# A close-up comparison of the misclassification error distance and the adjusted Rand index for external clustering evaluation

## TL;DR

This paper compares the misclassification error distance and the adjusted Rand index to understand their differences, properties, and what they measure in clustering evaluation through theoretical analysis and simulations.

## Contribution

It provides a detailed comparison of two popular clustering evaluation metrics, clarifying their properties and correcting misconceptions.

## Key findings

- The two criteria measure different aspects of clustering quality.
- Simulation results reveal distributional differences and biases.
- The study clarifies the interpretation of each metric in practice.

## Abstract

The misclassification error distance and the adjusted Rand index are two of the most commonly used criteria to evaluate the performance of clustering algorithms. This paper provides an in-depth comparison of the two criteria, aimed to better understand exactly what they measure, their properties and their differences. Starting from their population origins, the investigation includes many data analysis examples and the study of particular cases in great detail. An exhaustive simulation study allows inspecting the criteria distributions and reveals some previous misconceptions.