In this paper, by bringing in a user defined nonnegative control matrix to form a new objective function, I modify the update rules correspondingly and propose a novel decreasing accelerated gradient descent method for nonnegative matrix factorization (DAGDM) which can make the matrix of the decomposition results achieve sparse. The control matrix also contains the weighting information, which puts different weight on different parts of the result matrix to be produced. This will provide a control interface of nonnegative matrix factorization to make a sparse and light basis matrix. Experimental results demonstrate the effectiveness of the proposed method.
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