Comparison of Discriminant Analysis in Ear Recognition

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1 IPSJ SIG echnical Report PCA 288 XM2VS 97.8% Null space LDA Random LDA Comparison of Discriminant Analysis in Ear Recognition Yuki ajima oji Soma Sai Hideyasu Daishi Watae Discriminant analyses are popular algorithms for face recognition and various discriminant analysis are proposed in thus far. In this study various discriminant analysis algorithms are thoroughly examined for ear iometrics. Experiment performed on XM2VS dataase made 97.8% recognition rate using Null ernel discriminant analysis.. 2. Vol.2009-CVIM-67 No /6/0 890 Bertillon Iannarelli [] 40 Moreno [2] Compression Netork [3] Hurley [4] Gaussian Chen [5] 3 3 Yu [6] Liu [7] Loag [8] Liu [9] [0] 288 Saitama Institute of echnology 2009 Information Processing Society of Japan

2 IPSJ SIG echnical Report x y = Ax Discriminant Criterion S J = max c c c= = ( µ µ )( µ µ ) N c c = c c i µ c i µ c c= N i(c)= 2 N S S ( S = ( x )( x ) ) N µ = µ = N N N x c i c xi i= Nc i= 3 4 Nc c 3.2 SSS 3.2. PCA+LDA PCA LDA Belhumeur [] SSS PCA Direct LDA DLDA [6][] Z Y S Y = D > Z = YD 6 Z U U Z SZU = D U, Z A A = U Z 8 8 A A D D Ax x 9 2 * Null space LDA NLDA [7] Y Y S Y = 0 0 Y U U Y SYU = D 0 U Z A A= U Y 2 2 A Ax Vol.2009-CVIM-67 No /6/0 * x LDA Information Processing Society of Japan

3 IPSJ SIG echnical Report Poer LDA PLDA [0] LDA 4 HAD 5 J( A, m) = max A PS c c A c= J( A, m) = max P A Sc c A c= J( A, m) = max m m A PS c c A c= m> 0<m< m= LDA m=0 HDA Fractional LDA FLDA Fractional LDA G.Dai [2] Lee [3] ( ij ) ( ij ) ( )( )( ) S = nn ω d µ µ µ µ i j ij i j i j i= j= i+ p ω d = d p Weighted LDA WLDA [8] ( )( )( ) S = nn α µ µ µ µ 8 i j ij i j i j i= j= i+ ( µ µ ) S ( µ µ ) = ij i j W i j ij α ( ij ) = 2 erf 2 ij 2 2 erf ( ) = min J A /s /st t ( ) = max J A (2) 22 ( ) = ( 2 2) S S A λ A 2 D U S U D V = λv A= U D V 2 Vol.2009-CVIM-67 No /6/ H 23 Φ Information Processing Society of Japan

4 IPSJ SIG echnical Report 24 ( ), ( ) (, ), (, ) (, ) Φ x Φ y = k x k y = k x y 23 H 2 k( x, y) = exp y x 2 24 σ [4][5][6] 3.4. ernel PCA 25 PCA PCA x x 25 i φ ( ) n n S = φ x φ x ( φ x = φ x φ x ) ( ) ( ) ( ) ( ) ( ) i i i i m i= n m= i 26 ( λi S) V = 0 27 ( φ ( ) φ ( )) : = x, x 28 ij i j = x x x x x x + x x n n n (, ) (, ) (, ) 2 (, ) ij i j i a a j a 29 n a= n a= n a, = 29 V ( λi ) V = 0 30 g = λ 2 V 3 g ernel PCA ernel LDA DA LDA ernel PCA LDA GDA [7] Vol.2009-CVIM-67 No /6/ XM2VS[6] M2VS XM2VS[8] Information Processing Society of Japan

IPSJ SIG echnical Report 2 2 2 2 2 4.3 288 2 4.3. G P 32 33 G P, G P (32) 5. Vol.2009-CVIM-67 No.2 2009/6/0 288 DA NLDA PCA LDA DLDA 5.

5 IPSJ SIG echnical Report G P G P, G P (32) 5. Vol.2009-CVIM-67 No /6/0 288 DA NLDA PCA LDA DLDA 5. PCA LDA DLDA NLDA 3 Rank one Recognition Rate Cumulative Match Characteristic CMC 3 Rank one Recognition Rate G, Σ G P Σ Σ G GG P GP G (33) CMC Information Processing Society of Japan

6 IPSJ SIG echnical Report Rank one Recognition Rate 2 CMC 4 2 S St Rank one Recognition Rate Vol.2009-CVIM-67 No /6/0 3 LDA DLDA NLDA Rank one Recognition Rate 5 LDA DLDA NLDA CMC 6. 4 St S CMC 5.3 A PCA+LDA DLDA NLDA 3 Rank one Recognition Rate 3 CMC 5 PCA+LDA Null space LDA Null space LDA Information Processing Society of Japan

IPSJ SIG echnical Report Direct LDA Null space LDA Direct LDA LDA Null space LDA Null space LDA Random LDA Fuzzy LDA Gaor Jet ) A. Iannarelli, Ear Identification, Forensic Identification series.

on Security echnology, pp. 469-476, 999 3). Yuizono, Y. Wang,. Satoh, and S.

7 IPSJ SIG echnical Report Direct LDA Null space LDA Direct LDA LDA Null space LDA Null space LDA Random LDA Fuzzy LDA Gaor Jet ) A. Iannarelli, Ear Identification, Forensic Identification series. Paramont Pulishing Company, Fremont, California 989 2) B. Moreno and A. Sanchez, On the Use of Outer Ear Images for Personal Identification in Security Applications, IEEE 33rd Annual Intl. Conf. on Security echnology, pp , 999 3). Yuizono, Y. Wang,. Satoh, and S. Nakayama, Study on Individual Recognition for Ear Images y Using Genetic Local search, Proceedings of the 2002 Congress on Evolutionary Computation (CEC2002), pp , ) D. J. Hurley, M. S. Nixon, and J. N. Carter, Force Field Energy Functionals for Image Feature Extraction, Image and Vision Computing Journal, Vol. 20, pp. 3-37, ) H. Chen and B. Bhanu, Human Ear Recognition in 3D, IEEE ransactions on Pattern Analysis and Machine Intelligence, Vol. 29, 4, pp , ) H. Yu, J. Yang, "A direct LDA algorithm for high dimensional data ith application to face recognition", Pattern Recognition 34 (0) , 200 7) Wei Liu, Yunhong Wang, Stan Z. Li, ieniu an, "Null Space Approach of Fisher Discriminant Analysis for Face Recognition", ECCV Workshop BioAW, ) M. Loog, R.P.W. Duin, R. Hae-Umach, "Multiclass linear dimension reduction y eighted pairise Fisher criteria", IEEE rans. Pattern Anal. Mach. Intell, 23 (7) (200) ) Q.S.Liu, R.Huang, H.Q.Lu and S.D.Ma, Face Recognition Using ernel Based Fisher Discriminant Analysis, In the Proc. of. Int. Conf. Automatic Face and Gesture Recognition, pp , Washington DC, USA, May, ),,,,, " ", Signal Processing and Its Applications, ISSPA th International Symposium on Volume, Issue, 2-5 Fe Page(s): 4 ) H. Yu, J. Yang, "A direct LDA algorithm for high dimensional data ith application to face recognition", Pattern Recognition 34 (0) , 200 2) G. Dai, Y.. Qian, and S.Jia, "A kernel fractional-step nonlinear discriminant analysis for pattern recognition", In Proceedings of the Eighteeever nth international Conference on Pattern Recognition, volume 2, pages , August ) Lee Hui ueh, Jon-ark Lee, "Face Recognition Using Linear Discriminant Analysis (LDA) of Principal Component Analysis (PCA)", ISIS 2007 Proceedings of the 8th Symposium on advanced intelligent systems, ) Heiko Hoffmann, "ernel PCA for Novelty Detection", Pattern Recognition, Vol. 40,No. 3. (2006), pp ) Q.S.Liu, R.Huang, H.Q.Lu and S.D.Ma, Face Recognition Using ernel Based Fisher Discriminant Analysis, In the Proc. of. Int. Conf. Automatic Face and GestureRecognition, pp , Washington DC, USA, May, ) W.U. Xiao-Jun, J. ittler, Y. Jing-Yu,. Messer, W. Shi-ong, "A ne kernel direct discriminant analysis (DDA) algorithm for face recognition", in: Conference on British Machine Vision, ingston University, London, Septemer 7-9, ) G.Baudat and F.Anouar, Generalized Discriminant Analysis Using a ernel Approach, Neural Computation, vol. 2, no. 0, pp , ).Messer, J.Matas, J.ittler, J.Luettin, G.Maitre, XM2VSDB:the extended M2VS Dataase, Proceedings 2nd Conference on Audio and Video-ase Biometric Personal Verification (AVBPA 99) Washington DC, (999) SVSSP URL: Vol.2009-CVIM-67 No /6/ Information Processing Society of Japan

8 IPSJ SIG echnical Report Vol.2009-CVIM-67 No /6/ Information Processing Society of Japan

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