Related papers: Natural Graph Wavelet Packet Dictionaries
We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable…
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we…
For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first we derive bounds for the second largest and smallest eigenvalues of adjacency matrices of $k$-regular…
In 2003, van Dam and Haemers posed a fundamental question in spectral graph theory: does there exist a ``sensible'' matrix whose spectrum determines a random graph up to isomorphism? This paper introduces the class of {\em natural graph…
Graph databases in many applications---semantic web, transport or biological networks among others---are not only large, but also frequently modified. Evaluating graph queries in this dynamic context is a challenging task, as those queries…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
In this paper we consider the problem of defining transforms for signals on directed graphs, with a specific focus on defective graphs where the corresponding graph operator cannot be diagonalized. Our proposed method is based on the Schur…
In this paper, we introduce translation operators on graphs. Contrary to spectrally-defined translations in the framework of graph signal processing, our operators mimic neighborhood-preserving properties of translation operators defined in…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed…
In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
In recent years, tasks of machine learning ranging from image processing & audio/video analysis to natural language understanding have been transformed by deep learning. The data content in all these scenarios are expressed via Euclidean…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented…
In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…
We introduce and study Laplacians on a finite metric graph endowed with generalized densities, that is, measures of finite mass. One important motivation is that this setting provides a common framework for several interesting classes of…
Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…
In the field of natural language understanding, the intersection of neural models and graph meaning representations (GMRs) remains a compelling area of research. Despite the growing interest, a critical gap persists in understanding the…
Graph data, with its structurally variable nature, represents complex real-world phenomena like chemical compounds, protein structures, and social networks. Traditional Graph Neural Networks (GNNs) primarily utilize the message-passing…