Related papers: Cluster networks and Bruhat-Tits buildings

Recommender systems are one of the most applied methods in machine learning and find applications in many areas, ranging from economics to the Internet of things. This article provides a general overview of modern approaches to recommender…

This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…

The clustering coefficient is a valuable tool for understanding the structure of complex networks. It is widely used to analyze social networks, biological networks, and other complex systems. While there is generally a single common…

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…

Multiplex networks offer an important tool for the study of complex systems and extending techniques originally designed for single--layer networks is an important area of study. One of the most important methods for analyzing networks is…

Unsupervised clustering, also known as natural clustering, stands for the classification of data according to their similarities. Here we study this problem from the perspective of complex networks. Mapping the description of data…

We study the version of the C-Planarity problem in which edges connecting the same pair of clusters must be grouped into pipes, which generalizes the Strip Planarity problem. We give algorithms to decide several families of instances for…

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…

Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these attributes and find that ensembles with strong clustering display both high assortativity by degree and prominent community…

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…

We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the first stage of which entails a series of recursive binary splits to reduce the heterogeneity of the data…

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…

Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…

In this paper, a model reduction procedure for a network of interconnected identical passive subsystems is presented. Here, rather than performing model reduction on the subsystems, adjacent subsystems are clustered, leading to a…

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…

Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…

Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…

We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with error at discrete, and possibly random,…

We give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in…

Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In…