Related papers: Sample-and-Search: An Effective Algorithm for Lear…

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…

Many algorithms for approximate nearest neighbor search in high-dimensional spaces partition the data into clusters. At query time, in order to avoid exhaustive search, an index selects the few (or a single) clusters nearest to the query…

Deep learning models have become widely adopted in various domains, but their performance heavily relies on a vast amount of data. Datasets often contain a large number of irrelevant or redundant samples, which can lead to computational…

Quantum machine learning, though in its initial stage, has demonstrated its potential to speed up some of the costly machine learning calculations when compared to the existing classical approaches. Among the challenging subroutines,…

We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean…

We study two generalizations of classic clustering problems called dynamic ordered $k$-median and dynamic $k$-supplier, where the points that need clustering evolve over time, and we are allowed to move the cluster centers between…

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.…

The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for…

In longitudinal data analysis, observation points of repeated measurements over time often vary among subjects except in well-designed experimental studies. Additionally, measurements for each subject are typically obtained at only a few…

Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…

The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some…

Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains…

We study $k$-means clustering in a semi-supervised setting. Given an oracle that returns whether two given points belong to the same cluster in a fixed optimal clustering, we investigate the following question: how many oracle queries are…

This paper proposes a machine learning pre-sort stage to traditional supervised learning using Tsetlin Machines. Initially, K data-points are identified from the dataset using an expedited genetic algorithm to solve the maximum dispersion…

Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…

The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…

In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…

We study the task of differentially private clustering. For several basic clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient differentially private algorithms that achieve essentially…