Numerical Computation for Nonnegative Matrix Factorization

Explore advanced numerical computation techniques for nonnegative matrix factorization (NMF) in this 59-minute conference talk presented at ICBS2025. Delve into the mathematical foundations and computational challenges associated with NMF, a powerful dimensionality reduction technique widely used in machine learning, data mining, and signal processing. Learn about various algorithms and optimization methods for solving NMF problems, including multiplicative update rules, alternating least squares, and gradient-based approaches. Discover how to handle numerical stability issues, convergence criteria, and computational efficiency considerations when implementing NMF algorithms. Examine practical applications of NMF in areas such as image processing, text mining, and collaborative filtering, while understanding the theoretical properties that make certain numerical methods more suitable for different types of data and problem constraints. Gain insights into recent developments in NMF computation and best practices for selecting appropriate algorithms based on specific problem requirements and data characteristics.