Related papers: Data Stability in Clustering: A Closer Look
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…
The impact of an extreme climate event depends strongly on its geographical scale. Max-stable processes can be used for the statistical investigation of climate extremes and their spatial dependencies on a continuous area. Most existing…
The clustering problem, in its many variants, has numerous applications in operations research and computer science (e.g., in applications in bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown…
The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds.…
Despite its popularity, it is widely recognized that the investigation of some theoretical aspects of clustering has been relatively sparse. One of the main reasons for this lack of theoretical results is surely the fact that, whereas for…
Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…
We present approximation algorithms for some variants of center-based clustering and related problems in the fully dynamic setting, where the pointset evolves through an arbitrary sequence of insertions and deletions. Specifically, we…
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…
We define the notion of a well-clusterable data set combining the point of view of the objective of $k$-means clustering algorithm (minimising the centric spread of data elements) and common sense (clusters shall be separated by gaps). We…
We consider the robust algorithms for the $k$-means clustering problem where a quantizer is constructed based on $N$ independent observations. Our main results are median of means based non-asymptotic excess distortion bounds that hold…
We address here two major challenges presented by dynamic data mining: 1) the stability challenge: we have implemented a rigorous incremental density-based clustering algorithm, independent from any initial conditions and ordering of the…
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…
The performance (accuracy and robustness) of several clustering algorithms is studied for linearly dependent random variables in the presence of noise. It turns out that the error percentage quickly increases when the number of observations…
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition…
Data analysis often involves an iterative process, where solutions must be continuously refined in response to new data. Typically, as new data becomes available, an existing solution must be updated to incorporate the latest information.…
We study the problem of explainable clustering in the setting first formalized by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). A $k$-clustering is said to be explainable if it is given by a decision tree where each internal node…
This paper shows for the first time that distributed computing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size $O(\log N)$, each…
We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second…
It is well known that most of the common clustering objectives are NP-hard to optimize. In practice, however, clustering is being routinely carried out. One approach for providing theoretical understanding of this seeming discrepancy is to…