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Geometric Sparse Coding in Wasserstein Space by Mueller, Marshall; Aeron, Shuchin; Murphy, James M.; Tasissa, Abiy is a scholarly article available to read on EtoBox.

What is Geometric Sparse Coding in Wasserstein Space about?

Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary learning optimize an objective that seeks a dictionary with sufficient representation capacity via barycentric interpolation to approximate the observed training data, but without imposing additional structural properties on the coefficients associated to the dictionary. This leads to dictionaries that densely represent the observed data, which makes interpretation of the coefficients challenging and may also lead to poor empirical performance when using the learned coefficients in downstream tasks. In contrast and motivated by sparse dictionary learning in Euclidean spaces, we propose a geometrically sparse regularizer for Wasserstein space that promotes representations of a data point using only nearby dictionary elements. We show this approach leads to sparse representations in Wasserstein space and addresses the problem of non-uniqueness of barycentric representation. Moreover, when data is generated as Wasserstein barycenters of fixed distributi

Author

Mueller, Marshall; Aeron, Shuchin; Murphy, James M.; Tasissa, Abiy

Published

2022

Language

EN