相关论文: Outlier-Robust Clustering of Non-Spherical Mixture…

We consider the problem of spherical Gaussian Mixture models with $k \geq 3$ components when the components are well separated. A fundamental previous result established that separation of $\Omega(\sqrt{\log k})$ is necessary and sufficient…

Constrained clustering problems generalize classical clustering formulations, e.g., $k$-median, $k$-means, by imposing additional constraints on the feasibility of clustering. There has been significant recent progress in obtaining…

K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…

The Gaussian mixture model (GMM) provides a simple yet principled framework for clustering, with properties suitable for statistical inference. In this paper, we propose a new model-based clustering algorithm, called EGMM (evidential GMM),…

In this paper, we study the problem of learning a mixture of Gaussians with streaming data: given a stream of $N$ points in $d$ dimensions generated by an unknown mixture of $k$ spherical Gaussians, the goal is to estimate the model…

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…

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…

We investigate a novel non-parametric regression-based clustering algorithm for longitudinal data analysis. Combining natural cubic splines with Gaussian mixture models (GMM), the algorithm can produce smooth cluster means that describe the…

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…

In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…

This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set…

The $k$-means is a popular clustering objective, although it is inherently non-robust and sensitive to outliers. Its popular seeding or initialization called $k$-means++ uses $D^{2}$ sampling and comes with a provable $O(\log k)$…

We introduce general tools for designing efficient private estimation algorithms, in the high-dimensional settings, whose statistical guarantees almost match those of the best known non-private algorithms. To illustrate our techniques, we…

We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…

Determining the number of clusters is a fundamental issue in data clustering. Several algorithms have been proposed, including centroid-based algorithms using the Euclidean distance and model-based algorithms using a mixture of probability…

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…

This paper represents a preliminary (pre-reviewing) version of a sublinear variational algorithm for isotropic Gaussian mixture models (GMMs). Further developments of the algorithm for GMMs with diagonal covariance matrices (instead of…

We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of…

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…