A Unified Framework for Non-Negative Matrix and Tensor Factorisations With a Smoothed Wasserstein Loss

Stephen Y. Zhang; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2021, pp. 4195-4203

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.

Related Material


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[bibtex]
@InProceedings{Zhang_2021_ICCV, author = {Zhang, Stephen Y.}, title = {A Unified Framework for Non-Negative Matrix and Tensor Factorisations With a Smoothed Wasserstein Loss}, booktitle = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops}, month = {October}, year = {2021}, pages = {4195-4203} }