Confidence Lipschitz classifiers: an instrument of guaranteed reliability

Abstract

A new method of guaranteed solution for multiclass classification problem of stochastic objects is proposed. Within the framework of the proposed approach, the classification result is a finite set of class indices which with a predetermined confidence coefficient contains the index of the class to which the object being classified corresponds. In this case, the classification itself is realized on the basis of using a classifier of the new type which is called a confidence Lipschitz classifier. The definition of the confidence Lipschitz classifier is given and its main properties have been studied. Among them, the property of guaranteed reliability of the classification which is expressed in the construction of a confidence set of limited size containing the index of the true class with a predetermined coefficient of confidence, has been studied. The case of the assembly of Lipschitz classifiers, the properties of which are formalized in the form of a theorem, is considered. We consider a practically important example of using the proposed approach in the problems of compensation of the noise process dynamics in the channels of the fiber-optic monitoring system. The proposed approach is promising for use in those classification tasks in which the number of classes has an order higher than the second, including large-scale biometric identification systems as well as multi-channel systems for monitoring extended objects.