Related papers: Minimum adjusted Rand index for two clusterings of…
The Adjusted Rand Index ($ARI$) is arguably one of the most popular measures for cluster comparison. The adjustment of the $ARI$ is based on a hypergeometric distribution assumption which is unsatisfying from a modeling perspective as (i)…
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…
We consider the simultaneous clustering of rows and columns of a matrix and more particularly the ability to measure the agreement between two co-clustering partitions. The new criterion we developed is based on the Adjusted Rand Index and…
In unsupervised machine learning, agreement between partitions is commonly assessed with so-called external validity indices. Researchers tend to use and report indices that quantify agreement between two partitions for all clusters…
Adjusted for chance measures are widely used to compare partitions/clusterings of the same data set. In particular, the Adjusted Rand Index (ARI) based on pair-counting, and the Adjusted Mutual Information (AMI) based on Shannon information…
A measure of distance between two clusterings has important applications, including clustering validation and ensemble clustering. Generally, such distance measure provides navigation through the space of possible clusterings. Mostly used…
Rand (1971) proposed what has since become a well-known index for comparing two partitions obtained on the same set of units. The index takes a value on the interval between 0 and 1, where a higher value indicates more similar partitions.…
This paper investigates the application of consensus clustering and meta-clustering to the set of all possible partitions of a data set. We show that when using a "complement" of Rand Index as a measure of cluster similarity, the…
Adjusted similarity measures, such as Cohen's kappa for inter-rater reliability and the adjusted Rand index used to compare clustering algorithms, are a vital tool for comparing discrete labellings. These measures are intended to have the…
A well-known metric for quantifying the similarity between two clusterings is the adjusted mutual information. Compared to mutual information, a corrective term based on random permutations of the labels is introduced, preventing two…
The Deliberative Reason Index (DRI) is increasingly used to assess the coherence between considerations and preferences in deliberative settings, including applications to LLM-generated data. Under low-signal conditions, however, the…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
A key issue in cluster analysis is the choice of an appropriate clustering method and the determination of the best number of clusters. Different clusterings are optimal on the same data set according to different criteria, and the choice…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…
In empirical work it is common to estimate parameters of models and report associated standard errors that account for "clustering" of units, where clusters are defined by factors such as geography. Clustering adjustments are typically…
The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures. Until now, it was possible to find its solution only…
Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure…
We provide a more efficient algorithm for computing the Rand Index when the data cluster comes from a change-point detection problem. Given $N$ data points and two clusterings of size $r$ and $s$, the algorithm runs on $O(r+s)$ time…
There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering…
Clustering is at the very core of machine learning, and its applications proliferate with the increasing availability of data. However, as datasets grow, comparing clusterings with an adjustment for chance becomes computationally difficult,…