Fuzzy clustering has emerged as one of the fundamental conceptual and algorithmic frameworks supporting the development of information granules. Generic fuzzy clustering such as fuzzy C-means (FCM) has been utilized in a broad range of applications. However, the constructs resulting from fuzzy clustering, namely a partition matrix and prototypes, are numeric and as such are not capable of fully capturing the essence of the overall data. In this study, we propose an alternative augmented way of building information granules by generating hypercube-like information granules. A collection of hypercubes is referred to as a family of ε-information granules. This family is constructed around numeric prototypes generated through a modified version of the FCM algorithm whose running time is linear with respect to the number of clusters. By admitting a certain level of information granularity (ε), a collection of hypercubes is formed around the prototypes. The quality of information granules realized in this way is assessed by involving them in the granulation-degranulation process as well as determining a value of the coverage criterion. The level of information granularity and the number of the granular prototypes in the family of ε-information granules form an important design asset directly impacting the obtained coverage level of the data. The computational facet of the approach is stressed. It has been demonstrated that the granular enhancements of the description of data come with a very limited computing overhead. Experimental studies involve synthetic data as well as data coming from the UCI Machine Learning repository. The granular reconstruction capabilities delivered by the family of ε-information granules are discussed.

中文翻译：

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数据的粒度表示：系信息粒度族的设计


模糊聚类已成为支持信息颗粒发展的基本概念和算法框架之一。模糊 C 均值 (FCM) 等通用模糊聚类已在广泛的应用中得到利用。然而，模糊聚类产生的构造，即划分矩阵和原型，是数字的，因此不能完全捕捉整体数据的本质。在本研究中，我们提出了一种通过生成类似超立方体的信息颗粒来构建信息颗粒的替代增强方法。超立方体的集合称为 ε-信息颗粒族。该系列是围绕通过 FCM 算法的修改版本生成的数字原型构建的，该算法的运行时间与集群数量呈线性关系。通过承认一定程度的信息粒度（ε），围绕原型形成超立方体的集合。以这种方式实现的信息颗粒的质量是通过将它们参与颗粒化-去颗粒过程以及确定覆盖标准的值来评估的。信息粒度的水平和ε-信息颗粒族中的颗粒原型的数量形成了直接影响所获得的数据覆盖水平的重要设计资产。强调该方法的计算方面。事实证明，数据描述的粒度增强伴随着非常有限的计算开销。实验研究涉及合成数据以及来自 UCI 机器学习存储库的数据。讨论了 ε-信息颗粒族提供的颗粒重建能力。