FastNMF: A fast monotonic fixed-point non-negative Matrix Factorization algorithm with high ease of use

Non-negative Matrix Factorization (NMF) is a recently developed method for dimensionality reduction, feature extraction and data mining, etc. Currently no NMF algorithm holds both satisfactory efficiency for applications and enough ease of use. To improve the applicability of NMF, this paper proposes a new monotonic, fixed-point algorithm coined FastNMF by implementing least squares error-based non-negative factorization essentially according to the basic properties of parabola functions. The minimization problem corresponding to an operation in FastNMF can be analytically solved just by this algorithm, which is far beyond all existing algorithmspsila power. Therefore, FastNMF holds much higher efficiency, which is validated by a number of experimental results. For the simplicity of design philosophy, FastNMF is still one of NMF algorithms that are the easiest to use and the most comprehensible. Besides, theoretical analysis and experimental results also show that FastNMF tends to converge to better solutions than the popular multiplicative update-based algorithms.