Related papers: A framework for second order eigenvector centralit…
Clustering explores meaningful patterns in the non-labeled data sets. Cluster Ensemble Selection (CES) is a new approach, which can combine individual clustering results for increasing the performance of the final results. Although CES can…
We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted,…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
We present a new framework to measure the intrinsic properties of (deep) neural networks. While we focus on convolutional networks, our framework can be extrapolated to any network architecture. In particular, we evaluate two network…
We study the task of clustering in directed networks. We show that using the eigenvalue/eigenvector decomposition of the adjacency matrix is simpler than all common methods which are based on a combination of data regularization and SVD…
We introduce the notion of order-preserving multi-homogeneous mapping which allows to study Perron-Frobenius type theorems and nonnegative tensors in unified fashion. We prove a weak and strong Perron-Frobenius theorem for these maps and…
We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other…
The Perron-Frobenius theorem of nonnegative matrices is a classical result on spectral theory of matrices, which has wide applications in many domains. In this paper, we give the Perron-Frobenius theorem for dual tensors, that is, a dual…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
We utilize the PageRank vector to generalize the $k$-means clustering algorithm to directed and undirected graphs. We demonstrate that PageRank and other centrality measures can be used in our setting to robustly compute centrality of nodes…
Our primary objective is to conduct a brief survey of various classical and quantum neural net sequence models, which includes self-attention and recurrent neural networks, with a focus on recent quantum approaches proposed to work with…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…
Hypergraphs are generalizations of simple graphs that allow for the representation of complex group interactions beyond pairwise relationships. Clustering coefficients quantify local link density in networks and have been widely studied for…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…
Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…