Concept Factorization via Self-Representation and Adaptive Graph Structure Learning

TL;DR

This work tackles the sensitivity of graph-regularized clustering to the initial affinity graph by introducing CFSRAG, a method that learns a data-driven affinity via self-representation and uses it to perform dynamic graph regularization within concept factorization. By treating $X$ as being reconstructed through an adaptive affinity $Z$ and enforcing graph-aware regularization with a learned Laplacian $L$, the approach jointly optimizes $U,V,Z$ under nonnegativity constraints with multiplicative updates. Empirical results on four real datasets show that CFSRAG outperforms state-of-the-art methods, with substantial improvements in $\text{NMI}$, $\text{ACC}$, and $\text{PUR}$, and statistically significant gains in Friedman and Wilcoxon tests. The findings highlight the benefit of integrating self-representation-based graph learning with CF to better capture both global structure and local geometric relations, offering practical gains for clustering tasks in noisy or complex data settings.

Abstract

Concept Factorization (CF) models have attracted widespread attention due to their excellent performance in data clustering. In recent years, many variant models based on CF have achieved great success in clustering by taking into account the internal geometric manifold structure of the dataset and using graph regularization techniques. However, their clustering performance depends greatly on the construction of the initial graph structure. In order to enable adaptive learning of the graph structure of the data, we propose a Concept Factorization Based on Self-Representation and Adaptive Graph Structure Learning (CFSRAG) Model. CFSRAG learns the affinity relationship between data through a self-representation method, and uses the learned affinity matrix to implement dynamic graph regularization constraints, thereby ensuring dynamic learning of the internal geometric structure of the data. Finally, we give the CFSRAG update rule and convergence analysis, and conduct comparative experiments on four real datasets. The results show that our model outperforms other state-of-the-art models.

Figures (2)

• Figure 1: CFSRAG clustering performance changes on D1, D2, D3 and D4, respectively, when $\alpha$, $\beta$ and $\lambda$ change.
• Figure 2: The variation in clustering performance of different models on D1, D2, D3 and D4 as the number of nearest neighbors $p$ changes.