Histogram-Based Fisher Information Embedding for Manifolds Clustering and Visualization

In this paper, a nonparametric histogram-based fisher information embedding method is presented for clustering and visualizing data sets with non-Euclidean geometric structures. It is on the assumption that each data set is derived from a probability distribution that can be characterized by a probability density function (PDF) lying on a statistical manifold. The dissimilarities between data sets can be quantified with the corresponding geodesic distances on statistical manifold from the views of information geometry. Our method is designed to convert data distribution information into simplex discretely, thereby a similarity measure can be adopted with simplex geometry, further clustering or visualizing original manifolds can be performed on a low-dimensional Euclidean subspace via manifold learning. Experiments on clustering Swiss Roll and s-curve submanifolds and reconstructing a sphere demonstrate the effectiveness of our method.