Related papers: Hoeffding-type decomposition for $U$-statistics on…
Different classes of communication network topologies and their representation in the form of adjacency matrix and its eigenvalues are presented. A self-organizing feature map neural network is used to map different classes of communication…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…
An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning.…
Bipartite networks are a natural representation of the interactions between entities from two different types. The organization (or topology) of such networks gives insight to understand the systems they describe as a whole. Here, we rely…
We develop the theoretical foundations of a generalized Gromov-Hausdorff distance between functions on networks that has recently been applied to various subfields of topological data analysis and optimal transport. These functional…
An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This paper is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or…
We introduce a nonlinear operator to model diffusion on a complex undirected network under crowded conditions. We show that the asymptotic distribution of diffusing agents is a nonlinear function of the nodes' degree and saturates to a…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
We propose a novel subgraph image representation for classification of network fragments with the targets being their parent networks. The graph image representation is based on 2D image embeddings of adjacency matrices. We use this image…
In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…
In this paper we use a probabilistic approach to derive the expressions for the characteristic functions of basic statistics defined on permutation tableaux. Since our expressions are exact, we can identify the distributions of basic…
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
In this paper, we establish an exponential inequality for U-statistics of i.i.d. data, varying kernel and taking values in a separable Hilbert space. The bound are expressed as a sum of an exponential term plus an other one involving the…