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 Computer Optics, 2018, Volume 42, Issue 1, Pages 149–158 (Mi co489)

NUMERICAL METHODS AND DATA ANALYSIS

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

A. V. Savchenko

National Research University Higher School of Economics, Nizhny Novgorod, Russia

Abstract: 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.

Keywords: statistical pattern recognition, image processing, deep convolutional neural networks, probabilistic neural network, orthogonal series estimates, unconstrained face identification.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÄ-306.2017 Russian Science Foundation 14-41-00039 The work is supported by Russian Federation President grant no. ÌÄ-306.2017.9 and Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics. The research in Sections 3 and 4 was supported by RSF (Russian Science Foundation) project No. 14-41-00039.

DOI: https://doi.org/10.18287/2412-6179-2018-42-1-149-158

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Accepted:19.01.2018

Citation: A. V. Savchenko, “Trigonometric series in orthogonal expansions for density estimates of deep image features”, Computer Optics, 42:1 (2018), 149–158

Citation in format AMSBIB
\Bibitem{Sav18} \by A.~V.~Savchenko \paper Trigonometric series in orthogonal expansions for density estimates of deep image features \jour Computer Optics \yr 2018 \vol 42 \issue 1 \pages 149--158 \mathnet{http://mi.mathnet.ru/co489} \crossref{https://doi.org/10.18287/2412-6179-2018-42-1-149-158}