Statistical classification and purposeful projection of observations into a space of dimensionality no more than the number of classes

Consideration was given to the reduction of dimensionality in the problems of statistical classification. For the case where the observations from different classes have the same covariance matrix, the method of purposeful projection was used to transform the initial space of attributes into a space of dimensionality no more than the number of classes which do not modify the Mahalanobis interclass distances.