Probabilistic Anchor Graph Projection for Tensorized Unified Label Learning

Although anchor-graph-based multi-view clustering has achieved significant success in handling datasets with arbitrary shapes, current methods still face several challenges. First, many anchor-graph-based methods fail to fully exploit the structural information of the anchor graph. They directly apply regression or decomposition to the anchor graph, overlooking the similarity information between anchor points and data points, which leads to suboptimal clustering results. Second, many anchor-graph-based algorithms only consider sample labels, neglecting the impact of anchor point labels on sample labels. A further difficulty is that an imbalanced anchor distribution may not represent the sample distribution faithfully and can propagate biased assignments to the sample labels. To address these issues, this paper proposes a Probabilistic Anchor Graph Projection for Tensorized Unified Label Learning (PAGP-TULL) method. Specifically, we introduce a label propagation strategy into the regression process of the anchor graph, obtaining probabilistic projections of both anchor point labels and sample labels. Additionally, we stack the soft label matrices of all views into a third-order tensor and impose a tensor Schatten p-norm regularization to fully exploit the high-order complementary information and spatial low-rank structures embedded across different views. Furthermore, we introduce concept regression to reduce the number of variables and thus lower the algorithm’s complexity. We also fully exploit the structural information of the anchor graph, using anchor point labels to guide the learning of sample labels. At the same time, we design a novel balanced regularization term to prevent the occurrence of two trivial solutions for anchor point labels, thereby improving the robustness and performance of the method. Extensive experiments validate the effectiveness and superiority of the PAGP-TULL method.