Title :
Spline-Like Wavelet Filterbanks for Multiresolution Analysis of Graph-Structured Data
Author :
Ekambaram, Venkatesan N. ; Fanti, Giulia C. ; Ayazifar, Babak ; Ramchandran, Kannan
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, Berkeley, CA, USA
Abstract :
Multiresolution analysis is important for understanding graph signals, 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 semi-supervised learning and propose a wavelet-regularized semi-supervised learning algorithm that is competitive for certain synthetic and real-world data.
Keywords :
graph theory; high-pass filters; image filtering; image resolution; learning (artificial intelligence); low-pass filters; splines (mathematics); wavelet transforms; critical sampling; first-order spline wavelets; graph invariance; graph semisupervised learning; graph signal processing; graph-structured data; high-pass wavelet filterbank; large-scale data harvesting; low-pass wavelet filterbank; multiresolution analysis; multiscale analysis; perfect reconstruction; spline-like wavelet filterbanks; two-channel wavelet filterbank; wavelet-regularized semisupervised learning algorithm; Information processing; Matrix decomposition; Semisupervised learning; Signal processing; Splines (mathematics); Symmetric matrices; Wavelet analysis; Circulant graphs; Graph wavelets; circulant graphs; critical sampling; graph wavelets; semi-supervised learning; semisupervised learning;
Journal_Title :
Signal and Information Processing over Networks, IEEE Transactions on
DOI :
10.1109/TSIPN.2015.2480223
