# Clustering with Statistical Error Control

## TL;DR

This paper introduces a clustering method that incorporates statistical error control, enabling rigorous control over overestimation and underestimation probabilities of true clusters, with theoretical guarantees and practical applications.

## Contribution

It develops estimators for the number of clusters and the clusters themselves that incorporate a tunable significance level for error control, a novel approach in clustering.

## Key findings

- The estimators effectively control overestimation probability.
- The method provides asymptotic control over underestimation.
- Applications demonstrate practical utility in temperature and gene expression data.

## Abstract

This paper presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on a tuning parameter alpha which is similar to the significance level of a statistical hypothesis test. By choosing alpha, one can control the probability of overestimating the true number of clusters, while the probability of underestimation is asymptotically negligible. In addition, the probability that the estimated clusters differ from the true ones is controlled. In the theoretical part of the paper, formal versions of these statements on statistical error control are derived in a standard model setting with convex clusters. A simulation study and two applications to temperature and gene expression microarray data complement the theoretical analysis.