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In this paper, we test whether two datasets share a common clustering structure. As a leading example, we focus on comparing clustering structures in two independent random samples from two mixtures of multivariate normal distributions.…
The literature on cluster-randomized trials typically allows for interference within but not across clusters. This may be implausible when units are irregularly distributed across space without well-separated communities, as clusters in…
This paper is a chapter in the forthcoming Handbook of Cluster Analysis, Hennig et al. (2015). For definitions of basic clustering methods and some further methodology, other chapters of the Handbook are referred to. To read this version of…
Cluster analysis methods are used to identify homogeneous subgroups in a data set. In biomedical applications, one frequently applies cluster analysis in order to identify biologically interesting subgroups. In particular, one may wish to…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
This paper studies inference in cluster randomized trials where treatment status is determined according to a "matched pairs" design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
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…
We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…
A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. This work is primarily motivated by functional brain network construction from fMRI data, where brain…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…
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…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper,…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
In many modern statistical problems, the limited available data must be used both to develop the hypotheses to test, and to test these hypotheses-that is, both for exploratory and confirmatory data analysis. Reusing the same dataset for…