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• W3178270665 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." @default.
• W3178270665 created "2021-07-19" @default.
• W3178270665 creator A5087466081 @default.
• W3178270665 date "2021-04-04" @default.
• W3178270665 modified "2023-09-27" @default.
• W3178270665 title "A unified framework for non-negative matrix and tensor factorisations with a smoothed Wasserstein loss" @default.
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• W3178270665 hasPublicationYear "2021" @default.
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