Related papers: Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)

Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)

URL: http://arxiv.org/abs/2006.11220v2
Date: Wed, 5 Aug 2020 03:32:28 GMT
Title: Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)
Authors: David I Shuman
Abstract summary: Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data. We survey a particular class of dictionaries called localized spectral graph filter frames. We emphasize computationally efficient methods that ensure the resulting transforms and their inverses can be applied to data residing on large, sparse graphs.
Score: 1.52292571922932
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal processing and machine learning tasks. Designing collections of building block signals -- or more formally, dictionaries of atoms -- that specifically account for the underlying graph structure as well as any available representative training signals has been an active area of research over the last decade. In this article, we survey a particular class of dictionaries called localized spectral graph filter frames, whose atoms are created by localizing spectral patterns to different regions of the graph. After showing how this class encompasses a variety of approaches from spectral graph wavelets to graph filter banks, we focus on the two main questions of how to design the spectral filters and how to select the center vertices to which the patterns are localized. Throughout, we emphasize computationally efficient methods that ensure the resulting transforms and their inverses can be applied to data residing on large, sparse graphs. We demonstrate how this class of transform methods can be used in signal processing tasks such as denoising and non-linear approximation, and provide code for readers to experiment with these methods in new application domains.