Sequential analysis in Fourier probabilistic neural networks

Abstract

In this paper, the computational complexity of the probabilistic neural network for the classification of high-dimensional data is improved. At first, the class probability densities are estimated by using only a few principal components of an observed point. The Gaussian–Parzen kernel is replaced by the orthogonal series estimates of class-conditional densities for each principal component using the Fourier series to speed up a decision-making procedure. The unreliable classes are found for which a likelihood ratio to the maximal likelihood does not exceed a certain threshold. The next components are used to refine these estimates only for other classes, and such a sequential analysis of principal components is repeated until only one reliable class is obtained. Experimental study for image recognition with features extracted by deep convolutional neural networks including EfficientNets demonstrates that our approach is more accurate and 15–60 times faster than the baseline instance-based learning methods.