Dictionary learning is a prototypical machine learning problem with broad applications throughout computer vision and signal processing. Given a set of training data, the goal is to learn a dictionary of prototype patterns that provide a sparse (parsimonious) representation of the data. Such a dictionary then enables a variety of problems to be solved by exploiting sparse structure; example problems include noise removal, super-resolution, deblurring, imputing missing data, and classification. Like many problems in machine learning, dictionary learning can be formulated as an optimization problem. Unfortunately, this optimization problem is non-convex, making it potentially difficult to solve to global optimality. Additional questions arise in how to deal with multi-modal data and distributed data, such as might be collected by multiple satellites, UAVs, etc. This presentation will summarize our team’s research on theory and algorithms for solving non-convex matrix-valued optimization problems such as dictionary learning, particularly in multi-modal, distributed, and streaming contexts. We welcome the opportunity to discuss further transitioning this technology for Naval applications.

Michael Wakin

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