This paper is dedicated to the memory of Peter G. Hall. It concerns a deceptively simple question: if one observes variables corrupted with measurement error of possibly very complex form, can one recreate asymptotically the clusters that would have been found had there been no measurement error? We show that the answer is yes, and that the solution is surprisingly simple and general. The method itself is to simulate, by computer, realizations with the same distribution as that of the true variables, and then to apply clustering to these realizations. Technically, we show that if one uses K-means clustering or any other risk minimizing clustering, and a multivariate deconvolution device with certain smoothness and convergence properties, then, in the limit, the cluster means based on our method converge to the same cluster means as if there is no measurement error. Along with the method and its technical justification, we analyze two important nutrition data sets, finding patterns that make sense nutritionally.

中文翻译：

---

一般测量误差模型中的聚类。


谨以此文纪念彼得·G·霍尔 (Peter G. Hall)。它涉及一个看似简单的问题：如果观察到被可能非常复杂形式的测量误差破坏的变量，是否可以渐进地重新创建在没有测量误差的情况下会发现的簇？我们证明答案是肯定的，而且解决方案出奇地简单和通用。该方法本身就是通过计算机模拟与真实变量具有相同分布的实现，然后对这些实现应用聚类。从技术上讲，我们表明，如果使用 K 均值聚类或任何其他风险最小化聚类，以及具有一定平滑性和收敛特性的多元反卷积设备，那么在极限情况下，基于我们的方法的聚类均值会收敛到相同的聚类均值就好像没有测量误差一样。除了该方法及其技术论证之外，我们还分析了两个重要的营养数据集，寻找在营养上有意义的模式。