相关论文: Coresets for Clustering with Missing Values

We study the problem of $k$-center clustering with outliers in arbitrary metrics and Euclidean space. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm…

We study in this paper the problem of maintaining a solution to $k$-median and $k$-means clustering in a fully dynamic setting. To do so, we present an algorithm to efficiently maintain a coreset, a compressed version of the dataset, that…

Deep image clustering methods are typically evaluated on small-scale balanced classification datasets while feature-based $k$-means has been applied on proprietary billion-scale datasets. In this work, we explore the performance of…

A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as…

We study $k$-clustering problems with lower bounds, including $k$-median and $k$-means clustering with lower bounds. In addition to the point set $P$ and the number of centers $k$, a $k$-clustering problem with (uniform) lower bounds gets a…

Constrained clustering problems generalize classical clustering formulations, e.g., $k$-median, $k$-means, by imposing additional constraints on the feasibility of clustering. There has been significant recent progress in obtaining…

Although numerous clustering algorithms have been developed, many existing methods still leverage k-means technique to detect clusters of data points. However, the performance of k-means heavily depends on the estimation of centers of…

Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…

Among many clustering algorithms, the K-means clustering algorithm is widely used because of its simple algorithm and fast convergence. However, this algorithm suffers from incomplete data, where some samples have missed some of their…

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…

In this paper we initiate a systematic study of exact algorithms for well-known clustering problems, namely $k$-Median and $k$-Means. In $k$-Median, the input consists of a set $X$ of $n$ points belonging to a metric space, and the task is…

Clustering plays a crucial role in computer science, facilitating data analysis and problem-solving across numerous fields. By partitioning large datasets into meaningful groups, clustering reveals hidden structures and relationships within…

We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…

We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…

Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…

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…

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to…

Coreset Selection (CS) aims to identify a subset of the training dataset that achieves model performance comparable to using the entire dataset. Many state-of-the-art CS methods select coresets using scores whose computation requires…

Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…

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…