A Characterization of the Non-Uniqueness of Nonnegative Matrix Factorizations
This addresses the interpretability and reliability of NMF for researchers and practitioners in data analysis, though it is incremental as it builds on prior identifiability studies.
The paper tackles the problem of non-uniqueness in nonnegative matrix factorizations (NMF), characterizing exactly when and how non-identifiability occurs, which enables algorithms to efficiently find alternate solutions.
Nonnegative matrix factorization (NMF) is a popular dimension reduction technique that produces interpretable decomposition of the data into parts. However, this decompostion is not generally identifiable (even up to permutation and scaling). While other studies have provide criteria under which NMF is identifiable, we present the first (to our knowledge) characterization of the non-identifiability of NMF. We describe exactly when and how non-uniqueness can occur, which has important implications for algorithms to efficiently discover alternate solutions, if they exist.