Abstract This paper is addressing problems related to the construction of classifiers based on the Similarity Discriminant Function (SDF), in which the traditional vector representation of a pattern is replaced with matrix data. We introduce potential modifications of the matrix data structure and propose new variants of the SDF. The algorithms that we present were tested on images of handwritten digits and on photographs of human faces, taken from the ORL and CMU‐PIE databases. The results of experiments show that our modifications significantly improved the performance of the original SDF classifier.

This paper presents further discussion and development of the two-parameter Fisher criterion and describes its two modifications (weighted criterion and another multiclass form). The criteria are applied in two algorithms for training linear sequential classifiers. The main idea of the first algorithm is separating the outermost class from the others. The second algorithm, which is a generalization of the first one, is based on the idea of linear division of classes into two subsets. As linear division of classes is not always satisfactory, a piecewise-linear version of the sequential algorithm is proposed as well. The computational complexity of different algorithms is analyzed. All methods are verified on artificial and real-life data sets.

This paper proposes further generalization of a multiclass Fisher's criterion. A formula describing the dependence between the generalized multiclass Fisher's criterion F(Theta) and the variance criterion F(v)Theta has been obtained. Using this formula, it has been shown that the feature extraction methods based on the Karhunen-Loeve (K-L) expansions are special cases of the discriminant method. A full evaluation of heuristic methods for feature extraction based on the K-L expansion with regard to discriminant methods has been presented. A new algorithm for sequential feature extraction has been proposed and is illustrated with an example.

This correspondence considers the extraction of features as a task of linear transformation of an initial pattern space into a new space, optimal with respect to discriminating the data. A solution of the feature extraction problem is given for two multivariate normal distributed pattern classes using an extended Fisher criterion as the distance measure. The introduced distance measure consists of two terms. The first term estimates the distance between classes upon the difference of mean vectors of classes and the second one upon the difference of class covariance matrices. The proposed method is compared to some of the more popular alternative methods: Fukunaga-Koontz method and Foley-Sammon method.