Abstract: Clustering is the main task of machine learning, and is also the core work of granular computing, namely information granulation. At present, most of granular computing based clustering algorithms only utilize the granule features without taking the granule structure into account, especially in the information field where algebraic structure is widely used. From the perspective of granular computing, this paper proposes a clustering method based on algebraic granularity (CMAG). Firstly, the algebraic granularity is newly formulated with the granule structure of an algebraic binary operator.  Se- condly, the CMAG is proposed with granules of incorporating congruence partition and granule structure of homeomorphic projection. Finally, the CMAG is experimentally compared with the tolerance domain model and the quotient space model, and the results show that the CMAG has better structural completeness and practical robustness. The CMAG can enrich and extend the granular computing theory from granule structure, and will provide a theoretical basis for the combination of granular computing methods and machine learning theory.

Key words: granular computing, clustering, granulation, rough set, quotient space model