Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective
This work addresses graph clustering by generalizing symmetric matrix factorization, offering incremental improvements over existing methods.
The authors tackled the problem of symmetric matrix factorization for clustering by proposing a more general framework that allows factor matrices to be nonnegative or not, and includes regularization to improve performance, resulting in an efficient algorithm that enhances clustering outcomes.
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.