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Discovering and characterizing the large-scale topological features in empirical networks are crucial steps in understanding how complex systems function. However, most existing methods used to obtain the modular structure of networks…
Hierarchical clustering is one of the most powerful solutions to the problem of clustering, on the grounds that it performs a multi scale organization of the data. In recent years, research on hierarchical clustering methods has attracted…
Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive…
Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers…
Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the…
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…
Clustering algorithms are often used to find subpopulations in exploratory data analysis workflows. Not only the clusters themselves, but also their shape can represent meaningful subpopulations. In this paper, we present FLASC, an…
The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…
Most of the research on clustering ensemble focuses on designing practical consistency learning algorithms.To solve the problems that the quality of base clusters varies and the low-quality base clusters have an impact on the performance of…
This paper analyzes the statistical performance of a robust spectral clustering method for latent structure recovery in noisy data matrices. We consider eigenvector-based clustering applied to a matrix of nonparametric rank statistics that…
Analysis of higher-order organizations, usually small connected subgraphs called motifs, is a fundamental task on complex networks. This paper studies a new problem of testing higher-order clusterability: given query access to an undirected…
The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its…
Clustering algorithms have significantly improved along with Deep Neural Networks which provide effective representation of data. Existing methods are built upon deep autoencoder and self-training process that leverages the distribution of…
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these…
In mixture models, anisotropic noise within each cluster is widely present in real-world data. This work investigates both computationally efficient procedures and fundamental statistical limits for clustering in high-dimensional…
One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of…
In this work, we introduce a novel methodology for divisive hierarchical clustering. Our divisive (``top-down'') approach is motivated by the fact that agglomerative hierarchical clustering (``bottom-up''), which is commonly used for…
Hierarchical clustering studies a recursive partition of a data set into clusters of successively smaller size, and is a fundamental problem in data analysis. In this work we study the cost function for hierarchical clustering introduced by…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…