论文标题
关于度量和非现代K-摩托车的一致性
On the Consistency of Metric and Non-Metric K-medoids
论文作者
论文摘要
我们在度量空间的背景下建立了K-Medoids的一致性。我们首先证明K-Medoids在一般条件下渐近地等同于K均值的基础分布的支持，包括多种损失函数。反过来，这种渐近等效性使我们能够将Parna（1986）的工作应用于K-均值的一致性。这种一般方法也适用于仅可用的差异订购的非金属设置。我们考虑两种类型的序数信息：一个可用的四倍体比较的地方；还有一个只有三倍比较的地方。我们提供了一些数值实验来说明我们的理论。
We establish the consistency of K-medoids in the context of metric spaces. We start by proving that K-medoids is asymptotically equivalent to K-means restricted to the support of the underlying distribution under general conditions, including a wide selection of loss functions. This asymptotic equivalence, in turn, enables us to apply the work of Parna (1986) on the consistency of K-means. This general approach applies also to non-metric settings where only an ordering of the dissimilarities is available. We consider two types of ordinal information: one where all quadruple comparisons are available; and one where only triple comparisons are available. We provide some numerical experiments to illustrate our theory.
