Year: 2024
Type: conference-paper
Abstract: Symmetric nonnegative matrix tri-factorization (trisymNMF) factorizes a symmetric input n-by-n matrix,$X$, using two matrices, a nonnegative$n$-by-$r$matrix$W$and a nonnegative symmetric$r$-by-$r$matrix$S$, such that$X\approx WSW^{\mathrm{T}}$. trisym-NMF has been used in many applications, including topic modeling and community detection. In the latter application, each column of$W$corresponds to a community, and the entries of$S$indicate the interactions between the communities. In this paper, we focus on the particular case of an orthogonal matrix$W$, corresponding to the case of disjoint communities. We first analyse this problem, and in particular provide an identifiability result. Then we propose an efficient coordinate descent method that exploits the properties of the problem to solve it efficiently. We also propose a new initialization strategy, provably correct in the noiseless case and robust to noise, relying on smooth separable NMF. Empirically, we show that our method outperforms the state of the art on synthetic and real data.
Authors: Alexandra Dache, Arnaud Vandaele, Nicolas Gillis
Institution: University of Mons
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G5092193842
OpenAlex ID: W4404037685