Trigonometric series in orthogonal expansions for density estimates of deep image features

In this paper we study image recognition tasks in which the images are described by high dimensional feature vectors extracted with deep convolutional neural networks and principal component analysis. In particular, we focus on the problem of high computational complexity of a statistical approach with non-parametric estimates of probability density implemented by the probabilistic neural network. We propose a novel statistical classification method based on the density estimators with orthogonal expansions using trigonometric series. It is shown that this approach makes it possible to overcome the drawbacks of the probabilistic neural network caused by the memory-based approach of instance-based learning. Our experimental study with Caltech-101 and CASIA WebFace datasets demonstrates that the proposed approach reduces the error rate by 1-5 % and increases the computational speed by 1.5 - 6 times when compared to the original probabilistic neural network for small samples of reference images.