Related papers: Topological Signal Processing over Simplicial Comp…
One of the key challenges in many research fields is uncovering how different interconnected systems interact within complex networks, typically represented as multi-layer networks. Capturing the intra- and cross-layer interactions among…
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…
Sampling methods for graph signals in the graph spectral domain are presented. Though conventional sampling of graph signals can be regarded as sampling in the graph vertex domain, it does not have the desired characteristics in regard to…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target…
Important advances have been made using convolutional neural network (CNN) approaches to solve complicated problems in areas that rely on grid structured data such as image processing and object classification. Recently, research on graph…
The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…
Advances in machine learning technology have enabled real-time extraction of semantic information in signals which can revolutionize signal processing techniques and improve their performance significantly for the next generation of…
Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: I) clustering of vertices, II) semi-supervised…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic geometric…
This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence…
This paper is devoted to signal processing on point-clouds by means of neural networks. Nowadays, state-of-the-art in image processing and computer vision is mostly based on training deep convolutional neural networks on large datasets.…
The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph…
For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting. We define a pooling layer, nervePool, for data structured as simplicial…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…