非负矩阵分解（non-negative matrix factorization，NMF）端元生成方法可以同时获得端元和丰度，且支持乘式迭代实现目标函数优化，处理效率高，因此受到越来越多的关注。由于目标函数非凸，基于NMF的端元提取方法容易陷入局部极值。尽管采用增加约束的方式可以缓解局部极值问题，但往往会破坏NMF乘式迭代规则，从而降低NMF方法的处理效率。提出一种基于丰度分布约束的方法，利用矩阵迹运算实现目标函数乘式迭代优化。实验结果表明，该方法既能估计出准确的端元，又能提高端元生成的效率。
In recent years, the endmember generation method based on non-negative matrix factorization (NMF) attracted much attention. The NMF endmember generation method can be used to obtain endmembers and the abundance matrix simultaneously, and the multiplicative update rule works. Because of the non-convexity of the objective function, NMF endmember extraction easily goes into local extrema. Several constraints were imposed on NMF to alleviate the local extremum problem, but they often broke the multiplicative update rules and increased the processing time. In this work, we propose a new method based on abundance distribution constraint, and the multiplicative iterations can be used. The experimental results show that the method improves the efficiency and accuracy of endmember generation.
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