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In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…
Assessing where and how information is stored in biological networks (such as neuronal and genetic networks) is a central task both in neuroscience and in molecular genetics, but most available tools focus on the network's structure as…
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
Deep neural networks have significantly alleviated the burden of feature engineering, but comparable efforts are now required to determine effective architectures for these networks. Furthermore, as network sizes have become excessively…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
Graph sparsification is an area of interest in computer science and applied mathematics. Sparsification of a graph, in general, aims to reduce the number of edges in the network while preserving specific properties of the graph, like cuts…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
Network filtering is an important form of dimension reduction to isolate the core constituents of large and interconnected complex systems. We introduce a new technique to filter large dimensional networks arising out of dynamical behavior…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…
It is common knowledge that a key dynamical characteristic of a network is its spectrum (the collection of all eigenvalues of the network's weighted adjacency matrix). In \cite{BW10} we demonstrated that it is possible to reduce a network,…
A spectral sparsifier of a graph $G$ is a sparser graph $H$ that approximately preserves the quadratic form of $G$, i.e. for all vectors $x$, $x^T L_G x \approx x^T L_H x$, where $L_G$ and $L_H$ denote the respective graph Laplacians.…
Neuroimaging data can be represented as networks of nodes and edges that capture the topological organization of the brain connectivity. Graph theory provides a general and powerful framework to study these networks and their structure at…
In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral…
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to…
We present a spectral approach to design approximation algorithms for network design problems. We observe that the underlying mathematical questions are the spectral rounding problems, which were studied in spectral sparsification and in…
Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…
Understanding natural phenomenon through the interactions of different complex systems has become an increasing focus in scientific inquiry. Defining complexity and actually measuring it is an ongoing debate and no standard framework has…
An increasing abstraction has marked some recent investigations in network science. Examples include the development of algorithms that map time series data into networks whose vertices and edges can have different interpretations, beyond…