Information-Geometric Dimensionality Reduction

W e consider the problem of dimensionality reduction and manifold learning when the domain of interest is a set of probability distributions instead of a set of Euclidean data vectors. In this problem, one seeks to discover a low dimensional representation, called embedding, that preserves certain properties such as distance between measured distributions or separation between classes of distributions. This article presents the methods that are specifically designed for low-dimensional embedding of information-geometric data, and we illustrate these methods for visualization in flow cytometry and demography analysis.