An Endmember Initialization Scheme for Nonnegative Matrix Factorization and Its Application in Hyperspectral Unmixing

Abstract

Nonnegative matrix factorization (NMF) is a blind source separation (BSS) method often used in hyperspectral unmixing. However, it tends to converge to a local optimum. To overcome this limitation, we present a simple, but effective endmember initialization scheme for NMF, which is realized by improving initial values through the application of the automatic target generation process (ATGP) algorithm. The initial spectra and abundances of target endmembers are first obtained using the ATGP algorithm and nonnegative least squares (NNLS) method, respectively. The preliminary results are then optimized through iterative application of NMF. To validate the applicability and effectiveness of the proposed method, we analyzed the improvement of NMF by the ATGP algorithm, using the synthetic hyperspectral data and real hyperspectral images. The results from the proposed method are compared with those of the vertex component analysis (VCA)-NMF algorithm, which uses the VCA algorithm to perform initialization for NMF, the minimum volume constrained NMF (MVC-NMF) algorithm, the traditional two-step VCA-fully-constrained least squares (FCLS) algorithm, which uses the VCA to extract the endmember matrix, and the FCLS algorithm to estimate the abundance matrix. The comparison results prove that proper endmember initialization can help the NMF algorithm yield better estimation results. Through the optimization of target endmembers' initial values, the proposed ATGP-NMF algorithm can consistently produce good results at a lower computational cost, especially in the case of a real hyperspectral image for which pure pixels do not exist and there is little prior knowledge. With its high applicability and effectiveness, the ATGP-NMF algorithm has a great potential to solve hyperspectral unmixing problems.

Collaborative Coupled Hyperspectral Unmixing Based Subpixel Change Detection for Analyzing Coastal Wetlands

“…7 shows the synthetic hyperspectral image, Fig. 8 and Table II show the quantitative results by using SAM [25], spectral information divergence (SID) [26] and correlation coefficient (CC) [27], and our method is compared with Vertex Component Analysis (VCA) [28], N-FINDR [29], Simplex Identification via Split Augmented Lagrangian (SISAL) [30], Non-negative Matrix Factorization (NMF) (NMF) [31]. III show the abundance evaluation results of various methods, measured from CC [27], Abundance Information Divergence (AID) [32] and Abundance Angle Distance (AAD) [33].…”

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

“…Initialization schemes based on low-rank decomposition algorithms do not require a randomization step, so they can also be classified in the subclass of "deterministic" structured initialization methods. They include schemes using the Singular Value Decomposition and the Nonnegative Double Singular Value Decomposition (NNDSVD) [43,57,58] and its variants [59], rank-1 decomposition [39,60] [61], nonnegative PCA [62,63], nonnegative ICA [64], Vertex Component Analysis [65][66][67], Successive Projection Algorithm [68].…”

Improving hyperspectral sub-pixel target detection in multiple target signatures using a revised replacement signal model

“…To determine the virtual dimensionality, the "Harsanyi-Farrand-Chang" (also known as HFC) approach based on the "Neyman-Pearson" detection theory is an effective method (Chang & Du, 2004;Harsanyi et al, 1993). According to estimates (Cao et al, 2018), the selection of the initial target endmembers based on the HFC approach has a great impact on spectral unmixing. As a binary hypothesis problem, the virtual dimensionality determined by the HFC approach is q (number of endmembers).…”

“…The Automatic Target Generation Procedure (ATGP) is an unsupervised endmember extraction method in the target detection task, where can provide more accurate initial points to identify endmembers (Ren & Chang, 2003). Compared to conventional supervised and unsupervised endmember extraction approaches, such as the Pixel Purity Index (PPI) that require a very large number of skewers to find maximal/minimal orthogonal projections (Chang & Li, 2016), ATGP method requires less prior information to extract pure pixel vectors as the endmember spectrum from the hyperspectral data cube (Cao et al, 2018). ATGP method works by iterative orthogonal projections of the hyperspectral data cube then finding the largest magnitude vector in a sequence of orthogonal projection subspaces (Q.…”

“…The vertex component analysis approach is a developed structure of the ATGP method, included a sequence of successive orthogonal projection subspaces based on the maximal orthogonal projections (Tang et al, 2012). According to estimates (Cao et al, 2018), the vertex component analysis approach does not have stable performance when random initial values are used.…”