Related papers: Explainable $k$-Means and $k$-Medians Clustering

The classical $k$-means algorithm for partitioning $n$ points in $\mathbb{R}^d$ into $k$ clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been…

One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…

Big Data is a massive volume of both structured and unstructured data that is too large and it also difficult to process using traditional techniques. Clustering algorithms have developed as a powerful learning tool that can exactly analyze…

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…

Organizing data into semantically more meaningful is one of the fundamental modes of understanding and learning. Cluster analysis is a formal study of methods for understanding and algorithm for learning. K-mean clustering algorithm is one…

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size,…

Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that…

Deep learning models have become widely adopted in various domains, but their performance heavily relies on a vast amount of data. Datasets often contain a large number of irrelevant or redundant samples, which can lead to computational…

We introduce a novel problem for diversity-aware clustering. We assume that the potential cluster centers belong to a set of groups defined by protected attributes, such as ethnicity, gender, etc. We then ask to find a minimum-cost…

We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…

We study the $k$-median with discounts problem, wherein we are given clients with non-negative discounts and seek to open at most $k$ facilities. The goal is to minimize the sum of distances from each client to its nearest open facility…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

In a recent work, [19] studied the following "fair" variants of classical clustering problems such as $k$-means and $k$-median: given a set of $n$ data points in $\mathbb{R}^d$ and a binary type associated to each data point, the goal is to…

Finding a good clustering of vertices in a network, where vertices in the same cluster are more tightly connected than those in different clusters, is a useful, important, and well-studied task. Many clustering algorithms scale well,…

Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…

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…

Clustering is a fundamental tool in unsupervised learning, used to group objects by distinguishing between similar and dissimilar features of a given data set. One of the most common clustering algorithms is k-means. Unfortunately, when…

Clustering is a fundamental primitive in unsupervised learning. However, classical algorithms for $k$-clustering (such as $k$-median and $k$-means) assume access to exact pairwise distances -- an unrealistic requirement in many modern…

The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a…

We study the topic of dimensionality reduction for $k$-means clustering. Dimensionality reduction encompasses the union of two approaches: \emph{feature selection} and \emph{feature extraction}. A feature selection based algorithm for…