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1 一般社団法人電子情報通信学会 THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS 社団法人電子情報通信学会信学技報 IEICE Technical Report SP ( ) 信学技報 TECHNICAL REPORT OF IEICE. THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS Discriminant Non-negative Tensor Factorization を用いたエアコン音の印象関連脳活動の抽出矢野肇, 滝口哲也有木康雄神谷勝中川誠司, 神戸大学大学院システム情報学研究科兵庫県神戸市灘区六甲台町 1 1 国立研究開発法人産業技術総合研究所大阪府池田市緑丘株式会社デンソー愛知県刈谷市昭和町 1 1 千葉大学フロンティア医工学センター千葉県千葉市稲毛区弥生町 pi314@me.cs.scitec.kobe-u.ac.jp, {takigu,ariki}@kobe-u.ac.jp, s.nakagawa@chiba-u.ac.jp あらましエアコン音聴取時の脳活動からのエアコンの音の印象予測の精度向上を目指し脳活動特徴量の抽出手法の改善を試みた Discriminant Non-negative Tensor Factorization (DNTF) を用いて従来の Non-negaive Tensor Factorization (NTF) による特徴量にエアコン音の涼しさ好ましさに関する一対比較判断の情報を取り入れたエアコン音聴取時の脳磁界の時間周波数特徴から DNTF を用いて抽出された特徴量と比較判断を用いて印象予測モデルを学習しその予測精度から提案手法の評価を行ったキーワード聴感印象評価非負値テンソル分解 (NTF) Discriminant NTF 脳磁界計測プリファレンスエアコン音 Extraction of brain activities related to impressions induced by HVAC sound using discriminant non-negative tensor factorization Hajime YANO,, Tetsuya TAKIGUCHI, Yasuo ARIKI, Masaru KAMIYA, and Seiji NAKAGAWA, Graduate School of System Infomatics, Kobe University Rokkodai 1 1, Nada-ku, Kobe-shi, Hyogo, Japan National Institute of Advanced Industrial Science and Technology (AIST) Midorigaoka , Ikeda-shi, Osaka, Japan DENSO Corporation Showa-cho 1 1, Kariya-shi, Aichi Japan Center for Frontier Medical Engineering, Chiba University Yayoi-cho 1 33, Inage-ku, Chiba-shi, Chiba Japan pi314@me.cs.scitec.kobe-u.ac.jp, {takigu,ariki}@kobe-u.ac.jp, s.nakagawa@chiba-u.ac.jp Abstract To evaluate auditory impressions induced by HVAC (heating, ventilation and air conditioning) sound using a predictive model, which estimates auditory impressions from brain activities, we tried to improve the method of brain feature extraction. Information of paired-comparative judgments on coolness/preference induced by HVAC sound were combined with non-negative tensor factorization (NTF) by discriminant NTF (DNTF). First, the brain cortical feature was extracted from the time-frequency feature of magnetic cortical activities while hearing HVAC sound using DNTF. Second, the predictive model were trained from the brain cortical features and comparative judgments. The performance of feature extraction method using DNTF was evaluated based on prediction accuracy of comparative judgment. Key words auditory impression, non-negative tensor factorization (NTF), discriminant NTF, magnetoencephalography (MEG), preference, HVAC sound This article is a technical report without peer review, and its polished and/or extended version may be published elsewhere. Copyright 2017 by IEICE

2 1. [1] [3] [4], [5] [6] [6] Non-negative Tensor Factorization: NTF 60% NTF [7] [8] NTF NTF Discriminant Non-negative Tensor Factorization (DNTF) [9] NTF Linear Predictive Coding: LPC [10] Hz 5s Hz ch Neuromag-122, Neuromag Ltd. 122ch Hz 400 Hz 3. NTF ms raw data s(t) C(a, b) = 1 a ( s(t)ψ b t a ) dt (1) ψ(t) =π 1 4 e jω 0 t e t2 2 (2) a b ψ(t) ω 0 = Hz ms 3. 2 NTF X = {x i,j,k,l } R I J K L + NTF X (3) R 1 [11] (4)

3 X ˆX = R a r b r c r t r (3) r=1 x i,j,k,l ˆx i,j,k,l = R a i,rb j,rc k,r t l,r (4) r=1 A = {a i,r} =[a 1...a R] R I R + B = {bj,r} = [b 1...b R] R J R + C = {c k,r} = [c 1...c R] R K R + T = {t l,r } = [t 1...t R] R L R a r b r c r t r t l,r 1 T R NTF X R ˆX Frobenius 2 D F (X ˆX) = X ˆX 2 F = i,j,k,l (x i,j,k,l ˆx i,j,k,l ) 2 X 4 X (1) R I JKL + X (2) R J KLI + X (3) R K LIJ + X (4) R L IJK + NTF 4 [11], [12] X (1) A(T C B) T, X (2) B(A T C) T, X (3) C(B A T ) T, X (4) T (C B A) T (5) Khatri-Rao 2 (5) 1 Non-negative Matrix Factorization: NMF [13] NMF A A X (1)Z (1) AZ (1)T Z (1), B B X (2)Z (2) BZ (2)T Z (2), C C X (3)Z (3) CZ (3)T Z (3), T T X (4)Z (4) TZ (4)T Z (4) (6) Z (1) = T C B Z (2) = A T C Z (3) = B A T Z (4) = C B A A B C L Discriminant NTF NTF X ˆX Frobenius DNTF [9] DNTF (3) DNTF NTF L = D F (X ˆX)+αTr(S w) βtr(s b ) (7) S w S b Tr( ) α, β > 0 DNTF 2 d p = t A p, t B p, R 1 R d p S w S b S w = S b = 2 k=1 (d µ (k) ) T (d µ (k) ) (8) d C k 2 N k (µ (k) µ) T (µ (k) µ) (9) k=1 µ (k) = 1 N k d C k d, µ = 1 N 2 N k µ (k) (10) k=1 C k (k =1, 2) N k N k µ (k) µ k (7) NTF DNTF T A B C A B C NTF (6) T NTF (7) NTF (5) 4 T Z (4)T (7) NTF D F (X ˆX) Frobenius (11) t m,n t m,n P m,n + γ mt pair(m),n + ord(m)m m,n Q m,n + γ m (11) γ m = α α + β + β N cls(m) N M m,n = α + β d p,n β N cls(m) N d p C cls(m) p =ind(m) p =ind(m) (12) d p,n (13) P m,n =[X (4) Z (4) ] m,n Q m,n =[TZ (4)T Z (4) ] m,n

4 (6) T m n m pair(m) m cls(m) m ind(m) ord(m) m A B 1 1 d γ m t m,n R f : R R R f(x) = w, φ(x) + b (14), φ : R R R R x R <R w b 2 A B x A x B f(x A ) f(x B )= w, φ(x A ) φ(x B ) (15) (A, B) f(x A ) f(x B ) > 0 A f(x A ) f(x B ) < 0 B (15) b 2 w (15) d = φ(x A ) φ(x B ) 2 Support Vector Machine (SVM) [14] w (16) α (17) max α sub. to α i 1 α iα jy iy j d i, d j (16) 2 i 0 α i C i,j w = αi y i(φ(x A i ) φ(x B i )) (17) i y i { 1, 1} C(> 0) SVM 1 [%] Table 1 Prediction accuracies of paired-comparative judgment on coolness (%). NTF DNTF Sub. Closed Open Closed Open Ave NTF DNTF NTF DNTF R =3 DNTF 2 α = β A B C T A B C (5) 4 T Z (4)T =(C B A) T Moore-Penrose {Z (4)T } + (18) T = X (4) {Z (4)T } + = X (4) Z (4) [Z (4)T Z (4) ] 1 (18) T DNTF Closed Open DNTF α = β 3 Open 60%

5 Table [%] Prediction accuracies of paired-comparative judgment on preference (%). NTF DNTF Sub. Closed Open Closed Open Ave [%] Table 3 Mean prediction accuracies of paired-comparative judgment by changing the parameter of regularizer (%). NTF DNTF α, β Coolness Preference DNTF α = β =10 10 DNTF NTF NTF DNTF t 2 1 DNTF A B C T A B 10 Hz C 1 18 T 2 DNTF (7) DNTF DNTF (7) NTF α = β =10 8 T 0 (11) α β γ m (11) T 0 6. DNTF DNTF NTF 2 DNTF NTF DNTF [1] Y. Soeta, S. Nakagawa, and M. Tonoike, Magnetoencephalographic responses corresponding to individual subjective preference of sound fields, Journal of Sound and Vibration, vol. 258, pp , [2] Y. Soeta, S. Nakagawa, and M.Tonoike, Magnetoencephalographic responses correspond to individual annoyance of bandpass noise, Journal of Sound and Vibration, vol. 277, pp , [3] S. Nakagawa, Y. Kanemoto, T. Hotehama, Y. Soeta, and S. Ishimitsu, Evaluation of auditory impression of music using brain activity, ICIC Express Letters, vol. 7, pp , [4] 2015 pp [5] 2016 pp [6] 2017 pp [7] A. Shashua, and T. Hazan, Non-negative tensor factorization with applications to statistics and computer vision, Proceedings of ICML, [8] H. Lee, Y. Kim, A. Cichocki, and S. Choi, Nonnegative tensor factorization for continuous eeg classification, International Journal of Neural Systems, vol. 17, no. 4, [9] S. Zafeiriou, Discriminant nonnegative tensor factorization algorithms, IEEE Transactions on Neural Networks, vol

Time (ms) 5 4 3 2 1 0.2 0.16 0.12 0.08 0.04 Index of channel 10 8 6 4 2 0.6 0.4 0.2 Frequency (ms) 8 4 2 1 0.4 0.3 0.2 0.1 15 10 5 Index of trial 20 10-9 5. 4. 3. 2. 1. 5 1 DNTF 8 α = β =10 10 A B C T Fig.

6 Time (ms) Index of channel Frequency (ms) Index of trial DNTF 8 α = β =10 10 A B C T Fig. 1 Examples of basis matrix of DNTF (coolness, subject8, α = β =10 10 ). Four matrices show a temporal factor A (top left), a oscillatory factor B (bottom left), aspatialfactorc (top right), a matrix of feature vectors T (bottom right). Cost function Number of iterations Regularizer Number of iterations 2 DNTF 8 α = β = Fig. 2 An example of the cost fuction of DNTF for each iteration (coolness, subject 8, α = β =10 10 ). 3 DNTF 8 α = β = Fig. 3 An example of the regularizer of DNTF for each iteration (coolness, subject 8, α = β =10 10 ). 20, no. 2, pp , [10] T. Hotehama, and S. Nakagawa, Auditory impression of the coolness and warmness of automotive HVAC noise, Proceedings of INTER-NOISE 2015, in 15_915, [11] A. Cichocki, R. Zdunek, A.H. Phan, and S. Amari, Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation, Willey, [12] T. Kolda, and B. Bader, Tensor decompositions and applications, SIAM Review, vol. 51, no. 3, pp , [13] D.D. Lee and H.S. Seung, Algorithms for non-negative matrix factorization, Proceedings of NIPS, [14] R. Herbrich, T. Graepel, P. B. Sdorra, and K. Obermayer, Learning preference relations for information retrieval, Proceedings of AAAI Workshop Text Categorization and Machine Learning, pp ,

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