架構在分散矩陣上的模糊分類演算法

Fuzzy Clustering Algorithms Based on Scatter Matrices

吳國龍(Kuo-Lung Wu)

指導教授 ： 楊敏生

中原大學/理學院/數學研究所/博士(2003年)

https://doi.org/10.6840/cycu200300260

摘要

中文摘要

大部分的分類方法都是要最佳化一個架構在within-cluster scatter matrix 上的目標函數。在本論文中，我們先把scatter matrix模糊化，然後再提出一個架構在fuzzy scatter matrix上的模糊分類演算法〈FCS〉。FCS的目標是要最小化群組內的變異的同時也能使群組間的變異量愈大愈好。

關鍵字

分散矩陣 ； 模糊分類演算法

並列摘要

Abstract

Most clustering algorithms
are proposed by optimizing an objective function which is based on
a within-cluster scatter matrix. In this paper, we define the
fuzzy scatter matrix and propose a novel fuzzy clustering
algorithm, called the fuzzy compactness & separation (FCS), based
on a fuzzy scatter matrix which the FCS algorithm is derived by
the minimization of the compactness measure and simultaneously the
maximization of the separation measure. The compactness is
measured by a fuzzy within-cluster variation and the separation is
measured by a fuzzy between-cluster variation. The proposed FCS
objective function is a modification of the FS validity index
proposed by Fukuyama and Sugeno and also a generalization of the
fuzzy c-means (FCM) clustering model. The FCS algorithm assigns
a crisp boundary (cluster kernel) for each cluster such that hard
memberships and fuzzy memberships could be co-existed in the
clustering results. Thus, FCS can be seen as a clustering
algorithm with a novel sense between hard c-means and fuzzy
c-means. Some numerical examples are demonstrated to show its
robust properties and effectiveness.

並列關鍵字

Robust ； Scatter Matrices ； Fuzzy Clustering ； Outlier

參考文獻

[2] J.C. Bezdek, Cluster validity with fuzzy sets, J. Cybernet.

3 (1974) 58-73.

[3] J.C. Bezdek, Numerical taxonomy with fuzzy sets, J. Math.

Biol. 1 (1974) 57-71.

[4] J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum