運用高斯函數之具穩健性的核心化Ｋ均值分類演算法

A Robust K-means clustering algorithm based on Gaussian kernel

林宥均(You-Jun Lin)

指導教授 ： 吳國龍

崑山科技大學/資訊科技學院/資訊管理研究所/碩士(2012年)

摘要

在本篇論文中，我們提出了一種結合高斯核函數概念的K均值分類演算法，我們稱之為核心化K均值演算法。我們提出的演算法可以透過統計的方法來證明其穩健性，並且可以利用M-estimate推導出K均值演算法的群中心估計式的 函數，而且可以證明此 函數式有界的。實驗數據可以證實我們提出的方法確實優於其他分類演算法。

關鍵字

核方法 ； K均值 ； 穩健性

並列摘要

In this paper, we proposed a kernelized k-means algorithm based on the Gaussian kernel function according to the concepts of support vector clustering and kernel methods. A statistical point of view of robust properties of the proposed method is analyzed. The cluster center estimates obtained by the proposed method can be represented by an M-estimate with a bounded function. This provides the theoretical advance to support the robustness of our clustering method. Numerical examples also show the superiority of the proposed method.

並列關鍵字

kernel method ； k-means ； robust

參考文獻

[4]G. Gautam, and B.B Chaudhuri, “A Novel Genetic Algorithm for Automatic Clustering,” Pattern Recognition Letters, Vol. 25, 2004, pp. 173–187.

[6]J. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations,” In Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 1967, pp. 281-297.

[8]Kuo-Lung Wu, You-Jun Lin,” Kernelized K-means Algorithm Based On Gaussian Kernel,” ADVANCES IN CONTROL AND COMMUNICATION Lecture Notes in Electrical Engineering, Vol. 137, 2012, pp. 657-664

[11]Jain, A.K,Duin, R.P.W, Jianchang M., “Statistical Pattern recognition: a review” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 22, 2000, pp.4-37

[12]Jain, A.K, Murty, M.N and Flynn, P.J, “Data clustering: a review”, ACM Computing Surveys(CSUR), Vol. 31 NO. 3, Sept. 1999,pp.264-323