Error-Free Training via Information Structuring in the Classification Problem

The present paper solves the training problem that comprises the initial phases of the classification problem using the data matrix invariant method. The method is reduced to an approximate “slicing” of the information contained in the problem, which leads to its structuring. According to this method, the values of each feature are divided into an equal number of intervals, and lists of objects falling into these intervals are constructed. Objects are identified by a set of numbers of intervals, i.e., indices, for each feature. Assuming that the feature values within any interval are approximately the same, we calculate frequency features for objects of different classes that are equal to the frequencies of the corresponding indices. These features allow us to determine the frequency of any object class as the sum of the frequencies of the indices. For any number of intervals, the maximum frequency corresponds to a class object. If the features do not contain repeated values, the error rate of training tends to zero for an infinite number of intervals. If this condition is not fulfilled, a preliminary randomization of the features should be carried out.