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## Тригонометрическая система функций в проекционных оценках плотности вероятности нейросетевых признаков изображений

Компьютерная оптика. 2018. Т. 42. № 1. С. 149-158.

In this paper we study the image recognition tasks, in which 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 statistical approach with non-parametric estimates of probability density implemented by the probabilistic neural network. We propose the novel statistical classification method based on the density estimators with the 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 WebFaces demonstrates that the proposed approach reduces error rate at 1-5%, and increases computational speed in 1.5-6 times when compared to the original probabilistic neural network for small samples of reference images.