Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction

Branislav Popović (), Marko Janev, Lidija Krstanović, Nikola Simić and Vlado Delić
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Branislav Popović: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Marko Janev: Institute of Mathematics, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
Lidija Krstanović: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Nikola Simić: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia
Vlado Delić: Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia

Mathematics, 2022, vol. 11, issue 1, 1-22

Abstract: Gaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simple statistical representations of underlying data. Those representations typically require many high-dimensional GMM components that consume large computing resources and increase computation time. On the other hand, real-time applications require computationally efficient algorithms and for that reason, various GMM similarity measures and dimensionality reduction techniques have been examined to reduce the computational complexity. In this paper, a novel GMM similarity measure is proposed. The measure is based on a recently presented nonlinear geometry-aware dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices. The algorithm is applied over SPD representations of the original data. The local neighborhood information from the original high-dimensional parameter space is preserved by preserving distance to the local mean. Instead of dealing with high-dimensional parameter space, the method operates on much lower-dimensional space of transformed parameters. Resolving the distance between such representations is reduced to calculating the distance among lower-dimensional matrices. The method was tested within a texture recognition task where superior state-of-the-art performance in terms of the trade-off between recognition accuracy and computational complexity has been achieved in comparison with all baseline GMM similarity measures.

Keywords: Gaussian Mixture Models; similarity measures; dimensionality reduction; texture recognition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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