Related papers: Introduction to Coresets: Approximated Mean

Clustering stands as one of the most prominent challenges in unsupervised machine learning. Among centroid-based methods, the classic $k$-means algorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is a well-known fact that…

In a number of situations, collecting a function value for every data point may be prohibitively expensive, and random sampling ignores any structure in the underlying data. We introduce a scalable optimization algorithm with no correction…

Center-based clustering techniques are fundamental in some areas of machine learning such as data summarization. Generic $k$-center algorithms can produce biased cluster representatives so there has been a recent interest in fair $k$-center…

We study the problem of differentially private (DP) computation of coreset for the $k$-means objective. For a given input set of points, a coreset is another set of points such that the $k$-means objective for any candidate solution is…

While coresets have been growing in terms of their application, barring few exceptions, they have mostly been limited to unsupervised settings. We consider supervised classification problems, and non-decomposable evaluation measures in such…

Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…

In this work, we present a randomized coreset construction for projective clustering, which involves computing a set of $k$ closest $j$-dimensional linear (affine) subspaces of a given set of $n$ vectors in $d$ dimensions. Let $A \in…

Core decomposition is a classic technique for discovering densely connected regions in a graph with large range of applications. Formally, a $k$-core is a maximal subgraph where each vertex has at least $k$ neighbors. A natural extension of…

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…

Counting is among the most fundamental operations in computing. For example, counting the pth frequency moment has been a very active area of research, in theoretical computer science, databases, and data mining. When p=1, the task (i.e.,…

Quantum computing is anticipated to offer immense computational capabilities which could provide efficient solutions to many data science problems. However, the current generation of quantum devices are small and noisy, which makes it…

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…

The classical center based clustering problems such as $k$-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise…

The present paper constructs coresets for weight-constrained anisotropic assignment and clustering. In contrast to the well-studied unconstrained least-squares clustering problem, approximating the centroids of the clusters no longer…

Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…

We investigate the fine-grained complexity of approximating the classical $k$-median / $k$-means clustering problems in general metric spaces. We show how to improve the approximation factors to $(1+2/e+\varepsilon)$ and…

Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…

This paper presents universal algorithms for clustering problems, including the widely studied $k$-median, $k$-means, and $k$-center objectives. The input is a metric space containing all potential client locations. The algorithm must…

The success of deep learning requires large datasets and extensive training, which can create significant computational challenges. To address these challenges, pseudo-coresets, small learnable datasets that mimic the entire data, have been…

Among ensemble clustering methods, Evidence Accumulation Clustering is one of the simplest technics. In this approach, a co-association (CA) matrix representing the co-clustering frequency is built and then clustered to extract consensus…