Combining the full-space and block-coordinate approaches for exact non-negative matrix factorization

Details

Supervisors

François Glineur ; Leplat, Valentin

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

Finding an exactNMF for matrix X, i.e. factors W and H such that X = WH, has proved to be a difficult problem, even for a small factorization rank r. On this basis, his thesis explores the potential of using the conic reformulations of the NMF problem introduced in Lepat et al. (2021) as catalyzers to perform better solution space exploration towards exactNMFs. The heuristics proposed in this contribution are an attempt to reconcile, in an optimized way, the good properties of both the conic approach (i.e. fast full-space mobility) and the block-coordinate (BCD) approach (i.e. iteration speed and good convergence properties). We present classes of matrices for which the conic-based heuristics reach better factorizations and even find exactNMFs where BCD-based methods cannot. Note that the poor scalability of the conic-based heuristics remains a considerable limitation of the conic approach.