Classification Based on Invariants of the Data Matrix

Abstract

The paper proposes a solution to the problem classification by calculating the sequence of matrices of feature indices that approximate invariants of the data matrix. Here the feature index is the index of interval for feature values, and the number of intervals is a parameter. Objects with the equal indices form granules, including information granules, which correspond to the objects of the training sample of a certain class. From the ratios of the information granules lengths, we obtain the frequency intervals of any feature that are the same for the appropriate objects of the control sample. Then, for an arbitrary object, we find object probability estimation in each class and then the class of object that corresponds to the maximum probability. For a sequence of the parameter values, we find a converging sequence of error rates. An additional effect is created by the parameters aimed at increasing the data variety and compressing rare data. The high accuracy and stability of the results obtained using this method have been confirmed for nine data set from the UCI repository. The proposed method has obvious advantages over existing ones due to the algorithm’s simplicity and universality, as well as the accuracy of the solutions.