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.

聚类作为机器学习的主要任务之一，也是粒计算的核心工作，即粒化。近来大多数基于粒计算的聚类算法只利用普通粒特征而没有考虑粒结构，特别是在代数结构应用广泛的信息领域。本文旨在从粒计算的角度提出一种基于代数结构的聚类方法。具体地，基于代数结构的粒度首先基于代数二元算子的粒度结构被制定。然后，通过结合同余划分粒和同态投影粒结构，提出了一种基于代数结构的聚类方法。最后，多层次格的证明和实验案例的比较分析验证了所提出的聚类方法的有效性。基于代数结构的聚类方法可以提供一个通用框架来使用代数颗粒结构信息进行粒度聚类。同时结合粒计算理论和聚类理论，提出了粒计算方法。