Nonnegative Matrix Factorization through Canonical Edges
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Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: nonnegative matrix factorization, orthogonal
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TL;DR: New approach to NMF that produces a closed-form solution to ONMF and an improvement over EVA
Abstract: In this paper we present a novel approach to nonnegative matrix factorization (NMF) by introducing the concept of nonnegative canonical edges (NCEs). These NCEs are intersections of the principal subspace containing the data to be factored with canonical faces of the nonnegative orthant. Through this lens, our approach yields a closed-form solution to the special NMF case where (at least one of) the factors are required to be orthogonal. In the general NMF case, NCEs provide a deterministic optimal solution whenever the data resides within or in proximity to the cone formed by the NCEs. Furthermore, NCEs provide an improved initialization for classical NMF methods in general. Despite these advancements, numerous fundamental questions regarding NCEs in the context of NMF remain unexplored, offering exciting avenues for future research.
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Submission Number: 2103
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