The k points that optimally represent a distribution (usually in terms of a squared error loss) are called the k principal points. This paper presents a computationally intensive method that automatically determines the principal points of a parametric distribution. Cluster means from the k-means algorithm are nonparametric estimators of principal points. A parametric k-means approach is introduced for estimating principal points by running the k-means algorithm on a very large simulated data set from a distribution whose parameters are estimated using maximum likelihood. Theoretical and simulation results are presented comparing the parametric k-means algorithm to the usual k-means algorithm and an example on determining sizes of gas masks is used to illustrate the parametric k-means algorithm.

中文翻译：

---

参数 k 均值算法。

最佳地表示分布的 k 个点（通常根据平方误差损失）称为 k 个主要点。本文提出了一种计算密集型方法，可以自动确定参数分布的主要点。k-means 算法的聚类均值是主要点的非参数估计量。引入了参数 k-means 方法，通过在来自分布的非常大的模拟数据集上运行 k-means 算法来估计主要点，该分布的参数是使用最大似然估计的。将参数k-means算法与常用k-means算法进行了比较，给出了理论和仿真结果，并通过一个确定防毒面具尺寸的例子来说明参数k-means算法。