The clustering method based on the anchor graph has gained significant attention due to its exceptional clustering performance and ability to process large-scale data. One common approach is to learn bipartite graphs with K-connected components, helping avoid the need for post-processing. However, this method has strict parameter requirements and may not always get K-connected components. To address this issue, an alternative approach is to directly obtain the cluster label matrix by performing non-negative matrix factorization (NMF) on the anchor graph. Nevertheless, existing multi-view clustering methods based on anchor graph factorization lack adequate cluster interpretability for the decomposed matrix and often overlook the inter-view information. We address this limitation by using non-negative tensor factorization to decompose an anchor graph tensor that combines anchor graphs from multiple views. This approach allows us to consider inter-view information comprehensively. The decomposed tensors, namely the sample indicator tensor and the anchor indicator tensor, enhance the interpretability of the factorization. Extensive experiments validate the effectiveness of this method.

Anchor-based methods are a pivotal approach in handling clustering of large-scale data. However, these methods typically entail two distinct stages: selecting anchor points and constructing an anchor graph. This bifurcation, along with the initialization of anchor points, significantly influences the overall performance of the algorithm. To mitigate these issues, we introduce a novel method termed Anchor-free Clustering based on Anchor Graph Factorization (AFCAGF). AFCAGF innovates in learning the anchor graph, requiring only the computation of pairwise distances between samples. This process, achievable through straightforward optimization, circumvents the necessity for explicit selection of anchor points. More concretely, our approach enhances the Fuzzy k-means clustering algorithm (FKM), introducing a new manifold learning technique that obviates the need for initializing cluster centers. Additionally, we evolve the concept of the membership matrix between cluster centers and samples in FKM into an anchor graph encompassing multiple anchor points and samples. Employing Non-negative Matrix Factorization (NMF) on this anchor graph allows for the direct derivation of cluster labels, thereby eliminating the requirement for further post-processing steps. To solve the method proposed, we implement an alternating optimization algorithm that ensures convergence. Empirical evaluations on various real-world datasets underscore the superior efficacy of our algorithm compared to traditional approaches.