Wavelet-Based Visual Analysis for Data Exploration

The conventional wavelet transform is widely used in image and signal processing, where a signal is decomposed into a combination of known signals. By analyzing the individual contributions, the behavior of the original signal can be inferred. In this article, the authors present an introductory overview of the extension of this theory into graphs domains. They review the graph Fourier transform and graph wavelet transforms that are based on dictionaries of graph spectral filters, namely, spectral graph wavelet transforms. Then, the main features of the graph wavelet transforms are presented using real and synthetic data.