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f-Divergence Approximation for Gaussian Mixtures
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DOI：10.1007/978-3-032-03921-7_11.png)
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Abstract
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Gaussian Mixture Models (GMMs) are important tools for modeling complex data in machine learning tasks and computer vision applications. However, computing f-divergences between GMMs remains challenging due to the absence of a closed-form expression, which led to expensive numerical approximations that limit practical applications. In this paper, we give an efficient f-divergence approximation through the embedding of GMMs into the symmetric positive definite (SPD) matrices. Our main result is that for any compact set of non-degenerate GMM parameters, the f-divergence between two GMMs and the computationally efficient f-divergence between their corresponding centered multivariate normal distributions in the SPD space are uniformly equivalent. Our approach preserves the geometric structure of GMMs while enabling closed-form computation. As an instance the proposed framework is applied on the UIUC texture recognition datasets.
Keywords:
Gaussian Mixture Models
Symmetric Positive Definite Matrices
Divergence
Texture Recognition
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