相关论文: Coresets for Weight-Constrained Anisotropic Assign…

In the Min-Sum-Radii (MSR) clustering problem, we are given a finite set X of n points in a metric space. The objective is to find at most k clusters centered at a subset of these points such that every point of X is assigned to one of the…

Modern data analysis often involves massive datasets with hundreds of thousands of observations, making traditional inference algorithms computationally prohibitive. Coresets are selection methods designed to choose a smaller subset of…

Neural network-based clustering has recently gained popularity, and in particular a constrained clustering formulation has been proposed to perform transfer learning and image category discovery using deep learning. The core idea is to…

Accurate coresets are a weighted subset of the original dataset, ensuring a model trained on the accurate coreset maintains the same level of accuracy as a model trained on the full dataset. Primarily, these coresets have been studied for a…

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the…

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…

We study the robust geometric median problem in Euclidean space $\mathbb{R}^d$, with a focus on coreset construction.A coreset is a compact summary of a dataset $P$ of size $n$ that approximates the robust cost for all centers $c$ within a…

We refine and generalize what is known about coresets for classification problems via the sensitivity sampling framework. Such coresets seek the smallest possible subsets of input data, so one can optimize a loss function on the coreset and…

One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over…

Clustering is an essential technique for network analysis, with applications in a diverse range of fields. Although spectral clustering is a popular and effective method, it fails to consider higher-order structure and can perform poorly on…

We study fair clustering problems in a setting where distance information is obtained from two sources: a strong oracle providing exact distances, but at a high cost, and a weak oracle providing potentially inaccurate distance estimates at…

Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…

Clustering is the task of gathering similar data samples into clusters without using any predefined labels. It has been widely studied in machine learning literature, and recent advancements in deep learning have revived interest in this…

We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…

We study the construction of coresets for kernel density estimates. That is we show how to approximate the kernel density estimate described by a large point set with another kernel density estimate with a much smaller point set. For…

While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…

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…

Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…

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…