Related papers: Modal-set estimation with an application to cluste…
We consider the $k$-means clustering problem in the dynamic streaming setting, where points from a discrete Euclidean space $\{1, 2, \ldots, \Delta\}^d$ can be dynamically inserted to or deleted from the dataset. For this problem, we…
Coresets are among the most popular paradigms for summarizing data. In particular, there exist many high performance coresets for clustering problems such as $k$-means in both theory and practice. Curiously, there exists no work on…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
In real-world application scenarios, the identification of groups poses a significant challenge due to possibly occurring outliers and existing noise variables. Therefore, there is a need for a clustering method which is capable of…
The facility location problem is widely used for summarizing large datasets and has additional applications in sensor placement, image retrieval, and clustering. One difficulty of this problem is that submodular optimization algorithms…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we…
A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike…
Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…
We consider the estimation of Dirichlet Process Mixture Models (DPMMs) in distributed environments, where data are distributed across multiple computing nodes. A key advantage of Bayesian nonparametric models such as DPMMs is that they…
Density-based clustering methods often surpass centroid-based counterparts, when addressing data with noise or arbitrary data distributions common in real-world problems. In this study, we reveal a key property intrinsic to density-based…
Utilizing the sample size of a dataset, the random cluster model is employed in order to derive an estimate of the mean number of K-Means clusters to form during classification of a dataset.
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any…
Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all…
Sets of moving entities can form groups which travel together for significant amounts of time. Tracking such groups is an important analysis task in a variety of areas, such as wildlife ecology, urban transport, or sports analysis.…
Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to…
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…
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges…
The purpose of this paper is to improve the traditional K-means algorithm. In the traditional K mean clustering algorithm, the initial clustering centers are generated randomly in the data set. It is easy to fall into the local minimum…
We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random…