From the Subspace Methods to the Mutual Subspace Method.

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.