Anchor-free Clustering based on Anchor Graph Factorization

TL;DR

This paper introduces AFCAGF, a novel anchor-free clustering method that constructs an anchor graph directly from pairwise distances, improving efficiency and performance over traditional anchor-based methods.

Contribution

The paper proposes a new anchor-free clustering approach using anchor graph factorization and NMF, eliminating the need for anchor point selection and initialization.

Findings

Outperforms traditional anchor-based clustering methods on real datasets.

Eliminates the need for explicit anchor point selection and cluster center initialization.

Provides a convergent alternating optimization algorithm.

Abstract

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.