scholarly journals Active Set Type Algorithms for Nonnegative Matrix Factorization in Hyperspectral Unmixing

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Li Sun ◽  
Congying Han ◽  
Ziwen Liu
Keyword(s):  
Matrix Factorization ◽  
Quadratic Convergence ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Nonnegative Matrix ◽  
Image Mining ◽  
Active Set ◽  
Hyperspectral Unmixing ◽  
Numerical Tests ◽  
Sparse Features

Hyperspectral unmixing is a powerful method of the remote sensing image mining that identifies the constituent materials and estimates the corresponding fractions from the mixture. We consider the application of nonnegative matrix factorization (NMF) for the mining and analysis of spectral data. In this paper, we develop two effective active set type NMF algorithms for hyperspectral unmixing. Because the factor matrices used in unmixing have sparse features, the active set strategy helps reduce the computational cost. These active set type algorithms for NMF is based on an alternating nonnegative constrained least squares (ANLS) and achieve a quadratic convergence rate under the reasonable assumptions. Finally, numerical tests demonstrate that these algorithms work well and that the function values decrease faster than those obtained with other algorithms.

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

scholarly journals Retinal vessel segmentation with constrained-based nonnegative matrix factorization and 3D modified attention U-Net

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang Yu ◽  
Hongqing Zhu
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Three Dimensional ◽  
Nonnegative Matrix ◽  
Retinal Vessel ◽  
Classification Problem ◽  
Image Resolution ◽  
Retinal Vessels ◽  
Segmentation Task

AbstractDue to the complex morphology and characteristic of retinal vessels, it remains challenging for most of the existing algorithms to accurately detect them. This paper proposes a supervised retinal vessels extraction scheme using constrained-based nonnegative matrix factorization (NMF) and three dimensional (3D) modified attention U-Net architecture. The proposed method detects the retinal vessels by three major steps. First, we perform Gaussian filter and gamma correction on the green channel of retinal images to suppress background noise and adjust the contrast of images. Then, the study develops a new within-class and between-class constrained NMF algorithm to extract neighborhood feature information of every pixel and reduce feature data dimension. By using these constraints, the method can effectively gather similar features within-class and discriminate features between-class to improve feature description ability for each pixel. Next, this study formulates segmentation task as a classification problem and solves it with a more contributing 3D modified attention U-Net as a two-label classifier for reducing computational cost. This proposed network contains an upsampling to raise image resolution before encoding and revert image to its original size with a downsampling after three max-pooling layers. Besides, the attention gate (AG) set in these layers contributes to more accurate segmentation by maintaining details while suppressing noises. Finally, the experimental results on three publicly available datasets DRIVE, STARE, and HRF demonstrate better performance than most existing methods.

Block kernel nonnegative matrix factorization for face recognition

2019 ◽  
Vol 17 (01) ◽  
pp. 1850059
Author(s):  
Wen-Sheng Chen ◽  
Jingmin Liu ◽  
Binbin Pan ◽  
Yugao Li
Keyword(s):  
Face Recognition ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Superior Performance ◽  
Nonlinear Features ◽  
Data Points ◽  
Class Information ◽  
Sparse Features ◽  
Facial Images

Nonnegative matrix factorization (NMF) is a linear approach for extracting localized feature of facial image. However, NMF may fail to process the data points that are nonlinearly separable. The kernel extension of NMF, named kernel NMF (KNMF), can model the nonlinear relationship among data points and extract nonlinear features of facial images. KNMF is an unsupervised method, thus it does not utilize the supervision information. Moreover, the extracted features by KNMF are not sparse enough. To overcome these limitations, this paper proposes a supervised KNMF called block kernel NMF (BKNMF). A novel objective function is established by incorporating the intra-class information. The algorithm is derived by making use of the block strategy and kernel theory. Our BKNMF has some merits for face recognition, such as highly sparse features and orthogonal features from different classes. We theoretically analyze the convergence of the proposed BKNMF. Compared with some state-of-the-art methods, our BKNMF achieves superior performance in face recognition.

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