Related papers: Topological cluster synchronization via Dirac spec…
Following the work of arXiv:2101.09512, we are interested in clustering a given multi-variate series in an unsupervised manner. We would like to segment and cluster the series such that the resulting blocks present in each cluster are…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…
Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling.…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic…
Group synchronization is the problem of determining reliable global estimates from noisy local measurements on networks. The typical task for group synchronization is to assign elements of a group to the nodes of a graph in a way that…
When describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis of cluster…
We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…
Spectral clustering methodologies, when extended to accommodate signed graphs, have encountered notable limitations in effectively encapsulating inherent grouping relationships. Recent findings underscore a substantial deterioration in the…
Many real-world networks are directed, sparse and hierarchical, with a mixture of feed-forward and feedback connections with respect to the hierarchy. Moreover, a small number of 'master' nodes are often able to drive the whole system. We…
It has been shown that the adjacency eigenspace of a network contains key information of its underlying structure. However, there has been no study on spectral analysis of the adjacency matrices of directed signed graphs. In this paper, we…
We study the mechanism of formation of synchronized clusters in coupled maps on networks with various connection architectures. The nodes in a cluster are self- synchronized or driven-synchronized, based on the coupling strength and…
Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take…
Community structure is a key feature omnipresent in real-world network data. Plethora of methods have been proposed to reveal subsets of densely interconnected nodes using criteria such as the modularity index. These approaches have been…
Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…
Graph-based multi-view clustering has achieved better performance than most non-graph approaches. However, in many real-world scenarios, the graph structure of data is not given or the quality of initial graph is poor. Additionally,…
We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is…