scholarly journals A Convex Model for Matrix Factorization and Dimensionality Reduction on Physical Space and Its Application to Blind Hyperspectral Unmixing

2010 ◽  
Author(s):  
Michael Moeller ◽  
Ernie Esser ◽  
Stanley Osher ◽  
Guillermo Sapiro ◽  
Jack Xin
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Physical Space ◽  
Convex Model ◽  
Hyperspectral Unmixing

Nonnegative matrix factorization with entropy regularization for hyperspectral unmixing

2021 ◽  
Vol 42 (16) ◽  
pp. 6362-6393
Author(s):  
Junmin Liu ◽  
Shuai Yuan ◽  
Xuehu Zhu ◽  
Yifan Huang ◽  
Qian Zhao
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Hyperspectral Unmixing

Self-Supervised Robust Deep Matrix Factorization for Hyperspectral Unmixing

2021 ◽  
pp. 1-14
Author(s):  
Heng-Chao Li ◽  
Xin-Ru Feng ◽  
Dong-Hai Zhai ◽  
Qian Du ◽  
Antonio Plaza
Keyword(s):  
Matrix Factorization ◽  
Hyperspectral Unmixing

FastNMF

2010 ◽  
pp. 137-163
Author(s):  
Le Li ◽  
Le Li ◽  
Yu-Jin Zhang ◽  
Yu-Jin Zhang
Keyword(s):  
Feature Extraction ◽  
Fixed Point ◽  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Ease Of Use ◽  
Experimental Results ◽  
Fixed Point Algorithm ◽  
Popular Method ◽  
Face Images ◽  
Multiplicative Update

Non-negative matrix factorization (NMF) is a more and more popular method for non-negative dimensionality reduction and feature extraction of non-negative data, especially face images. Currently no NMF algorithm holds not only satisfactory efficiency for dimensionality reduction and feature extraction of face images but also high ease of use. To improve the applicability of NMF, this chapter proposes a new monotonic, fixed-point algorithm called FastNMF by implementing least squares error-based non-negative factorization essentially according to the basic properties of parabola functions. The minimization problem corresponding to an operation in FastNMF can be analytically solved just by this operation, which is far beyond existing NMF algorithms’ power, and therefore FastNMF holds much higher efficiency, which is validated by a set of experimental results. For the simplicity of design philosophy, FastNMF is still one of NMF algorithms that are the easiest to use and the most comprehensible. Besides, theoretical analysis and experimental results also show that FastNMF tends to extract facial features with better representation ability than popular multiplicative update-based algorithms.

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