Reducing Approximation Error with Rapid Convergence Rate for Non-Negative Matrix Factorization (NMF)

Abstract

Non-Negative Matrix Factorization (NMF) is utilized in many important applications. This paper presents development of an efficient low rank approximate NMF algorithm for feature extraction related to text mining and spectral data analysis. NMF can be used for clustering. NMF factorizes a positive matrix A to two positive matrices W and H matrices where A=WH. The proposal uses k-means clustering algorithm to determine the centroid of each cluster and assigns the centroid coordinates of each cluster as one column for W matrix. The initial choice of W matrix is positive. The H matrix is determined with gradient descent algorithm based on thin QR optimization. The performance comparison of the proposed NMF algorithm is illustrated with results. The accurate choice of initial positive W matrix reduces approximation error and the use of thin QR algorithm in combination with gradient descent approach provides rapid convergence rate for NMF. The proposed algorithm is implemented with the randomly generated matrix in MATLAB environment. The number of significant singular values of the generated matrix is selected as the number of clusters. The error and convergence rate comparison of the proposed algorithm with the current algorithms are demonstrated in this research. The accurate measurement of execution time for individual program is not possible in MATLAB. The average time execution over 200 iterations is therefore calculated with an increasing iteration count of the proposed algorithm and the comparative results are presented.