论文标题
对称NMF问题的SYMNMF-NET
SymNMF-Net for The Symmetric NMF Problem
论文作者
论文摘要
最近，许多作品表明，对称非负矩阵分解〜（SYMNMF）在各种聚类任务方面具有极大的优势。尽管SYMNMF的最新算法在综合数据上表现良好，但它们不能始终如一地获得令人满意的结果，并且可能会失败，例如聚类等现实世界任务。在本文中，考虑到神经网络的灵活性和强大的表示能力，我们提出了一个称为Symnmf-net的神经网络，以解决对称NMF问题，以克服传统优化算法的缺点。 SYMNMF-NET的每个块都是一个可区分的体系结构，具有反转层，线性层和relu，其灵感来自SymnMF的传统更新方案。我们表明，每个块的推断对应于优化的单个迭代。此外，我们分析了反转层的约束，以确保网络在一定程度上的输出稳定性。现实世界数据集的经验结果证明了我们的symnmf-net的优势，并确认了我们的理论分析的充分性。
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.
