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Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…

Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…

Most algorithms for decentralized learning employ a consensus or diffusion mechanism to drive agents to a common solution of a global optimization problem. Generally this takes the form of linear averaging, at a rate of contraction…

Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous…

Sparse prediction with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

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…

Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case…

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…

The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…

There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…

Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for…

The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

In this work, we consider learning sparse models in large scale settings, where the number of samples and the feature dimension can grow as large as millions or billions. Two immediate issues occur under such challenging scenario: (i)…

Real-world networks often come with side information that can help to improve the performance of network analysis tasks such as clustering. Despite a large number of empirical and theoretical studies conducted on network clustering methods…

Common clustering methods, such as $k$-means and convex clustering, group similar vector-valued observations into clusters. However, with the increasing prevalence of matrix-valued observations, which often exhibit low rank characteristics,…

The latent class model has been proposed as a powerful tool for cluster analysis of categorical data in various fields such as social, psychological, behavioral, and biological sciences. However, one important limitation of the latent class…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…