球形Wards聚类与广义沃罗诺伊图
Spherical Wards clustering and generalized Voronoi diagrams
摘要：
高斯混合模型在许多实际问题中有着广泛的应用。然而，它不能直接推广到非欧几里德空间。为了克服这个问题，我们提出了一个球形高斯为基础的聚类方法划分数据集的任意相异性措施。所提出的方法是一个球交叉熵聚类与广义Wards方法相结合。该算法通过自动删除不携带信息的组来找到最佳的聚类数。此外，它是尺度不变的，并允许形成任意大小的球形簇。为了图形化地表示和解释结果，将沃罗诺伊图的概念推广到非欧空间，并应用于引入聚类方法。
英文摘要：
Gaussian mixture model is very useful in many practical problems. Nevertheless, it cannot be directly generalized to non Euclidean spaces. To overcome this problem we present a spherical Gaussian-based clustering approach for partitioning data sets with respect to arbitrary dissimilarity measure. The proposed method is a combination of spherical Cross-Entropy Clustering with a generalized Wards approach. The algorithm finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, it is scale invariant and allows for forming of spherically-shaped clusters of arbitrary sizes. In order to graphically represent and interpret the results the notion of Voronoi diagram was generalized to non Euclidean spaces and applied for introduced clustering method.
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