  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.
