s q( Fmn MmNn 0, F. q( F T mn MmNn, F was obtaned through translaton. Then the condton of the score matrx F was: Fmn and F mn N, (1 T (,, F ( mn m n, F mn m1 n1 q F M N K F M N I Where I mn stands for ndcator functon, 0 Imn 1 means user m has scored tem n, and means user m has not scored tem n. As M and N could not nclude each other, the mean value of M and N was 0, and dstrbuton, then M I and ( M ( m 0, M m1 Q M K M I ( N ( n 0, N n1 Q N K N I mn N had Gaussan, (, (3 Where Q stands for probablty. The jont probablty dstrbuton of M and N can be obtaned from equaton (1, ( and (3. q M N F (,, F, M, N j T K( Fmn M mn, F Imn K( M m 0, M I K( Nn 0, NI m1 n1 m1 n1 (4 The logarthm of the probablty dstrbuton of M and N was calculated: ln q( M, N F,,, F M N j T T T ( Imn Fmn M mnn M mnn un Nn F m1 n1 M m1 N n1. (5 The maxmum soluton of equaton (5 was replaced wth the mnmum soluton of error functon contanng normalzaton parameters [6]: j 1 T M N Lmn Imn( Fmn M mn n ( M m Nn m1 n1 m1 n1, (6 F F M N Where M and N. As M N, then target functon was: j 1 T Lmn Imn( Fmn M mnn ( M m Nn m1 n1 m1 n1 (7 The relatonshp between regularzaton parameter and F, M, N can be obtaned from the equaton (7. The algorthm calculated functon usng stochastc gradent descent method [7]. It could obtan the declne drecton of numercal values usng dervatves and then calculate varables constantly on ths drecton untl the mnmal pont was obtaned. The soluton of the pont suggested that the updatng formulas of Mm, Nn were transformed to the followng formulas n each teraton: T lfmn M mnn, (8 MmM m( lnnm m, (9 NnNn( lm mnn, (10

3 Probablty Matrx Decomposton Based Informatca 4 ( Where stands for the learnng rate of the stochastc gradent descent. 3 Experment 3.1 Expermental data A 100k data set orgnated from the moves provded by GroupLens project team from Unversty of Mnnesota were used n the experment, denoted as data set A. Data set A ncluded 100,000 scores for 1,68 move tems gven by 943 users. Each user scored 0 move tems at least. The score was an nteger between 0 and 5. The more the user lked the move the hgher was the score. The sparseness of the data set A suggested the percentage of the move tems whch were not scored by the users,.e ,000/( The 100,000 scores n data set A were randomly dvded nto two dsjont sets, the tranng and the testng set. The tranng set whch ncluded 80% of the data was expressed as S1, whle the testng set whch ncluded 0% of the data was expressed as S. The data set A was dvded 10 tmes to perform cross valdaton on the algorthm. To enhance the recommendaton effcency of the algorthm, batch processng module was added. The scores were dvded nto 10 batches scores were processed every tme. Ths way, the computatonal quantty of the system and the convergence nstablty of the model produced n calculaton could be reduced. The collaboratve flterng recommendaton algorthm based on probablty matrx performed as follows. Input: tranng set and testng set Output: Predcted score and square root error Data such as regularzaton parameter were set The number of moves and users were set. If the teraton epoch < max epoch, then the scores were dvded nto 10 groups, 10,000 n each group, for separate processng. If the patch processng was lower than 10, then the loss functon q was calculated, and then matrx calculaton was performed. End The predcted scores n the testng set were revsed to postve ntegers through roundng off, and then square root error was calculated. End 3. Scorng crtera 3..1 MAE The MAE measure ncluded the calculaton of the absolute and average values of the dfference between a predcted score and a real score [8]; hence t could be used for detectng the average dfference between a predcted score and a real score. The smaller the value of MAE was, the more accurate the algorthm was. 1 MAE em and kn dek xek c, (11 where stands for the predcted score of the user e on tem k, d ek x ek stands for the real score of the user e on the tem k, set M and N stand for the sets of users and tems n the testng set, and c stands for the number of or. 3.. Root-mean-square error Root-mean-square error refers to the average value of quadratc sum of the error between the two scores. The smaller the root-mean-square error was, the more accurate the predcton was [9]. 1, (1 RMSE em and kn ( dek xek c where stands for the predcted score of the user e on tem k, d ek x ek d ek x ek stands for the real score of user the e on tem k, set M and N stand for the sets of users and tems n the testng set, and c stands for the number of or x ek. 3.. Accuracy Accuracy could be expressed as: X, (13 Accuracy R Where X d ek dek xek,.e. set X was the set of the predcted scores whch were equal to the real scores n the testng set, dek D (D was the set of the predcted scores, and xek R (R was the set of the real scores. Both, the corrected probablty of an tem and the predcton accuracy, could be recommended to users. 3.3 Desgn of experment The specfc content of the experment was as follows. To analyze the applcaton performance of probablty matrx based collaboratve flterng algorthm n the expermental aspect, the move evaluaton mentoned n the precedng text was taken as the data set, and the user based collaboratve flterng algorthm, the tem based collaboratve flterng algorthm and the probablty matrx based collaboratve flterng algorthm were compared. To better analyze the applcaton performance of the probablty matrx based collaboratve flterng algorthm, the other two algorthms,.e. the basc matrx based collaboratve flterng algorthm and the sngular value based collaboratve flterng algorthm, were also tested. The parameter settng of the algorthms s shown n Table 1. The user based collaboratve flterng algorthm and the tem based collaboratve flterng algorthm were tested sx tmes. The algorthm tself corresponds to the sx characterstc factor numbers (dmenson k of the probablty matrx collaboratve flterng algorthm and the sngular value based collaboratve flterng algorthm. The basc matrx d ek

4 68 Informatca 4 ( Y. Tan et al. Algorthm Neghbourhood or model Characterstc factor number (dmenson k User based collaboratve flterng algorthm Item based collaboratve flterng algorthm Probablty matrx collaboratve flterng algorthm Neghbourhood Neghbourhood Probablty matrx collaboratve flterng model Basc matrx collaboratve flterng algorthm Basc matrx collaboratve flterng model \ \ [10,60] [10,60] 6 Learnng rate \ \ \ Table 1: The parameter settng of the fve algorthms. Sngular value based collaboratve flterng algorthm Sngular value based collaboratve flterng model collaboratve flterng algorthm and the sngular value based collaboratve flterng algorthm used n the performance comparson were developed by referrng to the relevant lterature and revsed accordng to the data whch needed to be detected. The characterstc factor number of sngular value based collaboratve flterng algorthm was fxed, 6. The settng of characterstc factor number of the basc matrx collaboratve flterng algorthm was the same as the probablty matrx collaboratve flterng algorthm, [10, 60], and the unt steppng was set to10. 4 Expermental results and analyss 4.1 MAE and RMSE It could be noted from the Fgure 1 and that the predctve recommendaton performance of the user based collaboratve flterng algorthm was the poorest, and the predcton performance of the sngular value based collaboratve flterng algorthm was not affected by characterstc factor number, but was poorer than that of the user based collaboratve flterng algorthm. The performance of the user based collaboratve flterng algorthm was far worse than that of the probablty matrx collaboratve flterng algorthm and the basc matrx based collaboratve flterng algorthm. The performance of the probablty matrx collaboratve flterng algorthm and the basc matrx based collaboratve flterng algorthm was smlar, but the probablty matrx collaboratve flterng algorthm was stll superor. The reason why there was a sgnfcant dfference between the performance of the user based collaboratve flterng algorthm and the tem based collaboratve flterng algorthm s the score gven by a scorer was probably affected by the vew of other scorers who had the same nterests. The reason why the performance of the sngular value based collaboratve flterng algorthm n the predcton and recommendaton was sgnfcantly poorer than that of the basc matrx collaboratve flterng algorthm and the probablty matrx collaboratve flterng algorthm was the fact that the sngular value based collaboratve flterng algorthm was actually an mproved verson of the tem based collaboratve flterng algorthm and therefore had smlar shortcomngs as the orgnal algorthm,.e., the matrx obtaned after the preprocessng had data dstorton compared to the orgnal matrx, whch could have affected the accuracy and the smlarty of the score predcton. But the performance of the sngular value based collaboratve flterng algorthm was better than of the tem based collaboratve flterng algorthm, ndcatng the mproved accuracy of the sngular value based collaboratve flterng algorthm. It could be noted from the Fgure 1 that the values of the root-mean-square error (RMSE correspondng to the basc matrx based collaboratve flterng algorthm and the probablty matrx collaboratve flterng algorthm gradually decreased wth the ncrease of the characterstc factor number; the larger the characterstc factor number, the smaller the decrease ampltude. When the characterstc factor number was 50, the value of RMSE was the mnmum, and the predcton accuracy was the hghest; when the characterstc factor number was between 10 and 0, the decrease ampltude of RMSE of the basc matrx based collaboratve flterng algorthm and the probablty matrx collaboratve flterng algorthm was large, around 1.14% and 0.700% respectvely. It was found that the values of the RMSE of the two algorthms were lowly senstve to the characterstc factor number, especally of the probablty matrx collaboratve flterng algorthm. When the characterstc factor number was larger than 40, the fluctuaton of the RMSE was qute small. Smlar to Fgure 1, the MAE correspondng to the basc matrx based collaboratve flterng algorthm and

5 Probablty Matrx Decomposton Based Informatca 4 ( the probablty matrx based collaboratve flterng algorthm also decreased wth the ncrease of the characterstc factor number and reached the mnmum values, and respectvely, when the characterstc factor number was 60. Moreover t was noted that when MAE was taken as the evaluaton ndex, the curves of the basc matrx collaboratve flterng algorthm and the probablty matrx based collaboratve flterng algorthm nearly concded, and the predcton performance was also close. Moreover, snce the RMSE s more senstve to the measurement error, the probablty matrx based collaboratve flterng algorthm had an advantage over the basc matrx collaboratve flterng algorthm due to the addton of the regularzaton term. Fgure 1: Varaton of the RMSE of the fve algorthms wth the ncrease of the characterstc factor number. Fgure : Varaton of the MAE of the fve algorthms wth the ncrease of the characterstc factor number. 4. Accuracy It was found from the comparson of the RMSE and the MAE between the fve algorthms that the predcton performance of the CF-User, the tem based collaboratve flterng algorthm and the sngular value based collaboratve flterng algorthm was sgnfcantly dfferent from the basc matrx based collaboratve flterng algorthm and the probablty matrx based collaboratve flterng algorthm. Therefore, only the accuracy of the basc matrx based collaboratve flterng algorthm and the probablty matrx based collaboratve flterng algorthm were consdered. The results are shown n Table. It could be noted from Fgure 3 that the tendency of the accuracy of the basc matrx collaboratve flterng algorthm and the probablty matrx based collaboratve flterng algorthm was opposte to the tendences of the MAE and the RMSE. When the characterstc factor number was small, the accuracy was low; the accuracy ncreased frst and then tended to be stable wth the ncrease of the characterstc factor number Characterstc factor number PMF BMF Fgure 3: The accuracy of the basc matrx based collaboratve flterng algorthm and the probablty matrx based collaboratve flterng algorthm under dfferent characterstc factor numbers.

6 70 Informatca 4 ( Y. Tan et al. and nearly had no fluctuaton when the characterstc factor number was larger than 30. It was because the effectve nformaton ncreased wth the ncrease of the characterstc factor number. The accuracy of the probablty matrx based collaboratve flterng algorthm was much hgher than that of the basc matrx based collaboratve flterng algorthm. Therefore the proposed algorthm could mprove the searchng speed and precseness. Fgure 4: Comparson of the accuracy of the probablty matrx based collaboratve flterng algorthm (PMF and the basc matrx based collaboratve flterng algorthm (BMF. The recommendaton system whch can flter dversfed data s an effectve flterng approach [10]. It can recommend ndvdual nformaton to users accordng to users requrements. Therefore t can be convenent for nformaton collecton and has been extensvely appled on the Internet. We et al. [11] put forward project category smlarty and nterestngness measure based collaboratve flterng recommendaton algorthm whch could recommend nformaton to users through calculatng project categores and nterestngness and had hgh predcton precseness. In a study of Chen et al. [1], a mxed recommendaton system was put forward to recommend users wth learnng projects searchng. In the test, the algorthm effectvely collected nformaton, suggestng a favorable performance. 5 Concluson In concluson, the probablty matrx based collaboratve recommendaton algorthm was put forward n ths study, and then t was developed for data searchng recommendaton. Afterwards the MAE, the RMSE and the accuracy of the algorthm were tested. Moreover the MAE values, the RMSE values and the accuracy of the CF-User, the tem based collaboratve flterng algorthm, the sngular value based collaboratve flterng algorthm and the basc matrx based collaboratve flterng algorthm were compared. The testng results suggested that the mproved collaboratve recommendaton algorthm had the hghest precseness and accuracy, and the precseness and the accuracy became the largest and stable when the characterstc factor number was more than 40. Therefore t could be appled n a computer searchng system. Ths work provdes a reference for the progress of the collaboratve recommendaton algorthm. 6 Acknowledgement Ths study was supported by the Fund of Natural Scence of Hebe (A References [1] Wang W, Wu YH, Wu YY. (016. A Mult-stage Heurstc Algorthm for Matchng Problem n the Modfed Mnload Automated Storage and Retreval System of E-commerce. Chnese Journal of Mechancal Engneerng, 9(3:1-8. [] L L. (017. Analytcal Applcaton of Hadoop- Based Collaboratve Flterng Recommended Algorthm n Tea Sales System. Internatonal Conference on Applcatons and Technques n Cyber Securty and Intellgence. Edzon della Normale, Cham, [3] Yu Z Y, Wang J D, Zhang H W, Nu K. (016. Servces recommended trust algorthm based on cloud model attrbutes weghted clusterng. Automatc Control & Computer Scences, 50(4: [4] Zhang F, Yang J, Ta Y, Tang J. (015. Double Nuclear Norm Based Matrx Decomposton For Occluded Image Recovery and Background Modelng. IEEE Trans Image Process, 4(6: [5] Smpson R, Deveny G A, Jezzard P, Hennessy TJ, Near J. (017. Advanced processng and smulaton of MRS data usng the FID applance (FID-A-An open source, MATLAB-based toolkt. Magnetc Resonance n Medcne, 77(1:e [6] Ando T, Ba J. (015. Selectng the Regularzaton Parameters n Hgh-dmensonal Panel Data Models: Consstency and Effcency. Econometrc Revews, [7] Wu K, Sun Y, Hua Y, Ja SQ, Chen X, Jn YQ. (015. Mult-perturbaton stochastc parallel gradent descent method for wavefront correcton. Optcs Express, 3(3: [8] Franses P H. (015. A note on the Mean Absolute Scaled Error. Internatonal Journal of Forecastng, 3(1:0-. [9] Nuutnen M, Vrtanen T, Häkknen J. (016. Performance measure of mage and vdeo qualty assessment algorthms: subjectve root-mean-square error. Journal of Electronc Imagng, 5(:0301. [10] Knobelsdorff P M G V, Refersched F, Straakholder T M, Wrtz MS. (004. Wrd der Algorthmus des European Resusctaton Councl zur kardopulmonalen Reanmaton engehalten?. Intensvmedzn Und Notfallmedzn, 41(1:-8. [11] We S, Ye N, Zhang S, Huang X, Zhu J. (01. Item-Based Collaboratve Flterng Recommendaton Algorthm Combnng Item Category wth Interestngness Measure.

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8 7 Informatca 4 ( Y. Tan et al.