Spline-Like Wavelet Filterbanks for Multiresolution Analysis of Graph-Structured Data

摘要

Multiresolution analysis is important for understanding , which represent graph-structured data. Wavelet filterbanks permit multiscale analysis and processing of graph signals—particularly, useful for harvesting large-scale data. Inspired by first-order spline wavelets in classical signal processing, we introduce two-channel (low-pass and high-pass) wavelet filterbanks for graph signals. This class of filterbanks boasts several useful properties, such as critical sampling, perfect reconstruction, and graph invariance. We consider an application in graph semisupervised learning and propose a wavelet-regularized semisupervised learning algorithm that is competitive for certain synthetic and real-world data.