论文标题
重新思考对称矩阵分解：一个更通用，更好的聚类视角
Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective
论文作者
论文摘要
非负矩阵分解（NMF）广泛用于聚类，具有强大的解释性。在一般的NMF问题中，对称NMF是一个特殊的问题，它在图形聚类中起着重要作用，其中每个元素都测量了数据点之间的相似性。大多数现有的对称NMF算法都需要因子矩阵为非负数，并且仅着重于最大程度地减少相似性矩阵及其近似值之间的差距，而无需考虑其他潜在的正则化项，从而产生更好的聚类。在本文中，我们探索了不必不需要的对称矩阵，它具有有效的分解算法，具有正则化项以提高聚类性能。此外，提出了一个更一般的框架来解决因因子矩阵而具有不同限制的对称矩阵分解问题。
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in 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 similarity 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 factorizing 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 general framework is proposed to solve symmetric matrix factorization problems with different constraints on the factor matrices.
