Abstract

This work proposes a new clustering algorithm named FINFCM by converting original data into fuzzy interval number (FIN) firstly, then it proofs F that denotes the collection of FINs is a lattice and introduce a novel metric distance based on the results from lattice theory as well as combining them with Fuzzy c-means clustering. The relevant mathematical background about lattice theory and the specific procedure which is used to construct FIN have been presented in this paper. Three evaluation indexes including Compactness, RandIndex and Precision are applied to evaluate the performance of FINFCM, FCM and HC algorithm in four experiments used UCI public datasets. The FINFCM algorithm has shown better clustering performance compared to other traditional clustering algorithms and the results are also discussed specifically.

中文翻译：

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度量格上的模糊C均值

摘要

本文首先通过将原始数据转换为模糊区间数（FIN），提出了一种新的聚类算法FINFCM，然后证明了F表示FIN的集合是一个格，并根据格理论的结果并将其与Fuzzy c-means聚类相结合，引入了新的度量距离。本文介绍了有关晶格理论的相关数学背景以及用于构造FIN的特定过程。在使用UCI公共数据集的四个实验中，应用了紧实度，RandIndex和Precision这三个评估指标来评估FINFCM，FCM和HC算法的性能。与其他传统聚类算法相比，FINFCM算法表现出更好的聚类性能，并且还将具体讨论结果。