Diffusion process with structural changes for subspace clustering

Abstract

Spectral clustering-based methods have gained significant popularity in subspace clustering due to their ability to capture the underlying data structure effectively. Standard spectral clustering focuses on only pairwise relationships between data points, neglecting interactions among high-order neighboring points. Integrating the diffusion process can address this limitation by leveraging a Markov random walk. However, ensuring that diffusion methods capture sufficient information while maintaining stability against noise remains challenging. In this paper, we propose the Diffusion Process with Structural Changes (DPSC) method, a novel affinity learning framework that enhances the robustness of the diffusion process. Our approach broadens the scope of nearest neighbors and leverages the dropout idea to generate random transition matrices. Furthermore, inspired by the structural changes model, we use two transition matrices to optimize the iteration rule. The resulting affinity matrix undergoes self-supervised learning and is subsequently integrated back into the diffusion process for refinement. Notably, the convergence of the proposed DPSC is theoretically proven. Extensive experiments on benchmark datasets demonstrate that the proposed method outperforms existing subspace clustering methods. The code of our proposed DPSC is available at https://github.com/zhudafa/DPSC.