Learning unified anchor graph based on affinity relationships with strong consensus for multi-view spectral clustering

The anchor-based strategy has been successfully applied to multi-view spectral clustering for handling large-scale data. However, most recent methods have not made full use of the consensus information over multiple views, which limits their accuracies. To fill this gap, we introduce the strong consensus on the affinity relationship in which the opinion is accepted by all views and learn a unified anchor graph by a low-rank tensor approximation based on the affinity relationships with strong consensus. Concretely, we first initialize the affinity matrix of a unified anchor graph by averaging the anchor graphs of different views and construct a confidence affinity matrix to explicitly encode the affinity relationships with strong consensus. The two matrices are further combined into a third-order tensor. By computing a low-rank approximation of the tensor, the initial unified affinity matrix is refined with the reliable information from the confidence affinity matrix. To solve the derived low-rank tensor optimization problem, we design an alternating optimization algorithm with proven convergence. The experimental results on various benchmark datasets demonstrate the superiority of our method.