Correlations of random classifiers on large data sets

Classification of large data sets by feedforward neural networks is investigated. To deal with unmanageably large sets of classification tasks, a probabilistic model of their relevance is considered. Optimization of networks computing randomly chosen classifiers is studied in terms of correlations of classifiers with network input–output functions. Effects of increasing sizes of sets of data to be classified are analyzed using geometrical properties of high-dimensional spaces. Their consequences on concentrations of values of sufficiently smooth functions of random variables around their mean values are applied. It is shown that the critical factor for suitability of a class of networks for computing randomly chosen classifiers is the maximum of sizes of the mean values of their correlations with network input–output functions. To include cases in which function values are not independent, the method of bounded differences is exploited.