Implementation and evaluation distributed mixed pixels analysis algorithm for hyperspectral image based on constraint non-negative matrix factorization

As an effective blind source separation method, non-negative matrix factorization has been widely adopted to analyze mixed data in hyperspectral images. To avoid trapping in local optimum, appropriate constraints are added to the objective function of NMF, whose reflections of image essential attribute determine the performance finally. In this paper, a new NMF-based mixed data analysis algorithm is presented, with maximum overall coverage constraint introduced in traditional NMF. The new constraint was proposed using data geometrical properties in the feature space to maximizes the number of pixels contained in the simplex constructed by endmembers compulsorily and introduced in objective function of NMF, named maximum overall coverage constraint NMF (MOCC-NMF), to analyze mixed data in highly mixed hyperspectral data without pure pixels. For implementing easily, multiplicative update rules are applied to avoid step size selection problem occurred in traditional gradient-based optimization algorithm frequently. Furthermore, in order to handle huge computation involved, parallelism implementation of the proposed algorithm using MapReduce is described and the new partitioning strategy to obtain matrix multiplication and determinant value is discussed in detail. In the numerical experiments conducted on real hyperspectral and synthetic datasets of different sizes, the efficiency and scalability of the proposed algorithm are confirmed.