SymNMF-Net for The Symmetric NMF Problem

TL;DR

This paper introduces SymNMF-Net, a neural network designed to improve symmetric non-negative matrix factorization for clustering, outperforming traditional algorithms especially on real-world data.

Contribution

The paper proposes a novel neural network architecture for SymNMF that mimics traditional update schemes and enhances performance on real-world clustering tasks.

Findings

SymNMF-Net outperforms traditional algorithms on real-world datasets.

Each network block corresponds to a single optimization iteration.

Theoretical analysis ensures output stability of the network.

Abstract

Recently, many works have demonstrated that Symmetric Non-negative Matrix Factorization~(SymNMF) enjoys a great superiority for various clustering tasks. Although the state-of-the-art algorithms for SymNMF perform well on synthetic data, they cannot consistently obtain satisfactory results with desirable properties and may fail on real-world tasks like clustering. Considering the flexibility and strong representation ability of the neural network, in this paper, we propose a neural network called SymNMF-Net for the Symmetric NMF problem to overcome the shortcomings of traditional optimization algorithms. Each block of SymNMF-Net is a differentiable architecture with an inversion layer, a linear layer and ReLU, which are inspired by a traditional update scheme for SymNMF. We show that the inference of each block corresponds to a single iteration of the optimization. Furthermore, we analyze the constraints of the inversion layer to ensure the output stability of the network to a certain extent. Empirical results on real-world datasets demonstrate the superiority of our SymNMF-Net and confirm the sufficiency of our theoretical analysis.