基于代数粒的聚类方法

A clustering method based on algebraic granularity

聚类,是机器学习的主要任务之一,也是粒计算理论的核心任务,即信息粒化。目前,基于粒计算的聚类算法中,大多数只基于粒属性进行聚类,而没有考虑粒结构,尤其是在代数结构应用广泛的信息领域。从粒计算的角度,提出一种基于代数粒的聚类方法。基于二元代数运算定义代数粒;提出一种基于代数粒的聚类方法,通过粒集的同余划分和粒结构的同态映射进行粒度聚类;将提出的聚类方法与容差邻域模型和商空间模型进行对比分析。结果表明,该新型方法具有更好的结构完备性和应用鲁棒性。基于代数粒的聚类方法从结构上丰富和扩展了粒度计算理论,为粒计算与机器学习的融合研究提供了理论依据。

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.