A unified framework for non-negative matrix and tensor factorisations with a smoothed Wasserstein loss

Stephen Y. Zhang

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arXiv · 2104.01708

A unified framework for non-negative matrix and tensor factorisations with a smoothed Wasserstein loss

Stephen Y. Zhang

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Abstract

Non-negative matrix and tensor factorisations are a classical tool for finding low-dimensional representations of high-dimensional datasets. In applications such as imaging, datasets can be regarded as distributions supported on a space with metric structure. In such a setting, a loss function based on the Wasserstein distance of optimal transportation theory is a natural choice since it incorporates the underlying geometry of the data. We introduce a general mathematical framework for computing non-negative factorisations of both matrices and tensors with respect to an optimal transport loss. We derive an efficient computational method for its solution using a convex dual formulation, and demonstrate the applicability of this approach with several numerical illustrations with both matrix and tensor-valued data.

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Stephen Y. Zhang. 2021-04-04. A unified framework for non-negative matrix and tensor factorisations with a smoothed Wasserstein loss. https://arxiv.org/abs/2104.01708

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