SVD based initialization: A head start for nonnegative matrix factorization

Abstract

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Non‐negative Matrix Factorization for the identification of patterns of atmospheric pressure and geopotential for the Northern Hemisphere

“…As found out, the trick is to seek the strategy amongst other constrained low-rank factorization schemes like clustering and SVD. Boutsidis and Gallopoulos (2008) suggested the NNDSVD, an algorithm that contains no randomization and that can readily be combined with all existing NMF algorithms.…”

“…This truncation creates a matrix V r that is the best approximation of V of rank at most r in terms of the Frobenius norm (according to the Schmidt-Eckart-Young-Mirsky theory, see also Boutsidis and Gallopoulos, 2008). Considering the non-negativity constraint, each C (i) in (9) must be approximated by its non-negative section C (i)+ (i.e.…”

“…In particular, we need an initialization pushing the algorithms to converge to a certain meaningful minimum solution, so that every time the same conclusions can be drawn -even for different numbers r of NMF-factors. A possible answer to this question could be an algorithm developed by Boutsidis and Gallopoulos (2008), called Non-negative Double Singular Value Decomposition (NNDSVD) based on SVD. We consider this method to be an appropriate strategy, because SVD is closely related to PCA, and thus, with regard to climate variability provides reasonable starting values (see Subsection 2.6).…”

A Matrix Factorization Approach for Integrating Multiple Data Views

“…The sensitivity of NMF-like algorithms to the choice of initial factors has been noted by a number of authors [12,13]. While stochastic initialization is widely used in this context, ideally we would like to produce a single integrated clustering without requiring multiple runs of the integration process.…”

“…While stochastic initialization is widely used in this context, ideally we would like to produce a single integrated clustering without requiring multiple runs of the integration process. Therefore to initialize the integration process, we populate the pair (P, H) by employing the deterministic NNDSVD strategy described by Boutsidis & Gallopoulos [13]. This strategy applies two sequential SVD processes to the matrix X to produce a pair of initial factors.…”