Face Recognition Using Non-Negative Matrix Factorization (NMF) with Implemented Algorithm Source Code

This document discusses the application of Non-Negative Matrix Factorization (NMF) in face recognition and its algorithm source code implementation. Non-Negative Matrix Factorization is an algorithm widely used in image processing and pattern recognition fields. It achieves data feature extraction and dimensionality reduction by decomposing a matrix into two non-negative factor matrices. In face recognition applications, NMF can extract facial image features and represent them as a set of non-negative basis facial features. The implementation typically involves optimizing the factorization using multiplicative update rules to minimize the reconstruction error between the original image matrix and the product of the basis and coefficient matrices. This approach not only effectively reduces the dimensionality of image data but also preserves crucial facial image information, enabling accurate face recognition. The core algorithm involves initializing random non-negative matrices W (basis features) and H (coefficients), then iteratively updating them using optimization techniques like gradient descent or alternating least squares. Key functions in the implementation include feature normalization, convergence checking, and reconstruction error calculation. By utilizing the NMF algorithm for face recognition, we can develop a reliable and efficient facial recognition system that handles high-dimensional image data while maintaining interpretability through non-negative constraints on the decomposed components.