Related papers: Graph signal interpolation with Positive Definite …
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…
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…
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…
While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum,…
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Community detection is a central problem in graph analysis, with applications ranging from network science to graph signal processing. In recent years, Graph Neural Networks (GNNs) have emerged as effective tools for learning…
Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation…
This work develops \emph{mixup for graph data}. Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. Traditionally, Mixup can work on…
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our…
Graph Interpolation Grammars are a declarative formalism with an operational semantics. Their goal is to emulate salient features of the human parser, and notably incrementality. The parsing process defined by GIGs incrementally builds a…
In this paper we consider the problem of constructing graph Fourier transforms (GFTs) for directed graphs (digraphs), with a focus on developing multiple GFT designs that can capture different types of variation over the digraph…
This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal…
Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
Graph Neural Networks (GNNs) have emerged as formidable resources for processing graph-based information across diverse applications. While the expressive power of GNNs has traditionally been examined in the context of graph-level tasks,…
We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…