Abstract
Fisher’s linear discriminant analysis (FLDA) has been attracting many researchers and practitioners for several decades thanks to its ease of use and low computational cost. However, FLDA implicitly assumes that all the classes share the same covariance: which implies that FLDA might fail when this assumption is not necessarily satisfied. To overcome this problem, we propose a simple extension of FLDA that exploits a detailed covariance structure of every class by utilizing revealed by the class-wise auto-correlation matrices. The proposed method achieves remarkable improvements classification accuracy against FLDA while preserving two major strengths of FLDA: the ease of use and low computational costs. Experimental results with MNIST and other several data sets in UCI machine learning repository demonstrate the effectiveness of our method.
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Keywords
- Statistical Pattern Recognition
- Discriminant Axis
- MNIST Dataset
- Discriminative Feature Extractor
- Simple Matrix Operation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annals of Eigenics 7, 179–188 (1936)
Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Willey and Sons (1973)
Belhumeur, P.N., et al.: Eigenfaces vs Fisherfaces: Recognition using class specific linear projection. IEEE Transaction of Pattern analysis and Machine PAMI 19, 711–720 (1997)
Hastie, T., Buja, A., Tibshirani, R.: Penelized Discriminant Analysis. The Annals of Statistics 23(1), 73–102 (1995)
Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press (1990)
Baudat, G., Anouar, F.: Generalized Discriminant Analysis Using a Kernel Approach. Neural Computation 12(10), 2385–2404 (2006)
Sierra, A.: High-order Fishers discriminant analysis. Pattern Recognition 35(6), 1291–1302 (2002)
Hastie, T., Tibshirani, R.: Discriminant Analysis by Gaussian Mixture. J. Royal Society of Statistical. Soc. B. 58, 155–176 (1996)
Zhu, M., Martinez, A.M.: Subclass discriminant analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(8), 1274–1286 (2006)
Gkalelis, N., Mezaris, V., Kompatsiaris, I.: Mixture subclass discriminant analysis. IEEE Signal Processing Letters 18(5), 319–322 (2011)
Sakano, H.: A Brief History of the Subspace Methods. In: Koch, R., Huang, F. (eds.) ACCV Workshops 2010, Part II. LNCS, vol. 6469, pp. 434–435. Springer, Heidelberg (2011)
Decell, H.P., Mayekar, S.M.: Feature Combinations and the Divergence Criterion. Computers and Math. with Applications 3, 71–76 (1977)
Loog, M., Duin, R.P.W.: Linear dimensionality reduction via a heteroscedastic extension of LDA: the Chernoff criterion. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(6), 732–739 (2004)
Watanabe, S., Lambert, P.F., Kulikowski, C.A., Buxton, J.L., Walker, R.: Evaluation and selection of variables in pattern recognition. Comp. & Info. Sciences 2, 91–122 (1967)
Lim, G., Park, C.H.: Semi-supervised Dimension Reduction Using Graph-Based Discriminant Analysis. In: 2009 Ninth IEEE International Conference on Computer and Information Technology, pp. 9–13 (2009)
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Sakano, H., Ohashi, T., Kimura, A., Sawada, H., Ishiguro, K. (2012). Extended Fisher Criterion Based on Auto-correlation Matrix Information. In: Gimel’farb, G., et al. Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2012. Lecture Notes in Computer Science, vol 7626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34166-3_45
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DOI: https://doi.org/10.1007/978-3-642-34166-3_45
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