Spectral Embedding Representation Based on Random Anchor Graph Aggregation

Anchor-based strategies have been widely used to accelerate spectral clustering, yet their effectiveness is directly affected by the quality of the selected anchors. Random sampling has become one of the most important anchor determination methods due to its efficiency. However, the anchors obtained by a single random sampling often fail to adequately capture the topological structure of the original data, making it difficult for the constructed anchor graph to achieve satisfactory clustering performance. To solve this problem, we propose a novel spectral embedding representation model based on random anchor graph aggregation (RAGA), in which an aggregated anchor graph can be produced to obtain enhanced sample representation capability. Specifically, we perform multiple random samplings to make the distribution of the selected anchors approximate the original data within a reasonable sampling time. Subsequently, adaptive weighted learning is performed on the contribution of the constructed multiple anchor graphs, and then an aggregated anchor graph can be formed, which can portray the topological structure of the original samples more precisely. In addition, spectral embedding and spectral rotation are integrated into a joint learning framework to reduce the model learning error accumulation caused by the traditional two-stage framework. Notably, we propose a rigorous theorem for analyzing the approximation of samples by the selected anchors in multiple random samplings. Our proposed RAGA maintains the speed advantage of random sampling while obtaining a high-quality aggregated anchor graph, enabling it to handle large-scale data scenarios. Experimental results on several benchmark datasets show that the RAGA model outperforms other state-of-the-art (SOTA) anchor graph-based clustering methods.