Nantonac Collaborative Filtering Recommendation Based on Order Responces. 1 SD Recommender System [23] [26] Collaborative Filtering; CF

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1 Nantonac Collaborative Filtering Recommendation Based on Order Responces (Toshihiro KAMISHIMA) (National Institute of Advanced Industrial Science and Technology (AIST)) Abstract: A recommender system suggests the items expected to be preferred by the users. Recommender systems use collaborative filtering to recommend items by summarizing the preferences of people who have tendencies simliar to the user preference. Traditionally, the degree of preference is represented by a scale, for example, one that ranges from one to five. This type of measuring technique is called the semantic differential (SD) method. We adopted the ranking method, however, rather than the SD method, since the SD method is intrinsically not suited for representing individual preferences. In the ranking method, the preferences are represented by orders, which are sorted item sequences according to the users preferences. We here propose some methods to recommend items based on these order responses, and carry out the comparison experiments of these methods. 1 SD Recommender System [23] [26] Collaborative Filtering; CF CF 2 CF 3 CF 4 5 CF 1.1 Semantic Differential (SD ) [21] SD CF Stevens (scale level) [27] Stevens (nominal) (ordinal) (interval) (ratio) CF [10] 1

2 Central Tendency rator 1.2 Fig. 1: SD [30] J.-C. de Borda M. de Condorcet C. L Dodgson 2 20 K. Arrow Arrow s impossibility Thurstone [28] Semantic Differential (SD) [21] SD A B [19] A B ordinal regression [1] Cohen [3] Herbrich [7] Joachims [8] [20] SD [11] [14] Freund boosting RankBoost [5] CF SD Mannila Meek [18] Sai [24] [12, 13] [25] Lebanon Lafferty [16, 17] SD 1 Dwork [4] 4 [29] Amazon.com 1 Gionis [6] 0/1 2 Lewis Caroll 1 A.S.Weigend KDD2003 2

3 2 SD 2.1 X i Riedl GroupLens [22] i CF O i =x 1 x 2 x Xi i x 1 x 2 DB r(o i, x j ) s ij i x j O i j O i =x 1 x 3 x 2 r(o i, x 2 ) 3 {1, 2, 3, 4, 5} DB X i = {x 1,..., x Xi } D S ={O 1,..., O DS } X a i O a S i ={s ij x j X i } X ={x 1,..., x X } O a D S X X DB CF D S = {S 1,..., S DS } S i DB S a X a S a D S 2.2 CF [2] CF DB CF GroupLens DB D S i ( )( ) j I(X r ai = ai ) saj s a sij s i ( ) 2 ) 2 j I(Xai) saj s a j I(X ai)( sij s i X ai =X a X i I(X)={j x j X} s i X ai 3.1 i GroupLens j ( ) i I ŝ aj = s a + j r ai sij s i CF (1) i I j r ai s a = S a 1 GroupLens s aj S a s aj I j ={i S i D S s.t. s ij S i } ŝ aj ( )( ) x r(oa R ai = j X ai, x j ) r a r(oi, x j ) r i (r(o a, x j ) r a ) 2 (r(o i, x j ) r i ) 2 [2] x j X ai x j X ai 2 (2) X ai =X a X i r i = X ai 1 x j X ai r(o i, x j ) GroupLens O a = x 1 x 2 x SD 3 x 2 O i 3

4 k-o means(s, k, maxiter) D S = {O 1,..., O DS }: k: maxiter: 1) : D S π = {C 1,..., C k } 3 Thustone π := π t := 0 x l X j X j = Oi C j X i 2) t := t + 1, t > maxiter 6 3) C j π µ(x l ) = 1 Ō j Thustone X Φ 1( Pr[xl x ) ] (4) j x X j 4) S O i : Φ( ) C j arg min Cj d Spear (Ōl, O i ) 5) π = π 6 6) π π := π, 2 Fig. 2: k-o means x 1 x 3 x 3 C k } O a 2 3 O a j ( ) i I j R ai r(oi, x j ) r i r a + (3) i I j R ai r a = X a x j X a r(o a, x j ) I j = {i O i D S s.t. x j X i } DB [2] Pr[x l x ] 4 O i d Spear 2 Spearman k-o means DB D S k {C 1,..., C 3.2 C 4 k-o means [12, 13] k-o means Thu- stone Spearman [19] k-means 4.1 [9] 2 D S 3 4 maxiter k-means 4

5 WWW D 10 X D D 10 2 X i A (X A (Oi A ) 10, OB i, Si B : ) SB i O i B SD D Oi B (Si B) DB D S D Oi B (Si B) Oa B (Sa B ) D S O a B (Sa B ) X A Ô B (Xi B i A ) D Oi A 10 Ôi A Ôi A O i A Spearman ρ [15] X A X i B WWW DB 6 1: 1) i X A Oi A X 2: SD ) i Xi B i B X B SD S B i D , 4) : 2) i X i B Oi B SCR (2.1 ), RCR (3.1 ), CLS (3.2 ) HCR (3.3 ) 4.1 X A X B i 5000 (Oi A,OB i, Si B) Oi A O i B (1) (3) SD CLS Si B O i B HCR Oi B x a x b Si B x b x a % 20 SD D 5000 X B i 5

6 Table 1: ρ ( X B =10, D =5000) SCR RCR CLS HCR SCR RCR CLS HCR sizes of item sets 7 10 Fig. 3: X B X B ρ RCR X B CLS HCR Spearman ρ SD (b) D 1.1 SD D CF RCR CLS HCR SCR ρ SCR RCR SCR SCR 3 D 5000 t- 2 X B SCR t- X B 1% 2(a) CLS CLS X B SCR X B X B X B = 2 3 SCR CLS X B = 2 CLS 5 2(b) 4 X B 10 CLS D D ρ SCR RCR CLS HCR 1000 sizes of data sets Fig. 4: D ρ Table 2: SCR ρ t- (a) X B 6

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