A practical application of kernel-based fuzzy discriminant analysis
Jian-Qiang Gao; Li-Ya Fan; Li Li; Li-Zhong Xu
International Journal of Applied Mathematics and Computer Science (2013)
- Volume: 23, Issue: 4, page 887-903
- ISSN: 1641-876X
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top- Aydilek, I.B. and Arslan, A. (2012). A novel hybrid approach to estimating missing values in databases using k-nearest neighbors and neural networks, International Journal of Innovative Computing, Information and Control 7(8): 4705-4717.
- Baudat, G. and Anouar, F. (2000). Generalized discriminant analysis using a kernel approach, Neural Computation 12(10): 2385-2404.
- Belhumeur, P.N. and Kriegman, D.J. (1997). Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection, IEEE Transactions on Pattern Analysis Machine Intelligence 19(7): 711-720.
- Chen, L.F., Liao, H. Y.M., Ko, M.T., Lin, J.C. and Yu, G.J. (2000). A new LDA-based face recognition system which can solve the small sample size problem, Pattern Recognition 33(10): 1713-1726.
- Cover, T.M. (1965). Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition, IEEE Transactions on Electronic Computers 14(3): 326-334. Zbl0152.18206
- Demsar, J. (2006). Statistical comparisons of classifiers over multiple data sets, The Journal of Machine Learning Research 7(1): 1-30. Zbl1222.68184
- Dietterich, T.G. (1998). Approximate statistical tests for comparing supervised classification learning algorithms, Neural Computation 10(7): 1895-1923.
- Duda, R.O., Hart, P.E. and Stork, D.G. (2012). Pattern Classification, John Wiley and Sons, New York, NY. Zbl0968.68140
- Friedman, J.H. (1989). Regularized discriminant analysis, Journal of the American Statistical Association 84(405): 165-175.
- Fukunaga, K. (1990). Introduction to Statistical Pattern Recognition, San Diego, California, CA. Zbl0711.62052
- Gao, J. and Fan, L. (2011). Kernel-based weighted discriminant analysis with QR decomposition and its application face recognition, WSEAS Transactions on Mathematics 10(10): 358-367.
- Gao, J., Fan, L. and Xu, L. (2012). Solving the face recognition problem using QR factorization, WSEAS Transactions on Mathematics 11(1): 728-737.
- Gao, J.Q., Fan, L.Y. and Xu, L.Z. (2013). Median null (sw)-based method for face feature recognition, Applied Mathematics and Computation 219(12): 6410-6419. Zbl06281820
- Gao, Q.X., Zhang, L. and Zhang, D. (2008). Face recognition using FLDA with single training image per person, Applied Mathematics and Computation 205(2): 726-734. Zbl1152.68679
- Hastie, T., Buja, A. and Tibshirani, R. (1995). Penalized discriminant analysis, The Annals of Statistics 23(1): 73-102. Zbl0821.62031
- Hastie, T., Tibshirani, R. and Buja, A. (1994). Flexible discriminant analysis by optimal scoring, Journal of the American Statistical Association 89(428): 1255-1270. Zbl0812.62067
- Hastie, T., Tibshirani, R., Friedman, J. and Franklin, J. (1991). The elements of statistical learning: Data mining, inference and prediction, The Mathematical Intelligencer 27(2): 83-85.
- Hong, Z.Q. and Yang, J.Y. (2005). Optimal discriminant plane for a small number of samples and design method of classifier on the plane, Pattern Recognition 24(4): 317-324.
- Jain, A. and Zongker, D. (1997). Feature selection: Evaluation, application, and small sample performance, IEEE Transactions on Pattern Analysis and Machine Intelligence 19(2): 153-158.
- Keller, J.M., Gray, M.R. and Givens, J.A. (1985). A fuzzy k-nearest neighbor algorithm, IEEE Transactions on Systems, Man and Cybernetics 15(4): 580-585.
- Koc, M. and Barkana, A. (2011). A new solution to one sample problem in face recognition using FLDA, Applied Mathematics and Computation 217(24): 10368-10376. Zbl1221.62096
- Kwak, K.C. and Pedrycz, W. (2005). Face recognition using a fuzzy Fisherface classifier, Pattern Recognition 38(10): 1717-1732.
- Lee, H.M., Chen, C.M., Chen, J.M. and Jou, Y.L. (2001). An efficient fuzzy classifier with feature selection based on fuzzy entropy, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 31(3): 426-432.
- Liu, F. and Xue, X. (2012). Constructing kernels by fuzzy rules for support vector regressions, International Journal of Innovative Computing, Information and Control 8(7): 4811-4822.
- Liu, Y. (2006). Website of the ORL face database, http://www.cam-orl.co.uk.
- Liu, Y., Liu, X. and Su, Z. (2008). A new fuzzy approach for handling class labels in canonical correlation analysis, Neurocomputing 71(7): 1735-1740.
- Loog, M., Duin, R.P.W. and Haeb-Umbach, R. (2001). Multiclass linear dimension reduction by weighted pairwise fisher criteria, IEEE Transactions on Pattern Analysis and Machine Intelligence 23(7): 762-766.
- Pahasa, J. and Ngamroo, I. (2012). PSO based kernel principal component analysis and multi-class support vector machine for power quality problem classification, International Journal of Innovative Computing, Information and Control 8(3): 1523-1539.
- Pal, N.R. and Eluri, V.K. (1998). Two efficient connectionist schemes for structure preserving dimensionality reduction, IEEE Transactions on Neural Networks 9(6): 1142-1154.
- Phillips, P.J. (2004). Website of the facial recognition technology (FERET) database, http://www.itl.nist.gov/iad/humanid/feret/feret-master.html.
- Raudys, S.J. and Jain, A.K. (1991). Small sample size effects in statistical pattern recognition: Recommendations for practitioners, IEEE Transactions on Pattern Analysis and Machine Intelligence 13(3): 252-264.
- Schölkopf, B., Smola, A. and Müller, K.R. (1998). Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation 10(5): 1299-1319.
- Swets, D.L. and Weng, J.J. (1996). Using discriminant eigenfeatures for image retrieval, IEEE Transactions on Pattern Analysis and Machine Intelligence 18(8): 831-836.
- Świercz, E. (2010). Classification in the Gabor time-frequency domain of non-stationary signals embedded in heavy noise with unknown statistical distribution, International Journal of Applied Mathematics and Computer Science 20(1): 135-147, DOI: 10.2478/v10006-010-0010-x. Zbl1300.62045
- Vapnik, V.N. (1998). Statistical Learning Theory, Wiley, New York, NY. Zbl0935.62007
- Woźniak, M. and Krawczyk, B. (2012). Combined classifier based on feature space partitioning, International Journal of Applied Mathematics and Computer Science 22(4): 855-866, DOI: 10.2478/v10006-012-0063-0.
- Wu, X.H. and Zhou, J.J. (2006). Fuzzy discriminant analysis with kernel methods, Pattern Recognition 39(11): 2236-2239. Zbl1102.68606
- Yang, J., Frangi, A.F., Yang, J.Y., Zhang, D. and Jin, Z. (2005). KPCA plus LDA: A complete kernel Fisher discriminant framework for feature extraction and recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence 27(2): 230-244.
- Yang, J. and Yang, J.Y. (2001). An optimal FLD algorithm for facial feature extraction, Proceedings of SPIE Intelligent Robots and Computer Vision XX: Algorithms, Techniques, and Active Vision, Boston, MA, USA, pp. 438-444.
- Yang, J. and Yang, J.Y. (2003). Why can LDA be performed in PCA transformed space?, Pattern Recognition 36(2): 563-566.
- Yang, W., Wang, J., Ren, M., Zhang, L. and Yang, J. (2009). Feature extraction using fuzzy inverse FDA, Neurocomputing 73(13): 3384-3390.
- Yu, H. and Yang, J. (2001). A direct LDA algorithm for high-dimensional data with application to face recognition, Pattern Recognition 34(10): 2067-2070. Zbl0993.68091
- Zadeh, L.A. (1965). Fuzzy sets, Information and Control 8(3): 338-353. Zbl0139.24606
- Zheng, Y.J., Yang, J., Yang, J.Y. and Wu, X.J. (2006a). A reformative kernel Fisher discriminant algorithm and its application to face recognition, Neurocomputing 69(13): 1806-1810.
- Zheng, Y., Yang, J., Wang, W., Wang, Q., Yang, J. and Wu, X. (2006b). Fuzzy kernel Fisher discriminant algorithm with application to face recognition, 6th World Congress on Intelligent Control and Automation WCICA, Dalian, China, Vol. 2, pp. 9669-9672.
- Zhuang, X.S. and Dai, D.Q. (2005). Inverse Fisher discriminate criteria for small sample size problem and its application to face recognition, Pattern Recognition 38(11): 2192-2194.
- Zhuang, X.S. and Dai, D.Q. (2007). Improved discriminate analysis for high-dimensional data and its application to face recognition, Pattern Recognition 40(5): 1570-1578. Zbl1113.68086