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Nonnegative Matrix Factorization over Continuous Signals using Parametrizable Functions
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DOI：10.1016/j.neucom.2019.11.109.png)
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Abstract
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Nonnegative matrix factorization is a popular data analysis tool able to extract significant features from nonnegative data. We consider an extension of this problem to handle functional data, using parametrizable nonnegative functions such as polynomials or splines. Factorizing continuous signals using these parametrizable functions improves both the accuracy of the factorization and its smoothness. We introduce a new approach based on a generalization of the Hierarchical Alternating Least Squares algorithm. Our method obtains solutions whose accuracy is similar to that of existing approaches using polynomials or splines, while its computational cost increases moderately with the size of the input, making it attractive for large-scale datasets. (C) 2020 Elsevier B.V. All rights reserved.
Keywords:
Nonnegative matrix factorization
Hierarchical alternating least squares (HALS)
Functional nonnegative matrix factorization
(projection on) nonnegative polynomials
(projection on) nonnegative splines
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6.5
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2.5W
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6.5W
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