A self-contained walk through the math behind NMF — deriving the multiplicative update rules from first principles and proving they converge, following Lee & Seung (1999) and Lee & Seung (2001).
Covers:
- Problem setup and two objective functions (Frobenius norm, KL divergence)
- Matrix calculus preliminaries
- Derivation of multiplicative update rules for both objectives
- Full convergence proof via auxiliary functions (Euclidean case)
- Convergence sketch for the divergence case
- Summary of the proof architecture