A Simple Implementation of the NMF Algorithm

In the following paragraphs, we present a simple implementation of the Non-negative Matrix Factorization (NMF) algorithm, which decomposes a matrix into the product of two non-negative matrices. The algorithm is based on using NMF to uncover latent structures and features within matrices. NMF is an extremely popular technique with applications across various domains, including image processing, speech analysis, and text mining. This algorithm can be utilized for tasks such as data dimensionality reduction, feature extraction, and signal separation. The implementation typically involves initializing two non-negative matrices (W and H) with random values, then iteratively updating them using multiplicative update rules to minimize the reconstruction error between the original matrix and the product W*H. Key functions include calculating the Euclidean distance cost function and implementing convergence checks based on error thresholds or maximum iterations. In this article, we demonstrate how to implement the NMF algorithm using Python, including practical usage examples showing how to apply this algorithm to solve real-world problems with proper parameter tuning and result interpretation.