NMFs Algorithm (Non-negative Matrix Factorization with Sparsity Constraint)

The NMFs algorithm (Non-negative Matrix Factorization with Sparsity Constraint) is designed for face recognition based on local facial features. This method performs spatial dimensionality reduction through approximate matrix decomposition to extract critical features from facial images. By applying sparsity constraints via L1-norm regularization in the optimization objective function, NMFs effectively represents facial images as sets of sparse weight vectors. These sparse weight vectors serve as discriminative features for comparing and identifying different faces. The algorithm typically implements iterative updates using multiplicative rules or gradient descent with sparsity penalties, ensuring non-negativity while maintaining component sparsity. Consequently, the NMFs algorithm holds significant application value in the field of face recognition, particularly for handling high-dimensional image data with enhanced interpretability.