Deep Symmetric Matrix Factorization

Pierre De Handschutter, Nicolas Gillis, Wivine Blekic

Abstract: Deep matrix factorizations (deep MFs) are recent extensions of standard MFs to several layers. This allows one to extract hierarchical interleaved features in high-dimensional datasets. In this paper, we present a variant of deep MF where the input matrix is symmetric and nonnegative, dubbed deep symmetric nonnnegative matrix factorization (DSNMF). We compare several loss functions to tackle DSNMF and propose different possible initialization techniques. We apply successfully DSNMF to the extraction of several levels of communities, both on synthetic data and on a psychiatric network, a promising application in the medical field.