A New Classification Approach using Discriminant Functions

There are many algorithms for, and many applications of classification and discrimination (grouping of a set of objects into subsets of similar objects where the objects in different subsets are different) in several diverse fields [2-15, 23, 24], ranging from engineering to medicine, to econometrics, etc. Some examples are automatic target recognition (ATR), fault and maintenance-time recognition, optical character recognition (OCR), speech and speaker recognition, etc. In this study, a new approach and algorithm to the classification problem are described with the goal of finding a single (possibly vector-valued) linear discriminant function. This approach is in terms of some optimal centers of mass for the transformed feature vectors of each class, the transforms being performed via the discriminant functions. As such, it follows the same philosophy which is behind the approaches such as principal component analysis (PCA), Fisher’s linear discriminant functions (LDF), and minimum total covariance (MTC) [1-16, 22, 25-28], providing alternatives which extend this work. Linear discriminant functions (LDF) are often used in pattern recognition to classify a given object or pattern, based on its features, into one of several given classes. For simplicity, consider the discrimination problem for two classes. Let x = [x1, x2, ..., xm] be the