Non-negative matrix factorization (NMF) is a more and more popular method for non-negative dimensionality reduction and feature extraction of non-negative data, especially face images. Currently no NMF algorithm holds not only satisfactory efficiency for dimensionality reduction and feature extraction of face images but also high ease of use. To improve the applicability of NMF, this chapter proposes a new monotonic, fixed-point algorithm called 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 operation, which is far beyond existing NMF algorithms’ power, and therefore FastNMF holds much higher efficiency, which is validated by a set 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 extract facial features with better representation ability than popular multiplicative update-based algorithms.
An improved non-negative matrix factorization algorithm based on genetic algorithm