Vol.8 No (Mar. 2015) 1,a) , Anomaly Detection Based on Density Estimation of Normal Data in Cone-restr

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1 1,a) , Anomaly Detection Based on Density Estimation of Normal Data in Cone-restricted Subspace Yudai Yamazaki 1,a) Hirokazu Nosato 2 Masaya Iwata 2 Eiichi Takahashi 2 Ayumi Izumori 3 Takuji Iwase 4 Hidenori Sakanashi 2 Received: May 28, 2014, Revised: July 18, 2014, Accepted: September 5, 2014 Abstract: A cone-restricted subspace method can express learning patterns accurately by generating a convex cone for non-negative feature vectors. Classification of conventional method is performed based on the angle between the input vector and the cone. However, recognition performance is reduced if the spread of the convex cone is large, because it is impossible to distinguish between vectors near the surface and those around the center of the cone. This paper proposes an anomaly detection method based on probability density of normal data in cone-restricted subspace. Classification by the proposed method is based on the probability contained in the convex cone. We demonstrate anomaly detection from breast ultrasound images using proposed method, and confirmed effectiveness of the method. Keywords: cone-restricted subspace, density estimation, anomaly detection, pattern recognition 1 Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki , Japan 2 Information Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki , Japan 3 Department of Surgery, Takamatsu Heiwa Hospital, Takamatsu, Kagawa , Japan 4 Breast Oncology Center, The Cancer Institute Hospital of the Japanese Foundation for Cancer Research, Koto, Tokyo , Japan 1. a) [email protected] c 2015 Information Processing Society of Japan 28

2 [1] [2] [1], [3] HLAC [4] SIFT [5] LBP [6] [2] 2.2 D C N C = {x x = α i ξ i =Ξα,α i 0} (1) i=1 where Ξ = {ξ 1, ξ 2,...,ξ N } α = {α 1,α 2,...,α N } T N ξ i R D α i S N S = {x x = α i ξ i =Ξα} (2) i=1 (1) (2) C S α i 2.3 y C θ θ 1 y C x c 2015 Information Processing Society of Japan 29

3 Fig. 1 1 Angle between the input vector and the cone. θ = arcsin(min y x / y ) x C N / =arcsin min y α i ξ i 2 y (3) α i 0 i=1 (3) min αi 0 y N i=1 α iξ i 2 [7] y C y ξ i (3) y = N i=1 α iξ i θ 0 Algorithm 1 C input :X =[x 1,...,x M ](M ) :θ th ( 0) initialize :t 0 C :C X C N t :N 0 M repeat step1 X X S X S step2 x i X S X S x i C Sī θ i θ i <θ th X X S x i step3 x j X S X S C S θ j θ j <θ th X x j step4 :t t +1 C :C X C N :N t [X ] until (N t = N t 1 ) output :C θ 0 θ π [2] 3 X Algorithm 1 C (3) θ th (3) 2 y 1 y 2 C 0 2 Fig. 2 Feature vectors in cone. 1 [2] (3) 3. c 2015 Information Processing Society of Japan 30

4 3 Fig. 3 Flowchart of proposed method. Fig. 4 4 Space that represents the spread direction of cone N X =[x 1,...,x N ] x i D 1 ˆx i = x i x i (i =1,...,N) ˆX =[ˆx 1,...,ˆx N ] R ˆX R ˆX = ˆX ˆX T R ˆX R ˆXU = UΛ U = {u 1,...,u D } u i Λ =diag λ 1,...,λ D λ i 1 u 1 2 U E U E = {u 2,...,u M+1 } (1 M D 1) U E M M 4 3 D =3 2 M = [8] ˆx i x E i x E i = UE T ˆx i (i =1,...N) p(t) c 2015 Information Processing Society of Japan 31

5 p(t) = 1 N N i=1 where k(x) = 1 h M k( t xe i h ) (4) 1 (2π) M/2 exp( 1 2 xt x) t M h k(x) k(x) h M M h M h (4) y y E y E = UE T ŷ where ŷ = y y y E p(y E ) p th 4. 2 (1) 3 2 (2) 4.1 ROC Receiver Operating CharacteristicROC False Positive Rate True Positive Rate ROC 100% 0% ROC AUC Area Under the Curve AUC ROC (a) 1 (x, y, z) =(1, 1, 1), (2, 1, 2) μ =(0, 0) σ 2 =0.5 5(b) 6 (a) 2 1 6(b) ROC 7 (a) 7(b) 1 M =2 h = M =2 h =0.2 M =2 h AUC AUC c 2015 Information Processing Society of Japan 32

6 情報処理学会論文誌数理モデル化と応用 Vol.8 No (Mar. 2015) 図 5 人工データ 1 凸形状の錐 Fig. 5 Synthetic dataset1: Convex cone. 図 6 人工データ 2 非凸形状の錐 Fig. 6 Synthetic dataset2: None convex cone. 図 7 人工データに対する ROC 曲線 Fig. 7 ROC curve of synthetic dataset. 錐制約部分空間法では錐の中に含まれる特徴ベクトルと次に人工データ 2 を用いたときの結果について述べる錐とのなす角度がすべて 0 となり錐の中にある異常デー比較手法 1 と 2 では真陽性率が 1 に達することはなく異タをすべて正常として判定し異常を見落としてしまった常の見落としが発生している両手法ともに錐の表面付近ことが原因であると中心付近を区別できなかったためであると推察される c 2015 Information Processing Society of Japan 33

3 1 2 AUC AUC 2 1 3 AUC 1 2 AUC Fig. 8 8 Example of the breast ultrasound image. 4.

9 Examples of experiment data. 1 Table 1 Number of samples in each patients.

1 22041 1363 9 9 (a) 9(b) 1 Higher-order Local Autocorrelation; HLAC [4] 2 1 2

7 3 1 2 AUC AUC AUC 1 2 AUC Fig. 8 8 Example of the breast ultrasound image [9], [10] [11], [12] ROC fps 8 7 A G Fig. 9 Examples of experiment data. 1 Table 1 Number of samples in each patients. A B C D E F G (a) 9(b) 1 Higher-order Local Autocorrelation; HLAC [4] HLAC HLAC c 2015 Information Processing Society of Japan 34

8 M =1 h =0.25 M 1 34 h AUC (a) 2 11 (b) 11 (b) 11 (a) 2 11 (b) AUC AUC 2 AUC 1 2 AUC Fig ROC ROC curves of achieved by the proposal method and comparison methods. 11 Fig. 11 Examples of tumor images. 2 Table 2 AUC AUC values in each patients A B C D E F G c 2015 Information Processing Society of Japan 35

12 Fig. 12 Tumor images of different patients. AUC A E AUC 12 (a) 12 (b) A E HLAC E 5. 2 local autocorrelation feature extraction for classification of histopathological images, IPSJ Trans. CVA, Vol.

9 12 Fig. 12 Tumor images of different patients. AUC A E AUC 12 (a) 12 (b) A E HLAC E 5. 2 local autocorrelation feature extraction for classification of histopathological images, IPSJ Trans. CVA, Vol.3, pp (2011). [4] Otsu, N. and Kurita, T.: A new scheme for practical flexible and intelligent vision systems, pp (1988). [5] Lowe, D.: Object recognition from local scale-invariant features, Proc. 7th IEEE International Conference on Computer Vision, Vol.2 (1999). [6] Ojala, T., Pietikäinen, M. and Harwood, D.: A comparative study of texture measures with classification based on featured distributions, Pattern recognition, Vol.29, pp (1996). [7] Bro, R. and De Jong, S.: A fast non-negativityconstrained least squares algorithm, Journal of chemometrics, Vol.11, No.5, pp (1997). [8] Silverman, B.W.: Density estimation for statistics and data analysis, Vol.26, CRC press (1986). [9] statistics.html. [10] statistics/statistics.html. [11] Journal of N.D.I Vol.60, No.12, pp (2011). [12] CAD JABTS Journal of breast and thyroid sonology Vol.2, No.3, pp (2013) [1] Nanri, T. and Otsu, N.: Unsupervised abnormality detection in video surveillance, MVA, pp (2005). [2] D Vol.92, No.1, pp (2009). [3] Nosato, H., Kurihara, T., Sakanashi, H., Murakawa, M., Kobayashi, T., Furuya, T., Higuchi, T., Otsu, N., Terai, K. and Hiruta, N.: An extended method of higher-order c 2015 Information Processing Society of Japan 36

10 IEEE Best English Paper of the Year c 2015 Information Processing Society of Japan 37

1 Fig. 1 Extraction of motion,.,,, 4,,, 3., 1, 2. 2.,. CHLAC,. 2.1,. (256 ).,., CHLAC. CHLAC, HLAC. 2.3 (HLAC ) r,.,. HLAC. N. 2 HLAC Fig. 2

1 Fig. 1 Extraction of motion,.,,, 4,,, 3., 1, 2. 2.,. CHLAC,. 2.1,. (256 ).,., CHLAC. CHLAC, HLAC. 2.3 (HLAC ) r,.,. HLAC. N. 2 HLAC Fig. 2 CHLAC 1 2 3 3,. (CHLAC), 1).,.,, CHLAC,.,. Suspicious Behavior Detection based on CHLAC Method Hideaki Imanishi, 1 Toyohiro Hayashi, 2 Shuichi Enokida 3 and Toshiaki Ejima 3 We have proposed a method for