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• W3140783991 abstract "We consider the problem of sparse nonnegative matrix factorization (NMF) with archetypal regularization. The goal is to represent a collection of data points as nonnegative linear combinations of a few nonnegative sparse factors with appealing geometric properties, arising from the use of archetypal regularization. We generalize the notion of robustness studied in Javadi and Montanari (2019) (without sparsity) to the notions of (a) strong robustness that implies each estimated archetype is close to the underlying archetypes and (b) weak robustness that implies there exists at least one recovered archetype that is close to the underlying archetypes. Our theoretical results on robustness guarantees hold under minimal assumptions on the underlying data, and applies to settings where the underlying archetypes need not be sparse. We propose new algorithms for our optimization problem; and present numerical experiments on synthetic and real datasets that shed further insights into our proposed framework and theoretical developments." @default.
• W3140783991 created "2021-04-13" @default.
• W3140783991 creator A5045271820 @default.
• W3140783991 creator A5075423316 @default.
• W3140783991 date "2021-04-08" @default.
• W3140783991 modified "2023-09-26" @default.
• W3140783991 title "Archetypal Analysis for Sparse Nonnegative Matrix Factorization: Robustness Under Misspecification." @default.
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• W3140783991 hasPublicationYear "2021" @default.
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