Clustering Multivariate Normal Distributions
Clustering Multivariate Normal Distributions
复制标题
多元正态分布聚类
DOI：
10.1007/978-3-642-00826-9_7
复制
发表时间：
2009
影响因子：
8.2
通讯作者：
R. Nock
中科院分区：
文献类型：
--
作者：
F. Nielsen;R. Nock
在本文中，我们考虑使用Lloyd's k -means算法[1]的推广将相对于相对熵的多元正态分布聚类到指定数量k的聚类中的任务。我们在混合型Bregman发散的主持下重新审视了这个信息论聚类问题，并表明一旦定义了适当的向量/矩阵Legendre变换，通过应用Bregman k -均值算法，也可以直接导出Davis和Dhillon [2]（NIPS*06）的方法。本文进一步解释了边k -均值聚类的二元结构，提出了一种新的基于对称相对熵J -散度的k -均值聚类算法，并将其推广到统计学中相同指数族任意成员的微分熵聚类.
In this paper, we consider the task of clustering multivariate normal distributions with respect to the relative entropy into a prescribed number, k , of clusters using a generalization of Lloyd's k -means algorithm [1]. We revisit this information-theoretic clustering problem under the auspices of mixed-type Bregman divergences, and show that the approach of Davis and Dhillon [2] (NIPS*06) can also be derived directly, by applying the Bregman k -means algorithm, once the proper vector/matrix Legendre transformations are defined. We further explain the dualistic structure of the sided k -means clustering, and present a novel k -means algorithm for clustering with respect to the symmetrical relative entropy, the J -divergence.Our approach extends to differential entropic clustering of arbitrary members of the same exponential families in statistics.