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Hierarchical clustering is a common algorithm in data analysis. It is unique among many clustering algorithms in that it draws dendrograms based on the distance of data under a certain metric, and group them. It is widely used in all areas…
This paper introduces a hierarchical clustering algorithm, the Clustroid Hierarchical Nearest Neighbor ($\mathrm{CHN}^2$), designed for datasets with a countably infinite number of points. The method builds clusters across successive levels…
The problem of hierarchical clustering items from pairwise similarities is found across various scientific disciplines, from biology to networking. Often, applications of clustering techniques are limited by the cost of obtaining…
We propose a hierarchical correlation clustering method that extends the well-known correlation clustering to produce hierarchical clusters applicable to both positive and negative pairwise dissimilarities. Then, in the following, we study…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
We consider the classic correlation clustering problem in the hierarchical setting. Given a complete graph $G=(V,E)$ and $\ell$ layers of input information, where the input of each layer consists of a nonnegative weight and a labeling of…
When scholars suspect units are dependent on each other within clusters but independent of each other across clusters, they employ cluster-robust standard errors (CRSEs). Nevertheless, what to cluster over is sometimes unknown. For…
Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…
Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…
The well-known clustering algorithm of Miller, Peng, and Xu (SPAA 2013) is useful for many applications, including low-diameter decomposition and low-energy distributed algorithms. One nice property of their clustering, shown in previous…
Semi-supervised semantic segmentation has attracted increasing attention in computer vision, aiming to leverage unlabeled data through latent supervision. To achieve this goal, prototype-based classification has been introduced and achieved…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
In data clustering, it is often desirable to find not just a single partition into clusters but a sequence of partitions that describes the data at different scales (or levels of coarseness). A natural problem then is to analyse and compare…
A clustering termination procedure which is locally adaptive (with respect to the hierarchical tree of sets representative of the agglomerative merging) is proposed, for agglomerative hierarchical clustering on a set equipped with a…
We provide a complete taxonomic characterization of robust hierarchical clustering methods for directed networks following an axiomatic approach. We begin by introducing three practical properties associated with the notion of robustness in…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
The domain of explainable AI is of interest in all Machine Learning fields, and it is all the more important in clustering, an unsupervised task whose result must be validated by a domain expert. We aim at finding a clustering that has high…
The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its…
Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the…