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Published in:
2010 | OriginalPaper | Chapter
Designing a Metric for the Difference between Gaussian Densities
Authors : Karim T. Abou–Moustafa, Fernando De La Torre, Frank P. Ferrie
Published in: Brain, Body and Machine
Publisher: Springer Berlin Heidelberg
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Measuring the difference between two multivariate Gaussians is central to statistics and machine learning. Traditional measures based on the Bhattacharyya coefficient or the symmetric Kullback-Leibler divergence do not satisfy metric properties necessary for many algorithms. This paper proposes a metric for Gaussian densities. Similar to the Bhattacharyya distance and the symmetric Kullback-Leibler divergence, the proposed metric reduces the difference between two Gaussians to the difference between their parameters. Based on the proposed metric we introduce a symmetric and positive semi-definite kernel between Gaussian densities. We illustrate the benefits of the proposed metric in two settings: (1) a supervised problem, where we learn a low-dimensional projection that maximizes the distance between Gaussians, and (2) an unsupervised problem on spectral clustering where the similarity between samples is measured with our proposed kernel.