False learning function of an acoustic signal classifier

Abstract

In works on statistical pattern recognition that use learning and examination, results of the learning depend not only on the feature efficiencies, but also on the proportion between the capacity of the decision rule, length of the learning sample, and number of features. It is usually difficult to calculate the recognition errors, which connect these basic quantities for a particular classifier, while the calculations are approximate and do not clearly characterize the results obtained in the process of the study.

The purpose of this work is to develop a simple, clear, and efficient technique for the experimental estimation of the expected classification errors of the recognition engine employed in learning. The algorithm produces a sample of random noise segments, which is included in the recognition algorithm instead of the features of real signals. Portions of this uniform sample imitate different classes. The false learning function is produced as a result of a successive increase in the number of random features used in the recognition. The corresponding growth of the probability of recognizing artificial classes in such a false learning depends on the length of the learning sample and on the capacity of the decision rule employed.

The main result of this work is the false learning function proposed for any particular classifier. The function is obtained for the same length of the learning sample as that of the one used to recognize real signals. The validity of results obtained in real signals can be estimated by comparing this function with experimental signal recognition probabilities with the same number of features.

The simple false learning function is useful to characterize the validity of any experimental results on the statistical signal recognition in acoustics, seismoacoustics, and hydroacoustics; in speech recognition; in medical and industrial diagnostics; in radar; and in other fields.