Related papers: Geometric clustering in normed planes

We propose a novel clustering model encompassing two well-known clustering models: k-center clustering and k-median clustering. In the Hybrid k-Clusetring problem, given a set P of points in R^d, an integer k, and a non-negative real r, our…

One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em…

Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…

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…

Clustering is a fundamental unsupervised learning approach. Many clustering algorithms -- such as $k$-means -- rely on the euclidean distance as a similarity measure, which is often not the most relevant metric for high dimensional data…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

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…

In a geometric $k$-clustering problem the goal is to partition a set of points in $\mathbb{R}^d$ into $k$ subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering…

This work explores the clustering of wireless users by examining the distances between their channel covariance matrices, which reside on the Riemannian manifold of positive definite matrices. Specifically, we consider an estimator of the…

Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…

In the 1960s Moser asked how dense a subset of $\mathbb{R}^d$ can be if no pairs of points in the subset are exactly distance 1 apart. There has been a long line of work showing upper bounds on this density. One curious feature of dense…

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…

We initiate the study of the following general clustering problem. We seek to partition a given set $P$ of data points into $k$ clusters by finding a set $X$ of $k$ centers and assigning each data point to one of the centers. The cost of a…

Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high…

Many approximation algorithms and heuristic algorithms to find a fair clustering have emerged. In this paper we define a new and natural variant of fair clustering problem and design a polynomial time algorithm to compute an optimal fair…

This paper proposes a hierarchical clustering approach for the segmentation of mobile LiDAR point clouds. We perform the hierarchical clustering on unorganized point clouds based on a proximity matrix. The dissimilarity measure in the…

In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…

Sum-of-norms clustering is a convex optimization problem whose solution can be used for the clustering of multivariate data. We propose and study a localized version of this method, and show in particular that it can separate arbitrarily…

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…