Nonnegative Matrix Factorization Implementation Using ADMM

The Nonnegative Matrix Factorization Using ADMM is an optimization-based approach that decomposes a given matrix into two nonnegative factor matrices. This method is particularly effective for handling datasets with inherent nonnegative constraints, such as image pixel values, text frequency counts, or biological measurements. The ADMM algorithm solves the associated optimization problem by breaking it into smaller subproblems that are easier to solve, using Lagrange multipliers and penalty parameters to enforce nonnegativity constraints. In implementation, the algorithm typically involves three main steps per iteration: updating the first factor matrix while fixing the second, updating the second factor matrix while fixing the first, and adjusting the dual variables. Key functions include proximal operators for nonnegative projections and efficient matrix operations to handle large-scale data. The method features built-in convergence checks and parameter tuning mechanisms to ensure numerical stability. This technique finds applications across multiple domains including signal processing for source separation, image processing for feature extraction, and data analysis for dimensionality reduction and pattern discovery. By employing Nonnegative Matrix Factorization with ADMM, researchers can uncover latent structures within their data, enabling more interpretable results and data-driven decision making. The implementation typically includes options for different loss functions (such as Frobenius norm or KL-divergence) and supports various initialization strategies for improved convergence.