Fast Multi-View Discrete Clustering Via Spectral Embedding Fusion

Multi-view spectral clustering (MVSC) has garnered growing interest across various real-world applications, owing to its flexibility in managing diverse data space structures. Nevertheless, the fusion of multiple $n\times n$ similarity matrices and the separate post- discretization process hinder the utilization of MVSC in large-scale tasks, where $n$ denotes the number of samples. Moreover, noise in different similarity matrices, along with the two-stage mismatch caused by the post- discretization, results in a reduction in clustering effectiveness. To overcome these challenges, we establish a novel fast multi-view discrete clustering (FMVDC) model via spectral embedding fusion, which integrates spectral embedding matrices ($n\times c$, $c\ll n$) to directly obtain discrete sample categories, where $c$ indicates the number of clusters, bypassing the need for both similarity matrix fusion and post- discretization. To further enhance clustering efficiency, we employ an anchor-based spectral embedding strategy to decrease the computational complexity of spectral analysis from cubic to linear. Since gradient descent methods are incapable of discrete models, we propose a fast optimization strategy based on the coordinate descent method to solve the FMVDC model efficiently. Extensive studies demonstrate that FMVDC significantly improves clustering performance compared to existing state-of-the-art methods, particularly in large-scale clustering tasks.