Effective Missing Data Prediction for Collaborative Filtering

Transcription

1 Effective Missing Data Pediction fo Collaboative Filteing Hao Ma, Iwin King and Michael R. Lyu Dept. of Compute Science and Engineeing The Chinese Univesity of Hong Kong Shatin, N.T., Hong Kong { hma, king, lyu }@cse.cuhk.edu.hk ABSTRACT Memoy-based collaboative filteing algoithms have been widely adopted in many popula ecommende systems, although these appoaches all suffe fom data spasity and poo pediction quality poblems. Usually, the use-item matix is quite spase, which diectly leads to inaccuate ecommendations. This pape focuses the memoy-based collaboative filteing poblems on two cucial factos: (1) similaity computation between uses o items and (2) missing data pediction algoithms. Fist, we use the enhanced Peason Coelation Coefficient (PCC) algoithm by adding one paamete which ovecomes the potential decease of accuacy when computing the similaity of uses o items. Second, we popose an effective missing data pediction algoithm, in which infomation of both uses and items is taken into account. In this algoithm, we set the similaity theshold fo uses and items espectively, and the pediction algoithm will detemine whethe pedicting the missing data o not. We also addess how to pedict the missing data by employing a combination of use and item infomation. Finally, empiical studies on dataset MovieLens have shown that ou newly poposed method outpefoms othe stateof-the-at collaboative filteing algoithms and it is moe obust against data spasity. Categoies and Subject Desciptos: H.3.3 [Infomation Systems]: Infomation Seach and Retieval - Infomation Filteing Geneal Tems: Algoithm, Pefomance, Expeimentation. Keywods: Collaboative Filteing, Recommende System, Data Pediction, Data Spasity. 1. INTRODUCTION Collaboative filteing is the method which automatically pedicts the inteest of an active use by collecting ating infomation fom othe simila uses o items, and elated techniques have been widely employed in some lage, fa- Pemission to make digital o had copies of all o pat of this wok fo pesonal o classoom use is ganted without fee povided that copies ae not made o distibuted fo pofit o commecial advantage and that copies bea this notice and the full citation on the fist page. To copy othewise, to epublish, to post on seves o to edistibute to lists, equies pio specific pemission and/o a fee. SIGIR 07, July 23 27, 2007, Amstedam, The Nethelands. Copyight 2007 ACM /07/ $5.00. mous commecial systems, such as Amazon 1,Ebay 2. The undelying assumption of collaboative filteing is that the active use will pefe those items which the simila uses pefe. The eseach of collaboative filteing stated fom memoy-based appoaches which utilize the entie use-item database to geneate a pediction based on use o item similaity. Two types of memoy-based methods have been studied: use-based [2, 7, 10, 22] and item-based [5, 12, 17]. Use-based methods fist look fo some simila uses who have simila ating styles with the active use and then employ the atings fom those simila uses to pedict the atings fo the active use. Item-based methods shae the same idea with use-based methods. The only diffeence is use-based methods ty to find the simila uses fo an active use but item-based methods ty to find the simila items fo each item. Whethe in use-based appoaches o in item-based appoaches, the computation of similaity between uses o items is a vey citical step. Notable similaity computation algoithms include Peason Coelation Coefficient (PCC) [16] and Vecto Space Similaity (VSS) algoithm [2]. Although memoy-based appoaches have been widely used in ecommendation systems [12, 16], the poblem of inaccuate ecommendation esults still exists in both use-based and item-based appoaches. The fundamental poblem of memoy-based appoaches is the data spasity of the useitem matix. Many ecent algoithms have been poposed to alleviate the data spasity poblem. In [21], Wang et al. poposed a geneative pobabilistic famewok to exploit moe of the data available in the use-item matix by fusing all atings with a pedictive value fo a ecommendation to be made. Xue et al. [22] poposed a famewok fo collaboative filteing which combines the stengths of memoybased appoaches and model-based appoaches by intoducing a smoothing-based method, and solved the data spasity poblem by pedicting all the missing data in a use-item matix. Although the simulation showed that this appoach can achieve bette pefomance than othe collaboative filteing algoithms, the cluste-based smoothing algoithm limited the divesity of uses in each cluste and pedicting all the missing data in the use-item matix could bing negative influence fo the ecommendation of active uses. In this pape, we fist use PCC-based significance weighting to compute similaity between uses and items, which ovecomes the potential decease of similaity accuacy. Second, we popose an effective missing data pediction algo

2 ithm which exploits the infomation both fom uses and items. Moeove, this algoithm will pedict the missing data of a use-item matix if and only if we think it will bing positive influence fo the ecommendation of active uses instead of pedicting evey missing data of the use-item matix. The simulation shows ou novel appoach achieves bette pefomance than othe state-of-the-at collaboative filteing appoaches. The emainde of this pape is oganized as follows. In Section 2, we povide an oveview of seveal majo appoaches fo collaboative filteing. Section 3 shows the method of similaity computation. The famewok of ou missing data pediction and collaboative filteing is intoduced in Section 4. The esults of an empiical analysis ae pesented in Section 5, followed by a conclusion in Section RELATED WORK In this section, we eview seveal majo appoaches fo collaboative filteing. Two types of collaboative filteing appoaches ae widely studied: memoy-based and modelbased. 2.1 Memoy-based appoaches The memoy-based appoaches ae the most popula pediction methods and ae widely adopted in commecial collaboative filteing systems [12, 16]. The most analyzed examples of memoy-based collaboative filteing include usebased appoaches [2, 7, 10, 22] and item-based appoaches [5, 12, 17]. Use-based appoaches pedict the atings of active uses based on the atings of simila uses found, and itembased appoaches pedict the atings of active uses based on the infomation of simila items computed. Use-based and item-based appoaches often use PCC algoithm [16] and VSS algoithm [2] as the similaity computation methods. PCC-based collaboative filteing geneally can achieve highe pefomance than the othe popula algoithm VSS, since it consides the diffeences of use ating styles. 2.2 Model-based Appoaches In the model-based appoaches, taining datasets ae used to tain a pedefined model. Examples of model-based appoaches include clusteing models [11, 20, 22], aspect models [8, 9, 19] and latent facto model [3]. [11] pesented an algoithm fo collaboative filteing based on hieachical clusteing, which tied to balance obustness and accuacy of pedictions, especially when little data wee available. Authos in [8] poposed an algoithm based on a genealization of pobabilistic latent semantic analysis to continuousvalued esponse vaiables. The model-based appoaches ae often time-consuming to build and update, and cannot cove as divese a use ange as the memoy-based appoaches do [22]. 2.3 Othe Related Appoaches In ode to take the advantages of memoy-based and model-based appoaches, hybid collaboative filteing methods have been studied ecently [14, 22]. [1, 4] unified collaboative filteing and content-based filteing, which achieved significant impovements ove the standad appoaches. At the same time, in ode to solve the data spasity poblem, eseaches poposed dimensionality eduction appoaches in [15]. The dimensionality-eduction appoach addessed the spasity poblem by deleting unelated o insignificant uses o items, which would discad some infomation of the use-item matix. 3. SIMILARITY COMPUTATION This section biefly intoduces the similaity computation methods in taditional use-based and item-based collaboative filteing [2, 5, 7, 17] as well as the method poposed in this pape. Given a ecommendation system consists of M uses and N items, the elationship between uses and items is denoted by an M N matix, called the use-item matix. Evey enty in this matix m,n epesents the scoe value,, thatusem ates an item n, whee {1, 2,..., max}. If use m does not ate the item n, then m,n = Peason Coelation Coefficient Use-based collaboative filteing engaging PCC was used in a numbe of ecommendation systems [18], since it can be easily implemented and can achieve high accuacy when compaing with othe similaity computation methods. In use-based collaboative filteing, PCC is employed to define the similaity between two uses a and u basedontheitems they ated in common: Sim(a, u) = i I(a) I(u) i I(a) I(u) ( a,i a) ( u,i u) ( a,i a) 2 i I(a) I(u) ( u,i u) 2, (1) whee Sim(a, u) denotes the similaity between use a and use u, andi belongs to the subset of items which use a and use u both ated. a,i is the ate use a gave item i, and a epesents the aveage ate of use a. Fom this definition, use similaity Sim(a, u) is anging fom [0, 1], and a lage value means uses a and u ae moe simila. Item-based methods such as [5, 17] ae simila to usebased appoaches, and the diffeence is that item-based methods employ the similaity between the items instead of uses. The basic idea in similaity computation between two items i and j is to fist isolate the uses who have ated both of these items and then apply a similaity computation technique to detemine the similaity Sim(i, j) [17]. The PCCbased similaity computation between two items i and j can be descibed as: ( u,i i) ( u,j j) Sim(i, j) = u U(i) U(j) u U(i) U(j) ( u,i i) 2 u U(i) U(j) ( u,j j) 2, (2) whee Sim(i, j) is the similaity between item i and item j, and u belongs to the subset of uses who both ated item i and item j. u,i is the ate use u gave item i, and i epesents the aveage ate of item i. Like use similaity, item similaity Sim(i, j) is also anging fom [0, 1]. 3.2 Significance Weighting PCC-based collaboative filteing geneally can achieve highe pefomance than othe popula algoithms like VSS [2], since it consides the facto of the diffeences of use ating styles. Howeve PCC will oveestimate the similaities of uses who happen to have ated a few items identically, but may not have simila oveall pefeences [13]. Helocke et 40

3 al. [6, 7] poposed to add a coelation significance weighting facto that would devalue similaity weights that wee based on a small numbe of co-ated items. Helocke s latest eseach wok [13] poposed to use the following modified similaity computation equation: Sim Max( Ia Iu,γ) (a, u) = Sim(a, u). (3) γ This equation ovecomes the poblem when only few items ae ated in common but in case that when I a I u is much highe than γ, the similaity Sim (a, u) will be lage than 1, and even supass 2 o 3 in wose cases. We use the following equation to solve this poblem: Sim Min( Ia Iu,γ) (a, u) = Sim(a, u), (4) γ whee I a I u is the numbe of items which use a and use u ated in common. This change bounds the similaity Sim (a, u) to the inteval [0, 1]. Then the similaity between items could be defined as: Sim Min( Ui Uj,δ) (i, j) = Sim(i, j), (5) δ whee U i U j is the numbe of uses who ated both item i and item j. 4. COLLABORATIVE FILTERING FRAMEWORK In patice, the use-item matix of commecial ecommendation system is vey spase and the density of available atings is often less than 1% [17]. Spase matix diectly leads to the pediction inaccuacy in taditional use-based o item-based collaboative filteing. Some wok applies data smoothing methods to fill the missing values of the use-item matix. In [22], Xue et al. poposed a clustebased smoothing method which clustes the uses using K- means fist, and then pedicts all the missing data based on the atings of Top-N most simila uses in the simila clustes. The simulation shows this method could geneate bette esults than othe collaboative filteing algoithms. But cluste-based method limits the divesity of uses in each cluste, and the clusteing esults of K-means elies on the pe-selected K uses. Futhemoe, if a use does not have enough simila uses, then Top-N algoithm geneates a lot of dissimila uses which definitely will decease the pediction accuacy of the active uses. Accoding to the analysis above, we popose a novel effective missing data pediction algoithm which pedicts the missing data when it fits the citeia we set. Othewise, we will not pedict the missing data and keep the value of the missing data to be zeo. As illustated in Fig. 1(a), befoe we pedict the missing data, the use-item matix is a vey spase matix and evey use only ates few items with u,i; at the same time, othe unated data ae coveed with shade. Using this spase matix to pedict atings fo active uses always esults in giving bad ecommendations to the active uses. In ou appoach, we evaluate evey shaded block (missing data) using the available infomation in Fig. 1(a). Fo evey shaded block, if ou algoithm achieves confidence in the pediction, then we give this shaded block a pedicted ating value u,i. Othewise, we set the value of this missing data to zeo, as seen in Fig. 1(b). Accodingly, the collaboative filteing is simplified into two simple questions. The fist is Unde what cicumstance does ou algoithm have confidence to pedict the shaded block? and the second is How to pedict?. The following subsections will answe these two questions. 4.1 Simila Neighbos Selection Simila neighbos selection is a vey impotant step in pedicting missing data. If selected neighbos ae dissimila with the cuent use, then the pediction of missing data of this use is inaccuate and will finally affect the pediction esults of the active uses. In ode to ovecome the flaws of Top-N neighbos selection algoithms, we intoduce a theshold η. If the similaity between the neighbo and the cuent use is lage than η, then this neighbo is selected as the simila use. Fo evey missing data u,i, a set of simila uses S(u) towads use u can be geneated accoding to: S(u) ={u a Sim (u a,u) >η,u a u}, (6) whee Sim (u a,u) is computed using Eq. (4). At the same time, fo evey missing data u,i, a set of simila items S(i) towads item i can be geneated accoding to: S(i) ={i k Sim (i k,i) >θ,i k i}, (7) whee θ is the item similaity theshold, and Sim (i k,i)is computed by Eq. (5). The selection of η and θ is an impotant step since a vey big value will always cause the shotage of simila uses o items, and a elative small value will bing too many simila uses o items. Accoding to Eqs.(6) and (7), we define that ou algoithm will lack enough confidence to pedict the missing data u,i if and only if S(u) = S(i) =, which means that use u does not have simila uses and item i does not have simila items eithe. Then ou algoithm sets the value of this missing data to zeo. Othewise, it will pedict the missing data u,i following the algoithm descibed in Subsection Missing Data Pediction Use-based collaboative filteing pedicts the missing data using the atings of simila uses and item-based collaboative filteing pedicts the missing data using the atings of simila items. Actually, although uses have thei own ating style, if an item is a vey popula item and has obtained a vey high aveage ating fom othe uses, then the active use will have a high pobability to give this item a good ating too. Hence, pedicting missing data only using use-based appoaches o only using item-based appoaches will potentially ignoe valuable infomation that will make the pediction moe accuate. We popose to systematically combine use-based and item-based appoaches, and take advantage of use coelations and item coelations in the use-item matix. Given the missing data u,i, accoding to Eq. (6) and Eq. (7), if S(u) S(i), the pediction of missing 41

4 i1 i2 i i i i i i 8 i 9 i n i1 i2 i i i i i i 8 i 9 i n u 1 u 2 1,1 1, 4 2,2 2, 8 u 1 u 2 1,1,3 1, 4 1 1, 6 1, 8 1, 9 2,2 2,4 2, 5 2, 7 2, 8 ˆ2, n u 3 u 4 4,4 3,6 4, n u 3 u 4 3,1 3, 3 3, 4 5 4,1 2 4, 4,4 4, 5 3, 3,6 3, 8 3, 9 4, 6 4, 7 4, 9 4, n u 5 5,3 5, 7 u 5 5,3 5, 5, 7 5,1 5, 2 5 5, 8 5, 9 ˆ5, n u 6 u m m,2 6,9 m, n u 6 u m 6,1 6, 2 6, 4 6, 5 6, 6 6, 7 6,9 ˆm,1 m,2 ˆm, 4 ˆm, 6 ˆm, 8 ˆm, 9 ˆ6, n m, n Figue 1: (a) The use-item matix (m n) befoe missing data pediction. (b) The use-item matix (m n) afte missing data pediction. data P ( u,i) is defined as: Sim (u a,u) ( ua,i u a) P ( u,i) =λ (u + u a S(u) (1 λ) (i + u a S(u) i k S(i) Sim (u a,u) )+ Sim (i k,i) ( u,ik i k ) i k S(i) Sim (i k,i) ), (8) whee λ is the paamete in the ange of [0, 1]. The use of paamete λ allows us to detemine how the pediction elies on use-based pediction and item-based pediction. λ = 1 states that P ( u,i) depends completely upon atings fom use-based pediction and λ = 0 states that P ( u,i) depends completely upon atings fom item-based pediction. In pactice, some uses do not have simila uses and the similaities between these uses and all othe uses ae less than the theshold η. Top-N algoithms will ignoe this poblem and still choose the top n most simila uses to pedict the missing data. This will definitely decease the pediction quality of the missing data. In ode to pedict the missing data as accuate as possible, in case some uses do not have simila uses, we use the infomation of simila items instead of uses to pedict the missing data, and vice vesa, as seen in Eq. (9) and Eq. (10). This consideation inspies us to fully utilize the infomation of use-item matix as follows: If S(u) S(i) =, the pediction of missing data P ( u,i) is defined as: Sim (u a,u) ( ua,i u a) P ( u,i) =u + u a S(u) u a S(u) Sim (u a,u). (9) If S(u) = S(i), the pediction of missing data P ( u,i) is defined as: Sim (i k,i) ( u,ik i k ) P ( u,i) =i + i k S(i) i k S(i) Sim (i k,i). (10) The last possibility is given the missing data u,i, useu does not have simila uses and at the same time, item i also does not have simila items. In this situation, we choose not to pedict the missing data; othewise, it will bing negative influence to the pediction of the missing data u,i. Thatis: If S(u) = S(i) =, the pediction of missing data P ( u,i) is defined as: P ( u,i) =0. (11) This consideation is diffeent fom all othe existing pediction o smoothing methods. They always ty to pedict all the missing data in the use-item matix, which will pedict some missing data with bad quality. 4.3 Pediction fo Active Uses Afte the missing data is pedicted in the use-item matix, the next step is to pedict the atings fo the active uses. The pediction pocess is almost the same as pedicting the missing data, and the only diffeence is in the case fo a given active use a; namely,if S(a) = S(i) =, then pedicts the missing data using the following equation: P ( a,i) =λ a +(1 λ) i. (12) In othe situations, if (1) S(u) S(i), (2)S(u) S(i) = o (3) S(u) = S(i), we use Eq. (8), Eq. (9) and Eq. (10) to pedict a,i, espectively. 4.4 Paamete Discussion The thesholds γ and δ intoduced in Section 3 ae employed to avoid oveestimating the uses similaity and items similaity, when thee ae only few atings in common. If we set γ and δ too high, most of the similaities between uses o items need to be multiplied with the significance weight, and it is not the esults we expect. Howeve, if we set γ and δ too low, it is also not easonable because the oveestimate poblem still exists. Tuning these paametes is impotant to achieving a good pediction esults. The thesholds η and θ intoduced in Section 4.1 also play an impotant ole in ou collaboative filteing algoithm. If η and θ ae set too high, less missing data need to be pedicted; if they ae set too low, a lot of missing data need to be pedicted. In the case when η = 1 and θ =1,ou appoach will not pedict any missing data, and this algoithm becomes the geneal collaboative filteing without data smoothing. In the case when η =0andθ =0,ouappoach will pedict all the missing data, and this algoithm 42

5 Table 1: The elationship between paametes with othe CF appoaches Lambda Eta Theta Related CF Appoaches Use-based CF without missing data pediction Item-based CF without missing data pediction Use-based CF with all the missing data pedicted Item-based CF with all the missing data pedicted conveges to the Top-N neighbos selection algoithms, except the numbe N hee includes all the neighbos. In ode to simplify ou model, we set η = θ in all the simulations. Finally, paamete λ intoduced in Section 4.2 is the last paamete we need to tune, and it is also the most impotant one. λ detemines how closely the ating pediction elies on use infomation o item infomation. As discussed befoe, λ = 1 states that P ( u,i) depends completely upon atings fom use-based pediction and λ = 0 states that P ( u,i) depends completely upon atings fom item-based pediction. This physical intepetation also helps us to tune λ accodingly. With the changes of paametes, seveal othe famous collaboative filteing methods become special cases in ou appoach as illustated in Table EMPIRICAL ANALYSIS We conduct seveal expeiments to measue the ecommendation quality of ou new appoach fo collaboative filteing with othe methods, and addess the expeiments as the following questions: (1) How does ou appoach compae with taditional use-based and item-based collaboative filteing methods? (2) What is the pefomance compaison between ou effective missing data pediction appoach and othe algoithms which pedict evey missing data? (3) How does significance weighting affect the accuacy of pediction? (4) How do the thesholds η and θ affect the accuacy of pediction? How many missing data ae pedicted by ou algoithm, and what is the compaison of ou algoithm with the algoithms that pedict all the missing data o no missing data? (5) How does the paamete λ affect the accuacy of pediction? and (6) How does ou appoach compae with the published state-of-the-at collaboative filteing algoithms? In the following, Section 5.3 gives answes to questions 1 and 6, Section 5.4 addesses question 2, and Section 5.5 descibes expeiment fo the questions 3 to Dataset Two datasets fom movie ating ae applied in ou expeiments: MovieLens 3 and EachMovie 4. We only epot the simulation esults of MovieLens due to the space limitation. Simila esults can be obseved fom the EachMovie application. MovieLens is a famous Web-based eseach ecommende system. It contains 100,000 atings (1-5 scales) ated by 943 uses on 1682 movies, and each use at least ated 20 movies. The density of the use-item matix is: =6.30% It is etied by Hewlett-Packad (HP), but a postpocessed copy can be found on Table 2: Statistics of Dataset MovieLens Statistics Use Item Min. Num. of Ratings 20 1 Max. Num. of Ratings Avg. Num. of Ratings Table 3: compaison with othe appoaches (A smalle value means a bette pefomance). Taining Uses Methods EMDP MovieLens 300 UPCC IPCC EMDP MovieLens 200 UPCC IPCC EMDP MovieLens 100 UPCC IPCC The statistics of dataset MovieLens is summaized in Table 2. We extact a subset of 500 uses fom the dataset, and divide it into two pats: select 300 uses as the taining uses (100, 200, 300 uses espectively), and the est 200 uses as the active (testing) uses. As to the active uses, we vay the numbe of ated items povided by the active uses fom 5, 10, to 20, and give the name, and, espectively. 5.2 Metics We use the Mean Absolute Eo () metics to measue the pediction quality of ou poposed appoach with othe collaboative filteing methods. is defined as: u,i u,i u,i =, (13) N whee u,i denotes the ating that use u gave to item i, and u,i denotes the ating that use u gave to item i which is pedicted by ou appoach, and N denotes the numbe of tested atings. 5.3 Compaison In ode to show the pefomance incease of ou effective missing data pediction (EMDP) algoithm, we compae ou algoithm with some taditional algoithms: use-based algoithm using PCC (UPCC) and item-based algoithm using PCC (IPCC). The paametes o thesholds fo the expeiments ae empiically set as follows: λ =0.7, γ =30,δ =25, η = θ =0.4. In Table 3, we obseve that ou new appoach significantly impoves the ecommendation quality of collaboative filteing, and outpefoms UPCC and IPCC consistently. 43

6 Table 4: compaison with state-of-the-ats algoithms (A smalle value means a bette pefomance). Num. of Taining Uses Ratings Given fo Active Uses EMDP SF SCBPCC AM PD PCC EMDP PEMD EMDP PEMD EMDP PEMD Lambda Figue 2: Compaison of EMDP and PEMD (A smalle value means a bette pefomance). Next, in ode to compae ou appoach with othe stateof-the-ats algoithms, we follow the exact evaluation pocedues which wee descibed in [21, 22] by extacting a subset of 500 uses with moe than 40 atings. Table 4 summaizes ou expeimental esults. We compae with the following algoithms: Similaity Fusion (SF) [21], Smoothing and Cluste-Based PCC (SCBPCC) [22], the Aspect Model (AM) [9], Pesonality Diagnosis (PD) [14] and the use-based PCC [2]. Ou method outpefoms all othe competitive algoithms in vaious configuations. 5.4 Impact of Missing Data Pediction Ou algoithm incopoates the option not to pedict the missing data if it does not meet the citeia set in Section 4.1 and Section 4.2. In addition, it alleviates the potential negative influences fom bad pediction on the missing data. To demonstate the effectiveness of ou appoach, we fist conduct a set of simulations on ou effective missing data pediction appoach. The numbe of taining uses is 300, wheewesetγ = 30, δ = 25, η = θ =0.5, and vay λ fom zeo to one with a step value of We then plot the gaph with the atings of active uses of, and, espectively. As to the method in pedicting evey missing data (PEMD), we use the same algoithm, and keep the configuations the same as EMDP except fo Eq. (11). In PEMD, when S(u) = and S(i) =, we pedict the missing data u,i using the neaest neighbos of the missing data instead of setting the value to zeo. In this expeiment, we set the numbe of neaest neighbos to 10. The intention of this expeiment is to compae the pefomance of ou EMDP algoithm with PEMD unde the same configuations. In othe wods, we intend to detemine the effectiveness of ou missing data pediction algoithm, and whethe ou appoach is bette than the appoach which will pedict evey missing data o not. In Fig. 2, the sta, up tiangle, and diamond in solid line epesent the EMDP algoithm in, and atings espectively, and the cicle, down tiangle, and squae in dashed line epesent the PEMD algoithm in, and atings espectively. All the solid lines ae below the espectively compaative dashed lines, indicating ou effective missing data pediction algoithm pefoms bette than the algoithm which pedict evey missing data, and pedicting missing data selectively is indeed a moe effective method. 5.5 Impact of Paametes γ and δ in Significance Weighting Significance weighting makes the similaity computation moe easonable in pactice and devalues some similaities which look simila but ae actually not, and the simulation esults in Fig. 3 shows the significance weighting will pomote the collaboative filteing pefomance. In this expeiment, we fist evaluate the influence of γ, and select 300 taining uses, then set λ =0.7, η = θ =0.5, δ = 26. We vay the ange of γ fom 0 to 50 with a step value of 2. Fig. 3(a),(b),(c) shows how γ affects when given atings 20, 10, 5 espectively, and Fig. 3(d) shows that the value of γ also impacts the density of the use-item matix in the pocess of missing data pediction. The density of the use-item matix will decease accoding to the incease of the value of γ. Moe expeiments show that δ has the same featues and impacts on and matix density as γ; howeve, we do not include the simulation esults due to the space limitation Impact of λ Paamete λ balances the infomation fom uses and items. It takes advantages fom these two types of collaboative filteing methods. If λ = 1, we only extact infomation fom uses, and if λ = 0, we only mine valuable infomation fom items. In othe cases, we fuse infomation fom uses and items to pedict the missing data and futhemoe, to pedict fo active uses. Fig. 4 shows the impacts of λ on. In this expeiment, we test 300 taining uses, 200 taining uses and 100 taining uses and epot the expeiment esults in Fig. 4(a), Fig. 4(b) and Fig. 4(c) espectively. The initial values of othe paametes o thesholds ae: η = θ =0.5, γ =30, δ =25. 44

7 Density Gamma Gamma Gamma Gamma (a) (b) (c) (d) Figue 3: Impact of Gamma on and Matix Density 4 2 Taining Uses = Taining Uses = Taining Uses = Lambda Lambda Lambda (a) (b) (c) Figue 4: Impact of Lambda on 4 2 Taining Uses = Taining Uses = Taining Uses = (a) (b) (c) Taining Uses = 300 Taining Uses = 200 Taining Uses = Density Density Density (d) (f) (g) Figue 5: Impact of on and Density 45

8 Obseved fom Fig. 4, we daw the conclusion that the value of λ impacts the ecommendation esults significantly, which demonstates that combining the use-based method with the item-based method will geatly impove the ecommendation accuacy. Anothe inteesting obsevation is when following the incease of the numbe of atings given (fom 5 to 10, and fom 10 to 20), the value of ag min λ () of each cuve in Fig. 4 shifts fom 0.3 to smoothly. This implies the infomation fo uses is moe impotant than that fo items if moe atings fo active uses ae given. On the othe hand, the infomation fo items would be moe impotant if less atings fo active uses ae available; howeve, less atings fo active uses will lead to moe inaccuacy of the ecommendation esults Impact of η and θ η and θ also play a vey impotant ole in ou collaboative filteing appoach. As discussed in Section 4, η and θ diectly detemine how many missing data need to be pedicted. If η and θ ae set too high, most of the missing data cannot be pedicted since many uses will not have simila uses, and many items will not have simila items eithe. On the othe hand, if η and θ ae set too low, evey use o item will obtain too many simila uses o items, which causes the computation inaccuacy and inceases the computing cost. Accodingly, selecting pope values fo η and θ is as citical as detemining the value fo λ. In ode to simplify ou model, we set η = θ as employed in ou expeiments. In the next expeiment, we select 500 uses fom Movie- Lens dataset and extact 300 uses fo taining uses and othe 200 as the active uses. The initial values fo evey paamete and theshold ae: λ =0.7, γ = 30, δ = 25. We vay the values of η and θ fom 0 to 1 with a step value of Fo each taining use set (100, 200, 300 uses espectively), we compute the and density of the use-item matix. The esults ae showed in Fig. 5. As showed in Fig. 5(a), given 300 taining uses and given 20 atings fo evey active use, this algoithm will achieve the best pefomance aound η = θ =0.50, and the elated density of use-item matix in Fig. 5(d) is 92.64% which shows that 7.36% missing data of this use-item matix ae not pedicted. In this expeiment, the numbe of data that was not pedicted is = We obseve that aound η = θ =0.70, this algoithm aleady achieves a vey good value which is almost the same as the best values in Fig. 5(b). The elated matix density is 29.00%, which illustates that moe than 70% data of useitem matix ae not pedicted. Nevetheless, the algoithm can aleady achieve satisfactoy pefomance. 6. CONCLUSIONS In this pape, we popose an effective missing data pediction algoithm fo collaboative filteing. By judging whethe a use (an item) has othe simila uses (items), ou appoach detemines whethe to pedict the missing data and how to pedict the missing data by using infomation of uses, items o both. Taditional use-based collaboative filteing and item-based collaboative filteing appoaches ae two subsets of ou new appoach. Empiical analysis shows that ou poposed EMDP algoithm fo collaboative filteing outpefoms othe state-of-the-at collaboative filteing appoaches. Fo futue wok, we plan to conduct moe eseach on the elationship between use infomation and item infomation since ou simulations show the algoithm combining these two kinds of infomation geneates bette pefomance. Lastly, anothe eseach topic wothy of studying is the scalability analysis of ou algoithm. 7. ACKNOWLEDGMENTS We thank M. Shikui Tu, Ms. Tu Zhou and M. Haixuan Yang fo many valuable discussions on this topic. This wok is fully suppoted by two gants fom the Reseach Gants Council of the Hong Kong Special Administative Region, China (Poject No. CUHK4205/04E and Poject No. CUHK4235/04E). 8. REFERENCES [1] J. Basilico and T. Hofmann. Unifying collaboative and content-based filteing. In Poc.ofICML, [2] J. S. Beese, D. 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