A simple way to assess the spectral lines informativity of a chi-square molecule in analyzing small samples of biometric data

Abstract

The prerequisites for reducing the test sample chi-square Pearson test size from 400 to 32 or fewer examples while maintaining its power are considered. The urgency of the problem results from the fact that when learning and testing the biometric identification means to identify the personality, it is not possible to use large volumes of learning and test samples. The conditions under which the chi-square test on small samples from the continuous distribution of values becomes a discrete distribution of values are formalized. Normal and uniform laws of values distribution use histograms with uniform intervals, which accurately relate the central intervals of the histogram to the mathematical expectation calculated on the test sample. 16 experiments shown that the chi-square-synchronized test built on histograms with four equal intervals has a discrete probability spectrum consisting of only 20 significant spectral lines. A simple method for estimating the informativity of each of the important spectral components is proposed. Traditional statistical assessments can be strengthened by the following deeper level of the spectral components analysis of small samples of biometric data. The second deeper level of statistical processing should be substantially more powerful. Under the same conditions, the computational informativity increases from 2.22 bits to 24.95 bits due to the transition from simple continual calculations to discrete calculations of high computational complexity.