Related papers: A class of randomized Subset Selection Methods for…
Most of the real world networks such as the internet network, collaboration networks, brain networks, citation networks, powerline and airline networks are very large and to study their structure, and dynamics one often requires working…
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…
Graph sampling plays an important role in data mining for large networks. Specifically, larger networks often correspond to lower sampling rates. Under the situation, traditional traversal-based samplings for large networks usually have an…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…
Recent years are characterized by an unprecedented quantity of available network data which are produced at an astonishing rate by an heterogeneous variety of interconnected sensors and devices. This high-throughput generation calls for the…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
The topological information is essential for studying the relationship between nodes in a network. Recently, Network Representation Learning (NRL), which projects a network into a low-dimensional vector space, has been shown their…
A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…
In this paper, we study detection and fast reconstruction of the celebrated Watts-Strogatz (WS) small-world random graph model \citep{watts1998collective} which aims to describe real-world complex networks that exhibit both high clustering…
The hierarchical small-world network is a real-world network. It models well the benefit transmission web of the pyramid selling in China and many other countries. In this paper, by applying the spectral graph theory, we study three…
Community detection has been one of the central problems in network studies and directed network is particularly challenging due to asymmetry among its links. In this paper, we found that incorporating the direction of links reveals new…