Semi-Supervised Adaptive Symmetric Nonnegative Matrix Factorization for Multi-View Clustering

Multi-view clustering (MVC) has gained attention for its ability to efficiently handle complex high-dimensional data. Many existing MVC methods rely on a technique known as Nonnegative Matrix Factorization (NMF). Among these, Symmetric Nonnegative Matrix Factorization (SNMF) notably stands out for its ability to reduce dimensionality and provide easily interpretable representations. However, existing research highlights several challenges associated with SNMF. Firstly, it often necessitates the manual creation of the similarity matrix, which can be effort-intensive. Additionally, SNMF intrinsically employs an unsupervised learning approach, thus inherently neglecting the potential utility of label information. Lastly, while it concentrates on identifying shared information within multi-view data, it tends to overlook the valuable insights that different views might individually present. To overcome these limitations, we propose a novel semi-supervised multi-view clustering framework, termed Semi-supervised Adaptive Symmetric NMF (SSA-SNMF), which integrates adaptive learning and supervision into the SNMF model. The proposed method incorporates three essential components into its objective function: (1) adaptive similarity matrix construction to automatically capture data relationships, (2) integration of pairwise constraint information to leverage available supervision, and (3) a fusion mechanism that balances complementary and consensus information across views. We also derive an efficient optimization algorithm with convergence guarantees. Experimental results on six benchmark datasets show that SSA-SNMF consistently outperforms six state-of-the-art methods, demonstrating its effectiveness and robustness for multi-view clustering tasks.