KAUST Grant NumberOSR-2015-Sensors-2700
Permanent link to this recordhttp://hdl.handle.net/10754/669823
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AbstractThis paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the dataset consists of signals defined on many different graphs, and the learned filters should generalize to signals on new graphs, not present in the training set. A necessary condition for transferability (the ability to transfer filters) is stability. Namely, given a graph filter, if we add a small perturbation to the graph, then the filter on the perturbed graph is a small perturbation of the original filter. It is a common misconception that spectral filters are not stable, and this paper aims at debunking this mistake. We introduce a space of filters, called the Cayley smoothness space, that contains the filters of state-of-the-art spectral filtering methods, and whose filters can approximate any generic spectral filter. For filters in this space, the perturbation in the filter is bounded by a constant times the perturbation in the graph, and filters in the Cayley smoothness space are thus termed linearly stable. By combining stability with the known property of equivariance, we prove that graph spectral filters are transferable.
CitationLevie, R., Isufi, E., & Kutyniok, G. (2019). On the Transferability of Spectral Graph Filters. 2019 13th International Conference on Sampling Theory and Applications (SampTA). doi:10.1109/sampta45681.2019.9030932
SponsorsENTE. Isufi’s research is supported in part by the KAUST-MIT-TUDCaltech consortium grant OSR-2015-Sensors-2700 Ext. 2018. G. Kutyniok acknowledges partial support by the Bundesministerium fur Bildung und Forschung (BMBF) through the Berliner Zentrum ¨ for Machine Learning (BZML), Project AP4, by the Deutsche Forschungsgemeinschaft (DFG) through Grants CRC 1114 “Scaling Cascades in Complex Systems”, Project B07, CRC/TR 109 “Discretization in Geometry and Dynamics”, Projects C02 and C03, RTG DAEDALUS (RTG 2433), Projects P1 and P3, RTG BIOQIC (RTG 2260), Projects P4 and P9, SPP 1798 “Compressed Sensing in Information Processing”, Project Coordination and Project Massive MIMO-I/II, by the Berlin Mathematics Research Center MATH+, Projects EF1-1 and EF1-4, and by the Einstein Foundation Be
Conference/Event name13th International Conference on Sampling Theory and Applications, SampTA 2019