A Method for Determining Class Subspaces

The subspace approach to the design of a pattern recognition system assumes that pattern classes occupy different subspaces of the pattern representation space. If these subspaces were known then pattern vectors with unknown class membership could be classified into their categories by simply comparing the magnitudes of the projection of these patterns into individual c!ass subspaces. A number of methods for determining class subspaces have been suggested in the pattern recognition literature [1,2,3]. In all these methods candidate axes of the class subspaces are acquired using the KarhunenLoeve expansion [4]. Th2 individual methods then differ in the manner these candidate axes are used for construction of class subspaces. Thus, for instance, while Clafic [ l] utilizes the candidate axes directly without any modification, in both the orthogonal subspace method [2] and the nonorthogonal retrenched subspace method [2] the raw class subspaces defined by the candidate axes are amended so that the resulting subspaces satisfy required conditions. Although the latter two methods are considerably more sophisticated than the seminal procedure Clafic they both have certain limitations. The orthogonal subspace method, for instance, is too restrictive and, consequently, it often fails to yield a solution. The nonorthogonal retrenched subspace method, on the other hand. is difficult to implement eve,? if we resort