Related papers: Graph Canonical Coherence Analysis
Graph convolutional neural networks (GCNs) are powerful tools for learning graph-based knowledge representations from training data. However, they are vulnerable to small perturbations in the input graph, which makes them susceptible to…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…
In genome-wide interaction studies, to detect gene-gene interactions, most methods are divided into two folds: single nucleotide polymorphisms (SNP) based and gene-based methods. Basically, the methods based on the gene are more effective…
We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…
Integrative analyses of different high dimensional data types are becoming increasingly popular. Similarly, incorporating prior functional relationships among variables in data analysis has been a topic of increasing interest as it helps…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states…
We argue that when comparing two graphs, the distribution of node structural features is more informative than global graph statistics which are often used in practice, especially to evaluate graph generative models. Thus, we present…
We study estimation of piecewise smooth signals over a graph. We propose a $\ell_{2,0}$-norm penalized Graph Trend Filtering (GTF) model to estimate piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness across the…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
Retrieving cohesive subgraphs in networks is a fundamental problem in social network analysis and graph data management. These subgraphs can be used for marketing strategies or recommendation systems. Despite the introduction of numerous…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
This paper considers canonical correlation analysis for two longitudinal variables that are possibly sampled at different time resolutions with irregular grids. We modeled trajectories of the multivariate variables using random effects and…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
Graph Convolutional Networks (GCNs) have received increasing attention in the machine learning community for effectively leveraging both the content features of nodes and the linkage patterns across graphs in various applications. As…
Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is…