Related papers: Coresets for Constrained Clustering: General Assig…
In this paper, we study the problem of {\em $k$-center clustering with outliers}. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a…
Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…
Metric clustering is fundamental in areas ranging from Combinatorial Optimization and Data Mining, to Machine Learning and Operations Research. However, in a variety of situations we may have additional requirements or knowledge, distinct…
In discrete k-center and k-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center,…
Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…
Recent advances in center-based clustering continue to improve upon the drawbacks of Lloyd's celebrated $k$-means algorithm over $60$ years after its introduction. Various methods seek to address poor local minima, sensitivity to outliers,…
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…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from…
Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…
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…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative…
We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…
A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems…
The fuzzy $K$-means problem is a popular generalization of the well-known $K$-means problem to soft clusterings. We present the first coresets for fuzzy $K$-means with size linear in the dimension, polynomial in the number of clusters, and…
The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a…
We give relative error coresets for training linear classifiers with a broad class of loss functions, including the logistic loss and hinge loss. Our construction achieves $(1\pm \epsilon)$ relative error with $\tilde O(d \cdot…
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…