Adaptive Acceptance Threshold Control using Matching Distances with Confidence Values for ROC Curve Optimization

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1 (MIRU2010) ROC {makihara,hossain,yagi}@am.sanken.osaka-u.ac.jp ROC ( ) ROC 2 ROC Adaptive Acceptance Threshold Control using Matching s with Abstract Confidence Values for ROC Curve Optimization Yasushi MAKIHARA, Md. ALTAB HOSSAIN, and Yasushi YAGI Osaka university 8-1 Mihogaoka, Ibaraki, Osaka, {makihara,hossain,yagi}@am.sanken.osaka-u.ac.jp In two-class classification problems such as one-to-one verification and object detection, the performance is usually evaluated by a so-called Receiver Operating Characteristics (ROC) curve expressing a tradeoff between False Rejection Rate (FRR) and False Acceptance Rate (FAR). On the other hand, it is also well known that the performance is significantly affected by the situation differences between enrollment and test phases. This paper describes a method to adaptively control an acceptance threshold with confidence values derived from situation differences so as to optimize the ROC curve. We show that the optimal evolution of the adaptive threshold in the domain of the distance and confidence value is equivalent to a constant evolution in the domain of the error gradient defined as a ratio of a total error rate to a total acceptance rate. An experiment with simulation and real data demonstrates the effectiveness of the proposed method, particularly under a lower FAR or FRR tolerance condition. Key words rejection rate ROC curve, Acceptance threshold, Confidence values, Error gradient, False acceptance rate, False [1] 2 [2] ID ( ) ( ) 2

2 ( False Acceptance Rate: FAR ) ( False Rejection Rate: FRR) (ROC) [3] 2 [4] [5], [6] SN (Quality measure) [7] [8] [9] [10] Hossain [11] [12] [13] [14] [15] [16] Kryszczuk [17] evidence space [17] ROC ROC ROC ROC ROC ROC ROC 1 1 ( ) ( ) ( ) 1(a) (Probability Distribution Function: PDF) T A F R (False Rejection Rate: FRR) A F A T T (< T ) FRR FAR ( 1(a)) T L (> T ) FRR FAR ( 1(a)) FRR 100% FAR 0% +. FRR 0% FAR 100% ( ) ( + ) 1(b) FRR FAR ROC [3] ROC 1 1 FRR FAR FRR FAR (Equal Error Rate: EER) ROC 1 1 PDF FRR FAR 3( ) PDF

3 Probability 1 A FA A FR T T T T L (a) PDF Positive Negative False Rejection Rate P FR 1.0 T T Tight Loose 0.0 T T L False Acceptance Rate P FA (b) ROC PDF ROC Low confidence 2 High confidence Positive Negative Confidence ROC 3( ) PDF ROC ROC ROC PDF ROC ( 2 ) ( 2 ) PDF ROC 3 FAR 0% T L NoF A T H NoF A (> T L NoF A ) FRR 0% T L NoF R and T H NoF R (< T L NoF R ) ROC T L NoF A T L NoF A T H NoF A ( 3(a) ) T H NoF R T H NoF R T L NoF R T L NoF A T H NoF A T H NoF R T L NoF R 2. 3 t PDF p P (t) p N (t) T FAR R F A (T ) FRR R F R (T )

4 Probability Probability 3 T L NoFA T H NoFA False acceptance (a) PDF Positive Negative Positive Negative False Rejection Rate P FR False Rejection Rate P FR 1.0 T L NoFA T H NoFA False Acceptance Rate P FA 1.0 T L NoFA T H NoFA False Acceptance Rate P FA (b) ROC ( ) ( ) PDF ROC R F A (T ) = T R F R (T ) = 1 T p N (t)dt (1) p P (t)dt. (2) R E (T ) R A (T ) R E (T ) = R F A (T ) + R F R (T ) (3) R A (T ) = R F A (T ) + (1 R F R (T )). (4) R A (T ) R E (T ) g(t ) = dr E(T ) dr A (T ) = pn (T ) p P (T ) p N (T ) + p P (T ). (5) ( g(t ) 1.0) ( g(t ) 1.0) ( g(t ) 0.0) FAR FRR g(t ) g(t ) 2 t c g(t) g(t ) 2. 4 N P N N i (t P i, cp i ) (tn i, cn i ) t c t j =t min + js t, j Z, 0< = j < = (t max t min )/s t (6) c k =c min + ks c, k Z, 0< = k < = (c max c min )/s c (7) i k w P i,k w P i,k = max(1.0 c P i c k /s c, 0) (8) j k PDF p j,k p P j,k = 1 N P wi,k P exp ( (tp i t j ) 2 ) Z k 2σ 2, (9) i Z k PDF j pp j,k s t = 1 σ PDFp N j,k (t j, c k ) g j,k (5). c k g = {g j,k } g =arg min S(ĝ) (10) ĝ S(ĝ)= k,j {(ĝ j,k g j,k ) 2 +α(ĝ j,k ĝ j 1,k ) 2 } (11) subject to ĝ j 1,k > = ĝ j,k, (12) α 2

3. 3. 1 PDF c PDF 0 < = c < = 1 PDF N (µ P (c), σ P (c)) N (µ N (c), σ N (c)) PDF c µ P (c) = 5.0 3.0c, µ N (c) = 7.0 2.

01, s c = 0.1 t min = 0.0, t max = 10.0 α = 1.0 z [3] z 1 1 µ(c) σ(c) 4(b) z 0 1 3. 2 5 4 8.0 7.0 6.0 5.0 4.0 (a) (b) z 3.

5 PDF c PDF 0 < = c < = 1 PDF N (µ P (c), σ P (c)) N (µ N (c), σ N (c)) PDF c µ P (c) = c, µ N (c) = c, σ P (c) = c, σ N (c) = c, PDF 10,000 ( 4(a)) ( c = 1.0) ( c = 0.0) 10,000 PDF σ = 0.3, s t = 0.01, s c = 0.1 t min = 0.0, t max = 10.0 α = 1.0 z [3] z 1 1 µ(c) σ(c) 4(b) z (a) (b) z Confidence value 5 ( 0.1) 6 ( g = 0.0), ( g = 1.0) ( g = 0.0) ( g = 1.0) ROC 7(a) (AATC) (const) z (Z-norm)

9 10-1 +1 1 1 11 ROC z False Rejection Rate False

5 False Acceptance Rate 1.0 0.9 0.8 0.7 0.6 0.5 0.

E-02 1.E-01 False Acceptance Rate 1.0E-01 1.

6 False Rejection Rate Constant Z- norm AATC 6 FAR ( 7(b)) FRR ( 7(c)) z FAR FRR , Hossain [6] [6] [18] ROC z False Rejection Rate False Rejection Rate False Acceptance Rate (a) Z-Norm AATC 1.E-04 1.E-03 1.E-02 1.E-01 False Acceptance Rate 1.0E E E-03 (b) FAR Z-Norm AATC 1.0E False Acceptance Rate 8 (c) FRR 7 ROC 4. z

9 10 0.5 Constant False Rejection Rate 0.4 Z-norm AATC 0.3 0.2 0.1 1 1 N 2 1. 2 LDA [19] SVM [20] ROC FAR FRR ROC ROC 5. 2 ROC 2 21220003 0.0 0.0 0.1 0.2 0.3 0.4 0.

Dalal and B. Triggs, Histograms of oriented gradients for human detection, CVPR2005, II pp. 886 893, 2005. [3] P. Phillips, H. Moon, S. Rizvi, and P.

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8 Clothes-invariant gait identification using partbased adaptive weight control, Proc. of the 19th Int. Conf. on Pattern Recognition, Tampa, Florida USA, Dec [7] A. Harriero, D. Ramos, J. Gonzalez-Rodriguez, and J. Fierrez, Analysis of the utility of classical and novel speech quality measures for speaker verification, ICB 09: Proceedings of the Third International Conference on Advances in Biometrics, Berlin, Heidelberg Springer-Verlag pp , [8] F. Alonso Fernandez, F. Roli, G. Marcialis, J. Fierrez, and J. Ortega Garcia, Comparison of fingerprint quality measures using an optical and a capacitive sensor, BTAS07, pp. 1 6, [9] S. Muller, O. Henniger, and T. U. D. Darmstadt, Evaluating the biometric quality of handwritten signatures, In 2nd International Conference on Biometrics,, [10] E. Krichen, S. Garcia-Salicetti, and B. Dorizzi, A new probabilistic iris quality measure for comprehensive noise detection, Biometrics: Theory, Applications, and Systems, BTAS First IEEE International Conference on, pp. 1 6, [11] M. A. Hossain, Y. Makihara, J. Wang, and Y. Yagi, Clothing-invariant gait identification using partbased clothing categorization and adaptive weight control, Pattern Recognition,, 2010 (to appear). [12] H. Sellahewa and S. Jassim, Illumination and expression invariant face recognition: Toward quality-based adaptive fusion, BTAS08, pp. 1 6, [13] M. Gales and S. Young, Robust continuous speech recognition using parallel model combination, IEEE Transactions on Speech and Audio Processing, vol. 4, no. 5, pp , [14] N. Poh, J. Kittler, and T. Bourlai, Improving biometric device interoperability by likelihood ratio-based quality dependent score normalization, BTAS07, pp. 1 5, [15] J. Fierrez-Aguilar, Adapted Fusion Schemes for Multimodal Biometric Authentication PhD thesis Universidad Politecnica de Madrid, [16] S. Bengio, C. Marcel, S. Marcel, and J. Mariethoz, Confidence measures for multimodal identity verification, Information Fusion, vol. 3, no. 4, pp , [17] K. Kryszczuk and A. Drygajlo, Improving classification with class-independent quality measures: Q- stack in face verification, In 2nd International Conference on Biometrics, Seoul, South Korea,, [18],,,,,, vol. 48, no. SIG1(CVIM17), pp , Feb [19] J. H. P. Belhumeur and D. Kiregeman, Eigenfaces for recognition, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp , Jul [20] B. E. Boser, I. M. Guyon, and V. N. Vapnik, A discriminant analysis for underd data, Proc. of the 5th Annual ACM Workshop on Computational Learning Theory, pp , 1992.

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[1] DNA ATM [2] c 2013 Information Processing Society of Japan. Gait motion descriptors. Osaka University 2. Drexel University a) 1,a) 1,b) 2,c) 1,d) Gait motion descriptors 1. 12 1 Osaka University 2 Drexel University a) higashiyama@am.sanken.osaka-u.ac.jp b) makihara@am.sanken.osaka-u.ac.jp c) kon@drexel.edu d) yagi@am.sanken.osaka-u.ac.jp