# Comparing partitions through the Matching Error

## TL;DR

This paper investigates the Matching Error as a non-parametric method to compare data partitions, analyzing its properties and distribution, and proposing a hypothesis test to evaluate clustering similarity.

## Contribution

It introduces a new hypothesis test based on the Matching Error for comparing partitions, with a detailed analysis of its properties and distribution.

## Key findings

- Matching Error effectively compares partitions
- Proposed hypothesis test shows good efficiency in simulations
- Distribution function of ME analyzed for independent partitions

## Abstract

With the aim to propose a non parametric hypothesis test, this paper carries out a study on the Matching Error (ME), a comparison index of two partitions obtained from the same data set, using for example two clustering methods. This index is related to the misclassifica-tion error in supervised learning. Some properties of the ME and, especially, its distribution function for the case of two independent partitions are analyzed. Extensive simulations show the efficiency of the ME and we propose a hypothesis test based on it.