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In redistricting litigation, effective enforcement of the Voting Rights Act has often involved providing the court with districting plans that display a larger number of majority-minority districts than the current proposal (as was true,…
This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…
When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both…
There are various cluster validity indices used for evaluating clustering results. One of the main objectives of using these indices is to seek the optimal unknown number of clusters. Some indices work well for clusters with different…
VARCLUST algorithm is proposed for clustering variables under the assumption that variables in a given cluster are linear combinations of a small number of hidden latent variables, corrupted by the random noise. The entire clustering task…
The boundaries of electoral constituencies for assembly and parliamentary seats are drafted using a process referred to as delimitation, which ensures fair and equal representation of all citizens. The current delimitation exercise suffers…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
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…
Consensus clustering, a fundamental task in machine learning and data analysis, aims to aggregate multiple input clusterings of a dataset, potentially based on different non-sensitive attributes, into a single clustering that best…
Consensus clustering seeks to combine multiple clusterings of the same dataset, potentially derived by considering various non-sensitive attributes by different agents in a multi-agent environment, into a single partitioning that best…
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability,…
Clustering is a fundamental task in unsupervised learning, but most existing methods heavily rely on hyperparameters such as the number of clusters or other sensitive settings, limiting their applicability in real-world scenarios. To…
Clustering of variables is as a way to arrange variables into homogeneous clusters, i.e., groups of variables which are strongly related to each other and thus bring the same information. These approaches can then be useful for dimension…
Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…
The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical separability,…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…
The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element in several states' reform efforts has been the inclusion of…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
After every U.S. national census, a state legislature is required to redraw the boundaries of congressional districts in order to account for changes in population. At the moment this is done in a highly partisan way, with districting done…