Paper Info
Title
Wavelets on Graphs via Deep Learning.
Abstract
An increasing number of applications require processing of signals defined on weighted graphs. While wavelets provide a flexible tool for signal processing in the classical setting of regular domains, the existing graph wavelet constructions are less flexible -- they are guided solely by the structure of the underlying graph and do not take directly into consideration the particular class of signals to be processed. This paper introduces a machine learning framework for constructing graph wavelets that can sparsely represent a given class of signals. Our construction uses the lifting scheme, and is based on the observation that the recurrent nature of the lifting scheme gives rise to a structure resembling a deep auto-encoder network. Particular properties that the resulting wavelets must satisfy determine the training objective and the structure of the involved neural networks. The training is unsupervised, and is conducted similarly to the greedy pre-training of a stack of auto-encoders. After training is completed, we obtain a linear wavelet transform that can be applied to any graph signal in time and memory linear in the size of the graph. Improved sparsity of our wavelet transform for the test signals is confirmed via experiments both on synthetic and real data.
Year
Venue
Field
2013
NIPS
Signal processing,Lifting scheme,Computer science,Second-generation wavelet transform,Continuous wavelet transform,Artificial intelligence,Deep learning,Artificial neural network,Machine learning,Wavelet,Wavelet transform
DocType
Citations 
PageRank 
Conference
18
1.70
References 
Authors
14
2
Name
Order
Citations
PageRank
Raif M. Rustamov125119.58
Leonidas J. Guibas2130841262.73