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Related papers: Robustly Clustering a Mixture of Gaussians

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Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

Probability · Mathematics 2007-05-23 Sanjeev Arora , Ravi Kannan

Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…

Computation · Statistics 2023-02-09 Anastasiia Livochka , Ryan Browne , Sanjeena Subedi

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

Machine Learning · Computer Science 2022-03-30 Georgios Exarchakis , Omar Oubari , Gregor Lenz

Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…

Methodology · Statistics 2012-01-30 Alberto Cozzini , Ajay Jasra , Giovanni Montana

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…

Machine Learning · Statistics 2017-03-24 Thibault Lesieur , Caterina De Bacco , Jess Banks , Florent Krzakala , Cris Moore , Lenka Zdeborová

We consider the problem of clustering with $K$-means and Gaussian mixture models with a constraint on the separation between the centers in the context of real-valued data. We first propose a dynamic programming approach to solving the…

Computation · Statistics 2023-01-24 He Jiang , Ery Arias-Castro

In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the…

Methodology · Statistics 2012-07-05 Antonio Punzo

We consider the problem of clustering data points coming from sub-Gaussian mixtures. Existing methods that provably achieve the optimal mislabeling error, such as the Lloyd algorithm, are usually vulnerable to outliers. In contrast,…

Statistics Theory · Mathematics 2025-11-03 Soham Jana , Kun Yang , Sanjeev Kulkarni

We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…

Data Structures and Algorithms · Computer Science 2017-11-21 Samuel B. Hopkins , Jerry Li

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…

Databases · Computer Science 2020-03-11 Mujahid Sultan

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

Statistics Theory · Mathematics 2008-12-18 Luis A. García-Escudero , Alfonso Gordaliza , Carlos Matrán , Agustin Mayo-Iscar

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…

Data Structures and Algorithms · Computer Science 2017-11-27 Pranjal Awasthi , Aravindan Vijayaraghavan

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

Machine Learning · Statistics 2017-01-02 Andreas Henelius , Kai Puolamäki , Henrik Boström , Panagiotis Papapetrou

In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…

Computation · Statistics 2020-05-15 Hanyu Song , Yingjian Wang , David B. Dunson

In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…

Machine Learning · Statistics 2020-02-26 Ayush Jain , Alon Orlitsky

We consider model-based clustering methods for continuous, correlated data that account for external information available in the presence of mixed-type fixed covariates by proposing the MoEClust suite of models. These models allow…

Methodology · Statistics 2021-07-15 Keefe Murphy , Thomas Brendan Murphy

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Statistics Theory · Mathematics 2024-02-26 Dapeng Yao , Fangzheng Xie , Yanxun Xu

Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…

Statistics Theory · Mathematics 2022-03-23 Denis Gaidashev , Ralf Pihlström , Martin Ryner

Bayesian clustering typically relies on mixture models, with each component interpreted as a different cluster. After defining a prior for the component parameters and weights, Markov chain Monte Carlo (MCMC) algorithms are commonly used to…

Methodology · Statistics 2024-07-30 Alexander Dombowsky , David B. Dunson

A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…

Methodology · Statistics 2019-02-06 E. del Barrio , J. A. Cuesta-Albertos , C. Matrán , A. Mayo-Íscar