Recovery of constituent spectra using non-negative matrix factorization

Sajda, Paul; Du, Shan; Parra, Lucas C.

doi:10.1117/12.504676

Cited by 79 publications

(72 citation statements)

References 6 publications

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“…Alternative mostly used loss function that intrinsically ensures non-negativity constraints and it is related to the Poisson likelihood is a functional based on the Kullback-Leibler divergence [3,5]:…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

“…The non-negative matrix factorization (NMF approach is promising in many applications from engineering to neuroscience since it is designed to capture alternative structures inherent in the data and, possibly to provide more biological insight [1][2][3][4][5][6]. Lee and Seung introduced NMF in its modern formulation as a method to decompose patterns or images [3,7].…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms

Cichocki

Zdunek

Амари

2006

Lecture Notes in Computer Science

194

153

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Abstract. In this paper we discus a wide class of loss (cost) functions for non-negative matrix factorization (NMF) and derive several novel algorithms with improved efficiency and robustness to noise and outliers. We review several approaches which allow us to obtain generalized forms of multiplicative NMF algorithms and unify some existing algorithms. We give also the flexible and relaxed form of the NMF algorithms to increase convergence speed and impose some desired constraints such as sparsity and smoothness of components. Moreover, the effects of various regularization terms and constraints are clearly shown. The scope of these results is vast since the proposed generalized divergence functions include quite large number of useful loss functions such as the squared Euclidean distance,Kulback-Leibler divergence, Itakura-Saito, Hellinger, Pearson's chi-square, and Neyman's chi-square distances, etc. We have applied successfully the developed algorithms to blind (or semi blind) source separation (BSS) where sources can be generally statistically dependent, however they satisfy some other conditions or additional constraints such as nonnegativity, sparsity and/or smoothness.

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Section: Introduction and Problem Formulationmentioning

confidence: 99%

Section: Introduction and Problem Formulationmentioning

confidence: 99%

Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms

Cichocki

Zdunek

Амари

2006

Lecture Notes in Computer Science

194

153

View full text Add to dashboard Cite

show abstract

“…NMF has so far been used for purposes as diverse as identifying parts of visual images (for example, the parts of faces in photographs of faces (Lee and Seung, 1999)); for analysis of Raman spectroscopy data, hyperspectral images, and human brain chemical shift images (Sajda et al, 2003); and for transcription of music (Smaragdis and Brown, 2003). It is this last application that points the way from the plant visualis ation point of view, as it was the first to make use of a novel property of the NMF matrices.…”

Section: Whmentioning

confidence: 99%

Plant Data Visualization Using Non-Negative Matrix Factorization

Tapson

Greene

2005

IFAC Proceedings Volumes

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“…The key point is that the solution using only non-negativity is not unique, therefore the results provided by ALS and NMF methods depend on their initializations. In practice, the NMF method is randomly initialized [24], while the ALS method is initialized by the results obtained with a non-constrained decomposition method such as principal component analysis (PCA), factor analysis algorithms [25][26][27], or using pure variable detection methods such as simple-to-use interactive self modeling mixture analysis (SIMPLISMA) [28] and orthogonal projection approach (OPA) [29]. More recently ICA methods are also used [30,31] as an initialization method.…”

Section: Non-negative Least Squares Estimationmentioning

confidence: 99%

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

Moussaoui

Carteret

Brie

et al. 2006

Chemometrics and Intelligent Laboratory Systems

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This paper presents an original method for the analysis of multicomponent spectral data sets. The proposed algorithm is based on Bayesian estimation theory and Markov Chain Monte Carlo (MCMC) methods. Resolving spectral mixture analysis aims at recovering the unknown component spectra and at assessing the concentrations of the underlying species in the mixtures. In addition to non-negativity constraint, further assumptions are generally needed to get a unique resolution. The proposed statistical approach assumes mutually independent spectra and accounts for the non-negativity and the sparsity of both the pure component spectra and the concentration profiles. Gamma distribution priors are used to translate all these information in a probabilistic framework. The estimation is performed using MCMC methods which lead to an unsupervised algorithm, whose performances are assessed in a simulation study with a synthetic data set.

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Recovery of constituent spectra using non-negative matrix factorization

Cited by 79 publications

References 6 publications

Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms

Csiszár’s Divergences for Non-negative Matrix Factorization: Family of New Algorithms

Plant Data Visualization Using Non-Negative Matrix Factorization

Bayesian analysis of spectral mixture data using Markov Chain Monte Carlo Methods

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