Clustering with Self-Learned Graph Regression

Graph-based clustering algorithms aim to construct an affinity graph that accurately captures the intrinsic structure of a dataset. To achieve this goal, these algorithms often use the k-nearest-neighbor (k-nn) method to build a graph regularizer for the required affinity graph, enabling it to have a grouping effect. However, due to the complex nature of real-world data, the k-nn method often fails to capture the true neighborhood relationships of a dataset, which in turn limits the quality of the learned affinity graph. Motivated by the insight that a learned affinity graph itself can more effectively reflect the underlying data structure, we propose a new graph-based clustering method, termed Self-learned Graph Regression (SGR). Unlike traditional approaches, SGR constructs its graph regularizer directly from the affinity graph being learned, allowing the graph to adaptively capture more accurate structural information. To solve the proposed problem, we develop an optimization algorithm along with an acceleration strategy. We further analyze the convergence and computational complexity of the proposed algorithm. Extensive clustering experiments on various benchmark datasets demonstrate that our method outperforms the state-of-the-art graph-based clustering algorithms.