Joint Learning of Anchor Graph-Based Fuzzy Spectral Embedding and Fuzzy K-Means

As one of the classical clustering techniques, spectral embedding boasts extensive applicability across numerous domains. Traditional spectral embedding techniques entail the mapping of graph models to low-dimensional vector spaces (indicator vectors) to facilitate hard partitioning. However, data boundaries occasionally exhibit ambiguity, thereby constraining the utility of hard partitioning. In this article, we introduce an innovative spectral embedding method, namely, joint learning of anchor graph-based fuzzy spectral embedding model and fuzzy K-means (AFSEFK). Drawing inspiration from fuzzy logic, our method employs a membership vector in lieu of the conventional indicator vector for spectral embedding, amalgamating it with fuzzy K-means to concurrently optimize membership, thereby simultaneously learning the local and global structures inherent in the data. Moreover, to enhance the quality of similarity graphs and augment clustering performance, we implement the balanced K-means-based hierarchical K-means technique to generate representative anchors. Subsequently, an anchor-based similarity graph is devised through a parameter-free neighbor assignment strategy. Comprehensive extensive experimentation with synthetic and real-world datasets substantiates the efficacy of the AFSEFK algorithm.