Endmember extraction from hyper spectral data is an important procedure of hyper spectral unmixing. Nonnegative Matrix Factorization（ NMF） has been widely used in the last few years for endmember extraction without assuming the presence of pure pixels. Many methods that incorporate different types of constraints into the NMF objective function have been proposed to accurately extract endmembers. However

traditional constrained NMF algorithms generally have two limitations. First

controlling the tradeoff between the accurate reconstruction and constraint well through the fixed penalty coefficient is difficult. Second

most traditional methods are usually trapped in a local optimum that renders the global optimum difficult to find. To overcome these constraints

we present a novel method called the High-dimension Adaptive Particle Swarm Optimization（ HAPSO） for endmember extraction based on the minimum distance constrained NMF（ MDC-NMF） scheme. HAPSO enhances the global search ability through PSO. Two key improvements—the high-dimensional PSO and adaptive penalty coefficient method based on swarm information—are considered. The standard PSO algorithm particularly suffers from the"curse of dimensionality"

such that it is more likely to plunge into local optima as the dimensionality of the search space increases. To overcome this problem

high-dimensional PSO divides the complex high-dimensional constrained NMF problem into several simple low-dimensional sub problems according to the characteristics of objective function and hyper spectral data. Thus

each particle in the swarm can search for increasingly accurate positions in a detailed manner that significantly improves the accuracy of the results. Furthermore

particle information

such as the positions and feasibility of the PSO algorithm

can be easily applied to balance the search bias between objective functions and constraints. Thus

this study proposes an adaptive penalty coefficient method according to the proportion of feasible solutions in the swarm

instead of the fixed penalty coefficient. The penalty coefficient particularly increases when the proportion of feasible solutions is low in the preliminary stage and decreases as the proportion of feasible solutions increases. The proposed HAPSO algorithm

MDC-NMF

minimum volume constrained NMF

and vertex component analysis are compared. Both synthetic and real data are considered. For the synthetic data

different numbers of endmembers and signal-to-noise ratio are considered. Real hypers pectral data

including AVIRIS and HYDICE images are used. Results demonstrate that the proposed HAPSO algorithm outperforms other algorithms; it extracts more accurate endmembers and causes less reconstruction error. HAPSO is a method that applies PSO for endmember extraction based on the MDC-NMF scheme. The proposed method can effectively overcome the disadvantages of the traditional constrained NMF endmember extraction algorithms and solve high-dimensional and adaptive penalty coefficient problems for NMF endmember extraction. We will consider the influence of many endmembers that can decrease accuracy in future work.More reasonable and effective constraint handling approaches should be studied

although an adaptive penalty coefficient method performs well. The algorithm accuracy should also be further improved because not all endmembers are perfectly extracted by the proposed algorithm in the experiments.