Abstract
The Subspace Method [25, 21] is a classic method of pattern recognition, and has been applied to various tasks. The Mutual Subspace Method [19] is an extension of the Subspace Methods, in which canonical angles (principal angles) between two subspaces are used to define similarity between two patterns (or two sets of patterns). The method is applied to face recognition and character recognition in Toshiba Corporation. The Karhunen-Lo‘eve eigenvalue method or Principal Component Analysis (PCA) [8, 13, 17] is a well-known approach to form a subspace that approximates a distribution of patterns, and it was introduced as a tool of pattern recognition [10, 24]. The extension from the Subspace Methods to the Mutual Subspace Method corresponds to the difference between PCA and Canonical Correlation Analysis (CCA) [9]. In this chapter, the Mutual Subspace Method, its mathematical foundations and its applications are described.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)
Björck, Å., Golub, G.H.: Numerical Methods for Computing Angles between Linear Subspaces. Mathematics of Computation 27, 579–594 (1975)
Chatelin, F.: Valeurs Propres de Matrices, Masson, Paris (1988)
Dixmier, M.: Etude sur les Varietes et les Operaterns de Julia, avec Quelques Applications. Bull. Soc. Math. France 77, 11–101 (1949)
Fu, K.S., Yu, T.S.: Statistical Pattern Classification Using Contextual Information. John Wiley and Sons, New York (1980)
Fukui, K., Yamaguchi, O.: Face Recognition using multi-viewpoint patterns for robot vision. In: Proceedings of the 11th International Symposium of Robotics Research (ISRR 2003), pp. 192–201 (2003)
Grenander, U.: Abstract Inference. John Wiley, New York (1981)
Hotelling, H.: Analysis of a Complex Statistical Variables into Principal Components. J. Educ. Psych. 24, 417–441, 498–520 (1933)
Hotelling, H.: Relations between Two Sets of Variates. Biometrica 28, 321–377 (1936)
Iijima, T.: Basic Theory on Feature Extraction of Visual Pattern. J. IEICE 46, 1714 (1963)
Iijima, T., Genchi, H., Mori, K.: A Theoretical Study of Pattern Recognition by Matching Method. In: Proceedings of the First USA-Japan Computer Conference, pp. 42–48 (1972)
Iijima, T., Genchi, H., Mori, K.: A Theory of Character Recognition by Matching Method. In: Proceedings of the 1st International Conference on Pattern Recognition, pp. 50–56 (1973)
Karhunen, K.: Zur Spektraltheorie stochastischer Prozesse. Ann. Acad. Sci. Fennicae 34 (1946)
Kim, T., Wong, S., Cipolla, R.: Tensor Canonical Correlation Analysis for Action Classification. In: Proceedings of the International Conference on Computer Vision and Pattern Recognition (2007)
Kittler, J., Young, P.C.: A New Approach to Feature Selection Based on the Karhunen-Loeve Expansion. Pattern Recognition 5(4), 335–352 (1973)
Kohonen, T.: Associative Memory – a System-Theoretical Approach. Springer, Heidelberg (1977)
Loève, M.: Functions alèatoires du second ordre. Processus stochastique et mouvement Brownien (Lèvy, P.), 366–420, Gauthier-Villars, Paris (1948)
Maeda, K., Kurosawa, Y., Asada, H., Sakai, K., Watanabe, S.: Handprinted Kanji Recognition by Pattern Matching Method. In: Proceedings of the International Conference on Pattern Recognition, pp. 789–792 (1982)
Maeda, K., Yamaguchi, O., Fukui, K.: Towards 3-Dimensional Pattern Recognition. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 1061–1068. Springer, Heidelberg (2004)
Maeda, K., Yamaguchi, O., Fukui, K.: A Fundamental Discussion on 3-Dimensional Pattern Recognition Using Canonical Angles between Subspaces for the Purpose of Differentiating Face and its Photograph. Systems and Computers in Japan 38, 11–20 (2007)
Oja, E.: Subspace Methods of Pattern Recognition. Research Studies Press, Letchworth (1983)
Tauschek, G.: Reading Machine, US Patent 2,026,329 (1935)
Turk, M., Pentland, A.: Face Recognition Using Eigenfaces. In Proceedings of the International Conference on Compute Vision and Pattern Recognition, 453–458 (1993)
Watanabe, S.: Karhunen-Loève Expansion and Factor Analysis. In: Trans. 4th Prague Conf. on Inf. Theory, Stat. Decision Functions, and Random Proc., pp. 635–660 (1965)
Watanabe, S., Lambert, P.F., Kulikowsky, C.A., Buxton, J.L., Walker, R.: Evaluation and Selection of Variables in Pattern Recognition. In: Tou, J. (ed.) Computer and Information Science II, pp. 91–122. Academic Press, New York (1967)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Maeda, Ki. (2010). From the Subspace Methods to the Mutual Subspace Method. In: Cipolla, R., Battiato, S., Farinella, G.M. (eds) Computer Vision. Studies in Computational Intelligence, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12848-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-12848-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12847-9
Online ISBN: 978-3-642-12848-6
eBook Packages: EngineeringEngineering (R0)