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We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…
High-dimensional data clustering has become and remains a challenging task for modern statistics and machine learning, with a wide range of applications. We consider in this work the powerful discriminative latent mixture model, and we…
Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this…
We propose a new class of robust and Fisher-consistent estimators for mixture models. These estimators can be used to construct robust model-based clustering procedures. We study in detail the case of multivariate normal mixtures and…
We study the problem of downlink channel estimation in multi-user massive multiple input multiple output (MIMO) systems. To this end, we consider a Bayesian compressive sensing approach in which the clustered sparse structure of the channel…
Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…
We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances. The proposed method efficiently combines data density and geometry to…
Significant progress has been made in learning image classification neural networks under long-tail data distribution using robust training algorithms such as data re-sampling, re-weighting, and margin adjustment. Those methods, however,…
Gaussian mixture models (GMM) are the most widely used statistical model for the $k$-means clustering problem and form a popular framework for clustering in machine learning and data analysis. In this paper, we propose a natural semi-random…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
When approaching a clustering problem, choosing the right clustering algorithm and parameters is essential, as each clustering algorithm is proficient at finding clusters of a particular nature. Due to the unsupervised nature of clustering…
Clustering data into meaningful subsets is a major task in scientific data analysis. To date, various strategies ranging from model-based approaches to data-driven schemes, have been devised for efficient and accurate clustering. One…
We propose a robust clustering framework for high-dimensional data with heavy tails and a large fraction of irrelevant variables. The method replaces the mean updates of Lloyd's $K$-means with \emph{spatial medians} to enhance robustness.…
We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…
In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are…
High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…
Distributed data mining techniques and mainly distributed clustering are widely used in the last decade because they deal with very large and heterogeneous datasets which cannot be gathered centrally. Current distributed clustering…
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…