Machine learning on manifolds: Classifying PDFs

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This paper introduces a new framework for classifying probability density functions. The proposed method fits in the class of constrained Gaussian processes indexed by distribution functions. Firstly, instead of classifying observations directly, we consider their isometric transformations which enables us to satisfy both positiveness and unit integral hard constraints. Secondly, we introduce the theoretical proprieties and give numerical details of how to decompose each transformed observation in an appropriate orthonormal basis. As a result, we show that the coefficients are belonging to the unit sphere when equipped with the standard Euclidean metric as a natural metric. Lastly, the proposed methods are illustrated and successfully evaluated in different configurations and with various dataset.