Features of the process of object classification on the basis of discriminant functions

Abstract

An alternative approach to the processing of elements of linear discriminant functions for the classification of objects is proposed in the paper. This approach is based on the method of processing a vector array of data by differential slices which is distributed in the column of matrix representation of elements of discriminant functions. In its turn, it indicates the spatially distributed nature of the processing of matrix elements with dimension m×n, where m is the number of classes, n is the dimension of the input data vector. The linearity of the representation of each discriminant function in a set of discriminant functions allows not only to represent their terms in the form of matrix elements, but also apply to their processing some rules concerning such properties as associativity and commutativity of components (terms) of the sum. As a result, such complex procedures as multi-operand summation in the formation of each discriminant function are replaced. Moreover, it is followed by their comparison with each other with the aim of identifying the one with the maximum value. In each processing cycle of the proposed method, the basic operation is a simultaneous reduction in the magnitude of the elements similarity of the same name in the columns of the matrix, which allows determining the maximum value of the discriminant function. The operation of transposition (advancement) to the edge of all current zero elements in each row of the matrix is also involved. This approach is applied to linear discriminant functions as an apparatus of the statistical method of object classification. Consequently, according to the known decision rule, the maximum discriminant function determines the corresponding class to which the input object, represented as an n-dimensional feature vector, belongs. One of the options for the hardware application of such classifier is the decision support subsystem for medical diagnosis.