Nonnegative Matrix Factorization (NMF) is a linear dimensionality reduction technique for extracting hidden and intrinsic features of high-dimensional data sets. Recently, several Projective NMF (P-NMF) methods have been proposed for the purpose of resolving issues associated with the standard NMF approach. Experimental results show that P-NMF algorithms outperform the standard NMF method in some aspects. But some basic issues still affect the existing NMF and P-NMF methods, these include slow convergence rate, low reconstruction accuracy and dense basis factors. In this article, we propose a new and generalized hybrid algorithm by combining the concept of alternating least squares with the multiplicative update rules of the α-divergence-based P-NMF method. We have conducted extensive numerical experiments on 7 real-world data sets and compared the new algorithm with several state-of-the-art methods. The attractive features and added advantages of the new algorithm include remarkable clustering performances, providing highly “orthogonal” and very sparse basis factors, and extracting distinctive and better localized features of the original data than its counterparts.

Hybrid projective nonnegative matrix factorization based on α-divergence and the alternating least squares algorithm

Del Buono, Nicoletta
2020

Abstract

Nonnegative Matrix Factorization (NMF) is a linear dimensionality reduction technique for extracting hidden and intrinsic features of high-dimensional data sets. Recently, several Projective NMF (P-NMF) methods have been proposed for the purpose of resolving issues associated with the standard NMF approach. Experimental results show that P-NMF algorithms outperform the standard NMF method in some aspects. But some basic issues still affect the existing NMF and P-NMF methods, these include slow convergence rate, low reconstruction accuracy and dense basis factors. In this article, we propose a new and generalized hybrid algorithm by combining the concept of alternating least squares with the multiplicative update rules of the α-divergence-based P-NMF method. We have conducted extensive numerical experiments on 7 real-world data sets and compared the new algorithm with several state-of-the-art methods. The attractive features and added advantages of the new algorithm include remarkable clustering performances, providing highly “orthogonal” and very sparse basis factors, and extracting distinctive and better localized features of the original data than its counterparts.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/247637
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact