Integrating spatial information in unmixing using the nonnegative matrix factorization

2014 ◽  
Author(s):  
Miguel A. Goenaga-Jimenez ◽  
Miguel Vélez-Reyes
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Spatial Information ◽  
Nonnegative Matrix

scholarly journals Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization

2021 ◽  
Vol 7 (10) ◽  
pp. 194
Author(s):  
Pascal Fernsel
Keyword(s):  
Matrix Factorization ◽  
Clustering Algorithm ◽  
Nonnegative Matrix Factorization ◽  
Spatial Information ◽  
Nonnegative Matrix ◽  
Ground Truth ◽  
Optimization Techniques ◽  
Clustering Methods ◽  
Cluster Membership ◽  
Tv Regularization

Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.

Nonnegative matrix factorization with region sparsity learning for hyperspectral unmixing

2017 ◽  
Vol 15 (06) ◽  
pp. 1750063
Author(s):  
Bin Qian ◽  
Lei Tong ◽  
Zhenmin Tang ◽  
Xiaobo Shen
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Spatial Information ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Hyperspectral Data ◽  
Optimization Scheme ◽  
Hyperspectral Unmixing ◽  
Relationship Of ◽  
The Relationship

Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unmixing due to the strong discovery of the latent structure. Most NMFs put emphasize on the spectral information, but ignore the spatial information, which is very crucial for analyzing hyperspectral data. In this paper, we propose an improved NMF method, namely NMF with region sparsity learning (RSLNMF), to simultaneously consider both spectral and spatial information. RSLNMF defines a new sparsity learning model based on a small homogeneous region that is obtained via the graph cut algorithm. Thus RSLNMF is able to explore the relationship of spatial neighbor pixels within each region. An efficient optimization scheme is developed for the proposed RSLNMF, and its convergence is theoretically guaranteed. Experiments on both synthetic and real hyperspectral data validate the superiority of the proposed method over several state-of-the-art unmixing approaches.

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