Related papers: From Spatial to Spectral: Network Renormalization …
In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…
Deep learning has demonstrated remarkable achievements in medical image segmentation. However, prevailing deep learning models struggle with poor generalization due to (i) intra-class variations, where the same class appears differently in…
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…
Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to…
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Graph embedding has been proven to be efficient and effective in facilitating graph analysis. In this paper, we present a novel spectral framework called NOn-Backtracking Embedding (NOBE), which offers a new perspective that organizes graph…
Graph Neural Networks (GNNs) are the subject of intense focus by the machine learning community for problems involving relational reasoning. GNNs can be broadly divided into spatial and spectral approaches. Spatial approaches use a form of…
Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…
Accessing the network through which a propagation dynamics diffuse is essential for understanding and controlling it. In a few cases, such information is available through direct experiments or thanks to the very nature of propagation data.…
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…
We introduce the concept of self-healing in the field of complex networks. Obvious applications range from infrastructural to technological networks. By exploiting the presence of redundant links in recovering the connectivity of the…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be the zero-level set of a bandlimited function. We show that the exponential…
Graph rewiring has emerged as a key technique to alleviate over-squashing in Graph Neural Networks (GNNs) and Graph Transformers by modifying the graph topology to improve information flow. While effective, rewiring inherently alters the…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
Graph embeddings learn the structure of networks and represent it in low-dimensional vector spaces. Community structure is one of the features that are recognized and reproduced by embeddings. We show that an iterative procedure, in which a…