Anchor-free Clustering based on Anchor Graph Factorization
Shikun Mei Fangfang Li Quanxue Gao Ming Yang
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.