713 Brand-Choice Analysis using Non-negative Tensor Factorization Tatsushi Matsubayashi Masahiro Kohjima Aki Hayashi Hiroshi Sawada NTT NTT Service Evolusion Laboratories matsubayashi.tatsushi@lab.ntt.co.jp, http://kecl.cslab.ntt.co.jp/ tatsushi/ kohjima.masahiro@lab.ntt.co.jp hayashi.aki@lab.ntt.co.jp hiroshi.sawada@lab.ntt.co.jp keywords: clustering, brand choice, non negative tensor factorization, NTF Summary In marketing science field, modeling of purchase behavior and analysis of brand choice are important research tasks. This paper presents a method that enables such analysis by time-series pattern extraction based on Non-negative Tensor Factorization (NTF). The development of the scanning devices and electronic payments (e.g. online shopping, mobile-phone wallet and electronic money) has led to the accumulation of more detailed POS data including the information about purchase shop, amount of payment, time, location and so on and it brings possibilities for more deep understanding of purchasing behaviors. On the other hand, due to the increase of the number of attributes, it is still difficult to effectively and efficiently handle large feature quantities. In this paper, we consider feature quantities as high-order tensor. Then, using NTF for simultaneous decomposition of multiple attributes, we show analytic effectiveness of pattern factorization for real Beer Item/Brand purchase data. By applying NTF considering three axes: USER-ID TIME-STAMP ITEM-ID, we find several temporal tendencies depending on the season. In addition, by focusing on the purchase-pattern correlations between beer items and brands, we find that the tendencies of brand choice strategies appear on the graph drawing results. 1. [Guadagni 83] [Winer 86] [hardie 93, Revelt 98, Andrews 02] [Allenby 98, Arora 98] [Erdem 96, 99, 05]. POS (Non-negative Matrix Factorization NMF) [Lee 01, 12] [Takeuchi 13a, 13]. NMF 1 K-means clustering
714 30 6 SP1-C 2015 2 1 NMF (Non-negative Tensor Factorization NTF) [Shashua 05] NTF NTF 2 3 NTF 4 NTF 5 6 2. 3 2 A F 6 2 3 A F 6 3 1 3 3 NMF SCI 2013 1 1 12 31 1 [ 06, 14] 84,587 9 77,926 10 10 1,763 ID JAN 1 4 JAN 8 JAN 13 ID ID 7 1,404 A H 8 2
715 1 2013/1 2013/12 10 1,763 10 77,926 44.2 27 1,404 55.5 5 4 2 A 250 B 200 C 180 D 30 E 200 F 200 G 200 H 100 1,404 6 4 (a) (b) 5 B GW 6 A B C E 4 (a) (b) i S i (t) μ i =1/T T t=1 S i(t) σ i = 1/T T t=1 (S i(t) μ i ) 2 L i (t) M i (t) L i (t) =(S i (t) μ i )/σ i (1) t M i (t) = L i (t ) (2) t =1 1 T =53 6(b) A B C 11 3 A 3 10 B 5 GW 11 C 3 11 E 3 5 3. NTF NTF
716 30 6 SP1-C 2015 7 NTF X A B C [Takeuchi 13b, 14] NTF [I] [J] [K] 3 X =[x ijk ] R+ I J K (J =53) I = 1763 J =53 K = 1404 NTF CANDE- COMP/PARAFAC decomposition (CP ) [Kolda 09, Cichocki 09] 3 X R 3 A =[a ir ] R I R + B =[b jr] R J R + C =[c kr ] R K R + A B C A B C ˆX =[ˆx ijk ]=A B C (3) ˆX D = I i J j K d(x ijk, ˆx ijk ) (4) k 4. 4 1 NTF 8 NTF Ā =[ā ir ]= B =[ b jr ]= C =[ c kr ]= A B C d(x ijk, ˆx ijk ) 10 KL 5 KL 3 5 1 2 4 11 c kr KL ˆX =[ˆx ijk ] R I J K + ˆx 12 c kr R ˆx ijk = a ir b jr c kr (5) E F 2 r NTF A B C D A B C 7 NTF R R =5 6 8 10 20 30 50 100 R =5 5 3 3 J j I i I i K k K k J j x ijk ˆx ijk t ijkr (6) x ijk ˆx ijk t jikr (7) x ijk ˆx ijk t ijkr (8) t ijkr = a ir b jr c kr B 9 10 (2) 9 10 1 11 2 2 8 9 10 3 5 7 8 3 9 11 4 1 5 GW
717 8 NTF Ā B C ( 0) D 3 0 5. k k Sim kk = cos( c kr, c k r)= R r c kr c k r R R r c2 kr r c2 k r (9) 9 10 B r B Sim kk 0.92 1,305 38,025 13 14 [ 07] c kr 13 c kr / R r c kr 0.3 r r r cos( c kr, c kr ) 3 2 3 2 3 1 5 13 2 3
718 30 6 SP1-C 2015 11 5 1 13 14 13 14 3 10 3 10 A B C 3 2 NTF 12 3 r=1 r=2 r=3 r=4 r=5 r=1 0.754 0.762 0.802 0.608 r=2 0.754 0.890 0.692 0.713 r=3 0.762 0.890 0.801 0.803 r=4 0.802 0.692 0.801 0.781 r=5 0.608 0.713 0.803 0.781 6. (NTF) NTF NTF NTF
非負値テンソル因子分解を用いた購買行動におけるブランド選択分析 図 13 アイテムのランク類似度を元にグラフ可視化結果を行った結果１ 各ノードに対してランク r ごとに色 分けを行い 各ランクへの寄与度が高いノードのみを表示し 購買数に比例してノードサイズで描画を 行っている 図 14 アイテムのランク類似度を元にグラフ可視化結果を行った結果２ 各ノードに対してブランドごとに色 分けを行い 購買数に比例したノードサイズで描画を行っている 719
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