Two-stage Nonnegative Matrix Factorization Algorithm and Its Application in Hyperspectral Unmixing
The non-negative matrix factorization(NMF)model has been effectively applied in the hyperspectral unmixing.It is known that the objective function's nonconvexity results in the solution's instability.To address this issue,two main streams of approaches have been proposed.Starting NMF with a reasonable initialization or adding regularized terms to NMF.We propose a two-stages NMF method which combines the initialization method and definition of regularized NMF model.In the first stage,k-means is employed to find the initial end-member matrix.In the second stage,a regularized NMF problem is defined,which makes full use of the initial end-member matrix obtained in the first stage.In our algorithm,the initialization matrix of the end-member matrix in the first stage of our algorithm also contributes to the regularized term.The project gradient method is employed to solve the non-negative least square problems alternatively.Numerical results indicate that the new algorithm works well.
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