基于改进高斯核度量和KPCA的数据聚类新方法

大多数超椭球聚类（hyper-ellipsoidal clustering，HEC）算法都使用马氏距离作为距离度量，已经证明在该条件下划分聚类的代价函数是常量，导致HEC无法实现椭球聚类.本文说明了使用改进高斯核的HEC算法可以解释为寻找体积和密度都紧凑的椭球分簇，并提出了一种实用HEC算法-K-HEC，该算法能够有效地处理椭球形、不同大小和不同密度的分簇.为实现更复杂形状数据集的聚类，使用定义在核特征空间的椭球来改进K-HEC算法的能力，提出了EK-HEC算法.仿真实验证明所提出算法在聚类结果和性能上均优于K-means算法、模糊C-means算法、GMM-EM算法和基于最小体积椭球（minimum-volume ellipsoids，MVE）的马氏HEC算法，从而证明了本文算法的可行性和有效性.

Novel Data Clustering Method Based on A Modified Gaussian Kernel Metric and Kernel PCA

Most hyper-ellipsoidal clustering(HEC) algorithms use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that HEC with a modified Gaussian kernel metric can be interpreted as a problem of finding condensed ellipsoidal clusters(with respect to the volumes and densities of the clusters) and propose a practical HEC algorithm named K-HEC that is able to efficiently handle clusters that are ellipsoidal in shape and that are of different size and density. We then try to refine the K-HEC algorithm by utilizing ellipsoids defined on the kernel feature space to deal with more complex-shaped clusters. Simulation experiments demonstrate the proposed methods have a significant improvement in the clustering results and performance over K-means algorithm, fuzzy C-means algorithm, GMM-EM algorithm and HEC algorithm based on minimum-volume ellipsoids using Mahalanobis distance.