A Family of Metrics for Clustering Algorithms

TL;DR

This paper introduces a flexible family of metrics for evaluating clustering algorithms based on feature scores like stability and noise sensitivity, with a method to empirically determine scoring parameters.

Contribution

It proposes a new scoring metric for clustering algorithms that incorporates multiple feature-based scores with empirically derived parameters.

Findings

Defined a mathematical form for the metric M(A)

Provided a method to score features like stability and noise sensitivity

Presented a sample set of scores for evaluation

Abstract

We give the motivation for scoring clustering algorithms and a metric $M : A \rightarrow \mathbb{N}$ from the set of clustering algorithms to the natural numbers which we realize as \begin{equation} M(A) = \sum_i \alpha_i |f_i - \beta_i|^{w_i} \end{equation} where $\alpha_i,\beta_i,w_i$ are parameters used for scoring the feature $f_i$, which is computed empirically.. We give a method by which one can score features such as stability, noise sensitivity, etc and derive the necessary parameters. We conclude by giving a sample set of scores.