Related papers: Active Distance-Based Clustering using K-medoids

A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically…

In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…

Cluster analysis which focuses on the grouping and categorization of similar elements is widely used in various fields of research. Inspired by the phenomenon of atomic fission, a novel density-based clustering algorithm is proposed in this…

In this paper we tackle the issue of clustering trajectories of geolocalized observations. Using clustering technics based on the choice of a distance between the observations, we first provide a comprehensive review of the different…

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be…

Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…

Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

The classical k-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of k-means to missing data, namely k-POD, uses only the observed…

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…

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a…

Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…

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…

Time series clustering is the act of grouping time series data without recourse to a label. Algorithms that cluster time series can be classified into two groups: those that employ a time series specific distance measure; and those that…

K-Means clustering still plays an important role in many computer vision problems. While the conventional Lloyd method, which alternates between centroid update and cluster assignment, is primarily used in practice, it may converge to a…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Clustering is a cornerstone of data analysis that is particularly suited to identifying coherent subgroups or substructures in unlabeled data, as are generated continuously in large amounts these days. However, in many cases traditional…