Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one which plays an important role for graph clustering where each element measures the similarity between data points. Most existing symmetric NMF algorithms require factor matrices to be nonnegative, and only focus on minimizing the gap between the original matrix and its approximation for clustering, without giving a consideration to other potential regularization terms which can yield better clustering. In this paper, we explore to factorize a symmetric matrix that does not have to be nonnegative, presenting an efficient factorization algorithm with a regularization term to boost the clustering performance. Moreover, a more generalized framework is proposed to solve symmetric matrix factorization problems with different constraints on the factor matrices.

翻译：非负矩阵因子化(NMF)被广泛用于解释性强的集群,在一般的NMF问题中,对称的NMF是一个特殊问题,对于每个要素衡量数据点相似性的图形集群具有重要作用,大多数现有的对称的NMF算法要求要素矩阵必须是非负的,而仅仅侧重于尽可能缩小原矩阵与其近似的集群之间的差距,而没有考虑其他可能实现更佳集群的正规化条件。在本文中,我们探讨将一个不必非负的对称矩阵作为考虑因素,提出一种有效的因子化算法,并用正规化术语来提高集群的性能。此外,还提议了一个更为广泛的框架来解决对称矩阵因子化问题,同时对要素矩阵设置不同的限制。