Tensorized Graph Learning for Spectral Ensemble Clustering

Ensemble clustering based on co-association matrices integrates multiple connective matrices from base clusterings to achieve superior results. However, these methods primarily focus on inter-sample relationships, neglecting variations across different base clusterings, potentially introducing noise. Additionally, they overlook interactions between samples and base clusterings, which are crucial for extracting common information and avoiding post-processing steps that may cause information loss and instability in clustering results. To address these issues, we propose the Tensorized Graph Learning for Spectral Ensemble Clustering (TGLSEC) model. TGLSEC stacks all connective matrices into a third-order tensor, employs Fast Fourier Transform (FFT) for encoding, and elucidates inter-relations in the frequency domain. By minimizing the tensor Schatten p-norm, TGLSEC extracts common information in the low-rank space, eliminating noise and improving the quality of the common shared graph. Incorporating Laplacian rank constraints, TGLSEC learns a common shared graph with c-connected components, directly representing the clustering structure and avoiding post-processing steps, leading to more stable clustering results. To enhance computational efficiency for large-scale datasets, TGLSEC has been expanded into a bipartite-graph-based model, TGLSEC-BG, reducing complexity and computational time. Extensive experiments on real-world datasets demonstrate that TGLSEC and TGLSEC-BG exhibit superior clustering performance and robustness to noise.