Regularized active set least squares algorithm for nonnegative matrix factorization in application to Raman spectra separation

Authors:
Rafal Zdunek
Affiliations:
Institute of Telecommunications, Teleinformatics and Acoustics, Wroclaw University of Technology, Wroclaw, Poland
Venue:
IWANN'11 Proceedings of the 11th international conference on Artificial neural networks conference on Advances in computational intelligence - Volume Part II
Year:
2011

Citing 3
Cited 1

Non-negative Matrix Factorization with Orthogonality Constraints and its Application to Raman Spectroscopy

Journal of VLSI Signal Processing Systems
Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method

SIAM Journal on Matrix Analysis and Applications
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation

Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation

Approximation of feature vectors in nonnegative matrix factorization with gaussian radial basis functions

ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I

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Abstract

Nonnegative Matrix Factorization (NMF) is an important tool in spectral data analysis. Various types of numerical optimization algorithms have been proposed for NMF, including multiplicative, projected gradient descent, alternating least squares and active-set ones. In this paper, we discuss the Tikhonov regularized version of the FC-NNLS algorithm (proposed by Benthem and Keenan in 2004) that belongs to a class of active-set methods in the context of its application to spectroscopy data. We noticed that starting iterative updates from a large value of a regularization parameter, and then decreasing it gradually to a very small value considerably reduces the risk of getting stuck into unfavorable local minima of a cost function. Moreover, our experiments demonstrate that this algorithm outperforms the well-known NMF algorithms in terms of Peak Signal-to-Noise Ratio (PSNR).