Local Smoothness Constrained Nonnegative Matrix Factorization with Nonlinear Convergence Rate for Spectral Decomposition

With the development of the detection technology using multispectra sensors, spectral decomposition (SD) attracts more and more attention in the biomedical signal processing and image processing. In this paper, a local smoothness constrained nonnegative matrix factorization (NMF) with nonlinear convergence rate (NMF-NCR) is proposed to solve SD problem and our contributions are as follows. First, it proves that the gradients of the cost function with respect to each variable matrix are Lipschitz continuous. Then, a proximal function is constructed for optimizing the cost function. As a result, our method can achieve an NCR much faster than the traditional methods. Simulations show the advantage in solving SD of our algorithm over the compared methods.

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A Quasi-Likelihood Approach to Nonnegative Matrix Factorization

Neural Computation ◽

10.1162/neco_a_00853 ◽

2016 ◽

Vol 28 (8) ◽

pp. 1663-1693 ◽

Cited By ~ 2

Author(s):

Karthik Devarajan ◽

Vincent C. K. Cheung

Keyword(s):

Matrix Factorization ◽

Goodness Of Fit ◽

Nonnegative Matrix Factorization ◽

Linear Models ◽

Expectation Maximization Algorithm ◽

Nonnegative Matrix ◽

Nonlinear Effects ◽

Biomedical Signal Processing ◽

Link Functions ◽

Unified View

A unified approach to nonnegative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proved using the expectation-maximization algorithm. In addition, a measure to evaluate the goodness of fit of the resulting factorization is described. The proposed methods allow modeling of nonlinear effects using appropriate link functions and are illustrated using an application in biomedical signal processing.

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A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments

Mathematics ◽

10.3390/math9091006 ◽

2021 ◽

Vol 9 (9) ◽

pp. 1006

Author(s):

Flavia Esposito

Keyword(s):

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Biological Information ◽

Relevant Role ◽

Initialization Scheme ◽

The Cost ◽

The Impact ◽

Omic Data

Nonnegative Matrix Factorization (NMF) has acquired a relevant role in the panorama of knowledge extraction, thanks to the peculiarity that non-negativity applies to both bases and weights, which allows meaningful interpretations and is consistent with the natural human part-based learning process. Nevertheless, most NMF algorithms are iterative, so initialization methods affect convergence behaviour, the quality of the final solution, and NMF performance in terms of the residual of the cost function. Studies on the impact of NMF initialization techniques have been conducted for text or image datasets, but very few considerations can be found in the literature when biological datasets are studied, even though NMFs have largely demonstrated their usefulness in better understanding biological mechanisms with omic datasets. This paper aims to present the state-of-the-art on NMF initialization schemes along with some initial considerations on the impact of initialization methods when microarrays (a simple instance of omic data) are evaluated with NMF mechanisms. Using a series of measures to qualitatively examine the biological information extracted by a given NMF scheme, it preliminary appears that some information (e.g., represented by genes) can be extracted regardless of the initialization scheme used.

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Spectral unmixing based on nonnegative matrix factorization with local smoothness constraint

2015 IEEE China Summit and International Conference on Signal and Information Processing (ChinaSIP) ◽

10.1109/chinasip.2015.7230481 ◽

2015 ◽

Cited By ~ 2

Author(s):

Zuyuan Yang ◽

Liu Yang ◽

Zhaoquan Cai ◽

Yong Xiang

Keyword(s):

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Spectral Unmixing ◽

Local Smoothness ◽

Smoothness Constraint

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LOCALITY PRESERVING NONNEGATIVE MATRIX FACTORIZATION WITH APPLICATION TO FACE RECOGNITION

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691310003730 ◽

2010 ◽

Vol 08 (05) ◽

pp. 835-846 ◽

Cited By ~ 5

Author(s):

TAIPING ZHANG ◽

BIN FANG ◽

YUAN Y. TANG ◽

ZHAOWEI SHANG

Keyword(s):

Face Recognition ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

High Dimensional ◽

Face Space ◽

Manifold Structure ◽

Locality Preserving ◽

The Cost ◽

Dimensional Face

In this paper, we propose a Locality Preserving Nonnegative Matrix Factorization (LPNMF) method to discover the manifold structure embedded in high-dimensional face space that is applied for face recognition. It is done by incorporating locality preserving constraints inside the cost function of NMF, then a new decomposition of a face with locality preserving can be obtained. As a result, the proposed LPNMF method shares some properties with the Locality Preserving Projection (LPP) such that it can effectively discover the manifold structure embedded in a high-dimensional face space. Experimental results show that LPNMF provides a better representation and achieves higher recognition rates in face recognition.

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