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Abstract:
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High-dimensional datasets arise prominently in a range of contemporary problem domains throughout science and technology. In many of these settings, the data are often constrained structurally so that they only have a few degrees of freedom relative to their ambient dimension. Methods such as manifold learning, dictionary learning, and others aim at computationally identifying such latent low-dimensional structure. In this talk, we describe a new approach to inferring the low-dimensional structure underlying a dataset by fitting a convex set with favorable facial structure to the data (in a manner to be suitably defined). Our procedure is based on computing a structured matrix factorization, and it includes several previous techniques as special cases. We illustrate the utility of our method with experimental demonstrations in applications. (Joint work with Yong Sheng Soh)
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