Related papers: Hilbert Transform, Analytic Signal, and Modulation…
Graph Transformer is gaining increasing attention in the field of machine learning and has demonstrated state-of-the-art performance on benchmarks for graph representation learning. However, as current implementations of Graph Transformer…
Graph transformation systems (GTS) and constraint handling rules (CHR) are non-deterministic rule-based state transition systems. CHR is well-known for its powerful confluence and program equivalence analyses, for which we provide the basis…
Classical spectral graph theory and graph signal processing rely on a symmetry principle: undirected graphs induce symmetric (self-adjoint) adjacency/Laplacian operators, yielding orthogonal eigenbases and energy-preserving Fourier…
Efficient and robust prediction of graph signals is challenging when the signals are under impulsive noise and have missing data. Exploiting graph signal processing (GSP) and leveraging the simplicity of the classical adaptive sign…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
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,…
The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…
Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed…
We propose a generalization of transformer neural network architecture for arbitrary graphs. The original transformer was designed for Natural Language Processing (NLP), which operates on fully connected graphs representing all connections…
The Hilbert-Huang transform (HHT) consists of empirical mode decomposition (EMD), which is a template-free method that represents the combination of different intrinsic modes on a time-frequency map (i.e., the Hilbert spectrum). The…
Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and…
Graph Transformer (GT), as a special type of Graph Neural Networks (GNNs), utilizes multi-head attention to facilitate high-order message passing. However, this also imposes several limitations in node classification applications: 1) nodes…
Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
We present the method of complementary ensemble empirical mode decomposition (CEEMD) and Hilbert-Huang transform (HHT) for analyzing nonstationary financial time series. This noise-assisted approach decomposes any time series into a number…
We propose the Soft Graph Transformer (SGT), a soft-input-soft-output neural architecture designed for MIMO detection. While Maximum Likelihood (ML) detection achieves optimal accuracy, its exponential complexity makes it infeasible in…
Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges…
Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…
We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-CWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the…