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Related papers: Improvements on the k-center problem for uncertain…

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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…

Machine Learning · Computer Science 2022-06-16 Ahmed Imtiaz Humayun , Randall Balestriero , Anastasios Kyrillidis , Richard Baraniuk

K-means is a classical clustering algorithm with wide applications. However, soft K-means, or fuzzy c-means at m=1, remains unsolved since 1981. To address this challenging open problem, we propose a novel clustering model, i.e.…

Machine Learning · Computer Science 2020-11-23 Yujian Li , Bowen Liu , Zhaoying Liu , Ting Zhang

We study the consistent k-center clustering problem. In this problem, the goal is to maintain a constant factor approximate $k$-center solution during a sequence of $n$ point insertions and deletions while minimizing the recourse, i.e., the…

Data Structures and Algorithms · Computer Science 2023-07-27 Jakub Łącki , Bernhard Haeupler , Christoph Grunau , Václav Rozhoň , Rajesh Jayaram

The $K$-nearest neighbors is a basic problem in machine learning with numerous applications. In this problem, given a (training) set of $n$ data points with labels and a query point $p$, we want to assign a label to $p$ based on the labels…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-25 Reza Fathi , Anisur Rahaman Molla , Gopal Pandurangan

In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…

Data Structures and Algorithms · Computer Science 2026-03-12 Kangke Cheng , Shihong Song , Guanlin Mo , Hu Ding

We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a…

Computational Geometry · Computer Science 2013-04-17 Amirali Abdullah , Samira Daruki , Jeff M. Phillips

We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…

Data Structures and Algorithms · Computer Science 2017-10-17 Tamal K. Dey , Alfred Rossi , Anastasios Sidiropoulos

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…

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…

Optimization and Control · Mathematics 2016-08-04 Steffen Borgwardt , Andreas Brieden , Peter Gritzmann

We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration…

Data Structures and Algorithms · Computer Science 2021-09-27 Steven Chaplick , Magnús M. Halldórsson , Murilo S. de Lima , Tigran Tonoyan

$k-$means Clustering requires as input the exact value of $k$, the number of clusters. Two challenges are open: (i) Is there a data-determined definition of $k$ which is provably correct and (ii) Is there a polynomial time algorithm to find…

Data Structures and Algorithms · Computer Science 2020-12-09 Chiranjib Bhattacharyya , Ravindran Kannan , Amit Kumar

In this work, we study the $k$-median and $k$-means clustering problems when the data is distributed across many servers and can contain outliers. While there has been a lot of work on these problems for worst-case instances, we focus on…

Data Structures and Algorithms · Computer Science 2019-03-08 Pranjal Awasthi , Ainesh Bakshi , Maria-Florina Balcan , Colin White , David Woodruff

The increasing popularity of cloud computing has resulted in a proliferation of data centers. Effective placement of data centers improves network performance and minimizes clients' perceived latency. The problem of determining the optimal…

Networking and Internet Architecture · Computer Science 2018-02-06 Wuqiong Luo , Wee Peng Tay , Peng Sun , Yonggang Wen

This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…

Optimization and Control · Mathematics 2026-03-04 Jiayang Ren , Ningning You , Kaixun Hua , Chaojie Ji , Yankai Cao

Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a…

Machine Learning · Computer Science 2022-02-28 Paolo Pellizzoni , Andrea Pietracaprina , Geppino Pucci

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…

Machine Learning · Computer Science 2019-04-25 Yonatan Geifman , Guy Uziel , Ran El-Yaniv

We consider the well-studied Robust $(k, z)$-Clustering problem, which generalizes the classic $k$-Median, $k$-Means, and $k$-Center problems. Given a constant $z\ge 1$, the input to Robust $(k, z)$-Clustering is a set $P$ of $n$ weighted…

Individual fairness guarantees are often desirable properties to have, but they become hard to formalize when the dataset contains outliers. Here, we investigate the problem of developing an individually fair $k$-means clustering algorithm…

Machine Learning · Computer Science 2024-12-17 Binita Maity , Shrutimoy Das , Anirban Dasgupta

This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective…

Systems and Control · Electrical Eng. & Systems 2023-07-21 Saeed Azad , Daniel R. Herber

In the preprocessing model for uncertain data we are given a set of regions R which model the uncertainty associated with an unknown set of points P. In this model there are two phases: a preprocessing phase, in which we have access only to…

Computational Geometry · Computer Science 2021-01-18 Ivor van der Hoog , Irina Kostitsyna , Maarten Löffler , Bettina Speckmann