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This overview presents a collection of results from classical electrical network theory concerning properties of the network admittance matrix, and the relationship between electrical characteristics of the network and various mathematical…

Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…

Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…

A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…

This paper addresses the large-scale acquisition of end-to-end network performance. We made two distinct contributions: ordinal rating of network performance and inference by matrix completion. The former reduces measurement costs and…

A key concern in network analysis is the study of social positions and roles of actors in a network. The notion of "position" refers to an equivalence class of nodes that have similar ties to other nodes, whereas a "role" is an equivalence…

One of the most relevant tasks in network analysis is the detection of community structures, or clustering. Most popular techniques for community detection are based on the maximization of a quality function called modularity, which in turn…

A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…

Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…

Over the past years, embedding learning on networks has shown tremendous results in link prediction tasks for complex systems, with a wide range of real-life applications. Learning a representation for each node in a knowledge graph allows…

Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of "influence". While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the…

We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested…

We study deep neural networks and their use in semiparametric inference. We establish novel rates of convergence for deep feedforward neural nets. Our new rates are sufficiently fast (in some cases minimax optimal) to allow us to establish…

Link prediction is one of the fundamental problems in network analysis. In many applications, notably in genetics, a partially observed network may not contain any negative examples of absent edges, which creates a difficulty for many…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

The resolution matrix is a mathematical tool for analyzing inverse problems such as computational imaging systems. When treating network connectivity estimation as an inverse problem, the resolution matrix describes the degree to which…

Neural systems are networks, and strategic comparisons between multiple networks are a prevalent task in many research scenarios. In this study, we construct a statistical test for the comparison of matrices representing pairwise aspects of…

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the…

Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix…