Open AccessPosted Content
Wavelets on Graphs via Spectral Graph Theory
TLDR
In this paper, the spectral graph wavelet operator is defined based on spectral decomposition of the discrete graph Laplacian, and a wavelet generating kernel and a scale parameter are used to localize this operator to an indicator function.Abstract:
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian $\L$. Given a wavelet generating kernel $g$ and a scale parameter $t$, we define the scaled wavelet operator $T_g^t = g(t\L)$. The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on $g$, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing $\L$. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.read more
Citations
More filters
Posted Content
Computational Analysis of Deformable Manifolds: from Geometric Modelling to Deep Learning
TL;DR: This thesis will explore geometric methods for shape processing and data analysis through a variety of mathematical tools including, but not limited to, computational differential geometry, variational PDE modeling, and deep learning and propose a novel auto-regressive model for capturing the intrinsic geometry and topology of data.
Posted Content
Exploring Hypergraph Representation on Face Anti-spoofing Beyond 2D Attacks
TL;DR: Zhang et al. as mentioned in this paper proposed Hypergraph Convolutional Neural Networks (HGCNN) for 3D face anti-spoofing via hypergraph convolutional neural networks.
Posted Content
GAIN: Graph Attention & Interaction Network for Inductive Semi-Supervised Learning over Large-scale Graphs.
TL;DR: GAIN as mentioned in this paper uses multiple types of aggregators to gather neighboring information in different aspects and integrate the outputs of these aggregators through the aggregator-level attention mechanism, and design a graph regularized loss to better capture the topological relationship of the nodes in the graph.
Posted Content
A Flexible Convolutional Solver with Application to Photorealistic Style Transfer
Gilles Puy,Patrick Pérez +1 more
TL;DR: A new flexible deep convolutional neural network (convnet) to perform fast visual style transfer and shows how to modify it to obtain a photorealistic result with no retraining.
Proceedings ArticleDOI
Point Cloud Attribute Inpainting in Graph Spectral Domain
TL;DR: This work proposes an efficient inpainting method for the attribute (e.g., color) of point clouds, exploiting non-local self-similarity in graph spectral domain, and formulates attribute in Painting as a sparse coding problem, imposing sparsity on the GFT representation of the attribute for hole filling.
References
More filters
Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Proceedings ArticleDOI
Object recognition from local scale-invariant features
TL;DR: Experimental results show that robust object recognition can be achieved in cluttered partially occluded images with a computation time of under 2 seconds.
Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.