Related papers: Near-Optimal Quantum Coreset Construction Algorith…
Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups…
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…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
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…
Recent work has proposed solving the k-means clustering problem on quantum computers via the Quantum Approximate Optimization Algorithm (QAOA) and coreset techniques. Although the current method demonstrates the possibility of quantum…
The k-means objective is arguably the most widely-used cost function for modeling clustering tasks in a metric space. In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located…
In temporal ordered clustering, given a single snapshot of a dynamic network in which nodes arrive at distinct time instants, we aim at partitioning its nodes into $K$ ordered clusters $\mathcal{C}_1 \prec \cdots \prec \mathcal{C}_K$ such…
Given a metric space, the $(k,z)$-clustering problem consists of finding $k$ centers such that the sum of the of distances raised to the power $z$ of every point to its closest center is minimized. This encapsulates the famous $k$-median…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…
We present a $k$-means-based clustering algorithm, which optimizes the mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In the $k$-means assignment…
We study subtrajectory clustering under the Fr\'echet distance. Given one or more trajectories, the task is to split the trajectories into several parts, such that the parts have a good clustering structure. We approach this problem via a…
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In…
The Fr\'echet distance is a popular distance measure for curves. We study the problem of clustering time series under the Fr\'echet distance. In particular, we give $(1+\varepsilon)$-approximation algorithms for variations of the following…
We study the approximate range searching for three variants of the clustering problem with a set $P$ of $n$ points in $d$-dimensional Euclidean space and axis-parallel rectangular range queries: the $k$-median, $k$-means, and $k$-center…
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…
We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging,…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
We introduce the $(p,q)$-Fair Clustering problem. In this problem, we are given a set of points $P$ and a collection of different weight functions $W$. We would like to find a clustering which minimizes the $\ell_q$-norm of the vector over…
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…