A theoretical study on the orthonormal discriminant vector method for pattern recognition

Discriminant analysis has a serious shortcoming, namely, that in the m-class problems the maximum number of features is m - 1. To overcome this shortcoming, Okada and Tomita proposed the orthonormal discriminant vector (ODV) method. In the two-class problem, the ODV method is equivalent to the method of Foley and Sammon. Experimental results show that the ODV method is more powerful than discriminant analysis. However, no attempt has been made to investigate the properties of the ODV method theoretically. In this paper the properties of the ODV method are studied from a theoretical viewpoint. In particular, the condition that discriminant analysis produces an ortho-normal coordinate system is discussed. Based on this condition, the ODV method is compared with discriminant analysis.