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Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…

Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated…

Analysis of the topology of a graph, regular or bipartite one, can be done by clustering for regular ones or co-clustering for bipartite ones. The Stochastic Block Model and the Latent Block Model are two models, which are very similar for…

Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…

The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical separability,…

Finite mixture models have become a popular tool for clustering. Amongst other uses, they have been applied for clustering longitudinal data and clustering high-dimensional data. In the latter case, a latent Gaussian mixture model is…

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…

Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to…

In this paper, we investigate the problem of recovering hidden communities in the Labeled Stochastic Block Model (LSBM) with a finite number of clusters whose sizes grow linearly with the total number of nodes. We derive the necessary and…

Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face…

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define…

Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust)…

As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…

We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…

In this work, we present randomized compression algorithms for flat rank-structured matrices with shared bases, termed uniform Block Low-Rank (BLR) matrices. Our main contribution is a technique called tagging, which improves upon the…

A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple…

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…

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…

Clustering is a fundamental primitive in unsupervised learning which gives rise to a rich class of computationally-challenging inference tasks. In this work, we focus on the canonical task of clustering d-dimensional Gaussian mixtures with…