Signal Representations on Graphs: Tools and Applications
arXiv:1512.05406
Abstract
We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For each class, we provide an explicit definition of the graph signals and construct a corresponding graph dictionary with desirable properties. We then study how such graph dictionary works in two standard tasks: approximation and sampling followed with recovery, both from theoretical as well as algorithmic perspectives. Finally, for each class, we present a case study of a real-world problem by using the proposed methodology.
References in corpus (6)
- Discrete Signal Processing on Graphs
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- Signals on Graphs: Uncertainty Principle and Sampling
- Local-set-based Graph Signal Reconstruction
- Reconstruction of Graph Signals through Percolation from Seeding Nodes
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- Towards Interpretable Sparse Graph Representation Learning with Laplacian Pooling
- Detecting Localized Categorical Attributes on Graphs
- Signal Recovery on Graphs: Fundamental Limits of Sampling Strategies
- Graph Signal Processing: Overview, Challenges and Applications
- Fast Path Localization on Graphs via Multiscale Viterbi Decoding
- Analysis vs Synthesis with Structure - An Investigation of Union of Subspace Models on Graphs