Related papers: Cluster networks and Bruhat-Tits buildings

We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebra does not depend on the choice of…

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

Clustering mechanisms are essential in certain multiuser networks for achieving efficient resource utilization. This lecture note presents the theory of coalition formation as a useful tool for distributed clustering problems. We reveal the…

A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…

The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…

A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…

Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…

Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…

We present an approach to design stabilizing controllers for a set of linear systems without restrictions regarding their modeling order. To this end, the systems are treated as abstract objects in the space of the $\nu$-gap metric. Via a…

We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle…

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…

With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…

We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…

Heterogeneity in efficacy is sometimes observed across baskets in basket trials. In this study, we propose a model-free clustering framework that groups baskets based on transition probabilities derived from the trajectories of treatment…

Clustering algorithms may unintentionally propagate or intensify existing disparities, leading to unfair representations or biased decision-making. Current fair clustering methods rely on notions of fairness that do not capture any…

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…

A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease. The…

A novel family of twelve mixture models with random covariates, nested in the linear $t$ cluster-weighted model (CWM), is introduced for model-based clustering. The linear $t$ CWM was recently presented as a robust alternative to the better…