Algebraic Structure Based Clustering Method from Granular Computing Prospective

Clustering, as one of the main tasks of machine learning, is also the core work of granular computing, namely granulation. Most of the recent granular computing based clustering algorithms only utilize the plain granule features without taking the granule structure into account, especially in information area with widespread application of algebraic structure. This paper aims at proposing an algebraic structure based clustering method from granular computing prospective. Specifically, the algebraic structure based granularity is firstly formulated based on the granule structure of an algebraic binary operator. An algebraic structure based clustering method is then proposed by incorporating congruence partitioning granules and homomorphically projecting granule structure. Finally, proof of the lattice at multiple hierarchical levels and comparative analysis of experimental cases validate the effectiveness of the proposed clustering method. The algebraic structure based clustering method can provide a general framework to perform granularity clustering using the algebraic granule structure information. It meanwhile advances the granular computing methods by combing the granular computing theory and the clustering theory.