Related papers: Provable Imbalanced Point Clustering

We study how to learn multiple dictionaries from a dataset, and approximate any data point by the sum of the codewords each chosen from the corresponding dictionary. Although theoretically low approximation errors can be achieved by the…

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…

Given a set of points $P \subset \mathbb{R}^d$, the $k$-means clustering problem is to find a set of $k$ {\em centers} $C = \{c_1,...,c_k\}, c_i \in \mathbb{R}^d,$ such that the objective function $\sum_{x \in P} d(x,C)^2$, where $d(x,C)$…

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…

One of the most promising approaches for unsupervised learning is combining deep representation learning and deep clustering. Some recent works propose to simultaneously learn representation using deep neural networks and perform clustering…

Multi-model fitting has been extensively studied from the random sampling and clustering perspectives. Most assume that only a single type/class of model is present and their generalizations to fitting multiple types of models/structures…

We design coresets for Ordered k-Median, a generalization of classical clustering problems such as k-Median and k-Center, that offers a more flexible data analysis, like easily combining multiple objectives (e.g., to increase fairness or…

Given their widespread usage in the real world, the fairness of clustering methods has become of major interest. Theoretical results on fair clustering show that fairness enjoys transitivity: given a set of small and fair clusters, a…

We present a $k$-means-based clustering algorithm, which optimizes the mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In the $k$-means assignment…

Coreset, which is a summary of the original dataset in the form of a small weighted set in the same sample space, provides a promising approach to enable machine learning over distributed data. Although viewed as a proxy of the original…

Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…

``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also…

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…

In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center.…

Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which…

In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on centroid clustering--one of the fundamental tasks in unsupervised machine learning. We propose a new axiom ``proportionally…

Traditional k-means clustering underperforms on non-convex shapes and requires the number of clusters k to be specified in advance. We propose a simple geometric enhancement: after standard k-means, each cluster center is assigned a radius…

There has been much interest recently in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and gender. We observe that clustering algorithms could…

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation…

In real applications, there are situations where we need to model some problems based on uncertain data. This leads us to define an uncertain model for some classical geometric optimization problems and propose algorithms to solve them. In…