Groups and interactions in data, networks and biology

A multiscale adaptive learning algorithm for high-dimensional data

Wenjing Liao

Johns Hopkins University

Many data sets in applications are in a high-dimensional space but exhibit a low-dimensional structure and we are interested in building a dictionary which provides sparse representations for these data. In this talk I will present adaptive Geometric Multi-Resolution Analysis (GMRA), a dictionary learning method based on a multiscale partition of the data and constructing piecewise affine approximations. It features adaptivity in the sense that our algorithm can automatically learn the distribution of the data and chooses the right partition to use. The finite sample behavior of adaptive GMRA will be provided for certain class of distributions. This is a joint work with Mauro Maggioni at Duke University.