The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep cascade of additions, subtractions and absolute values, which iteratively compute orthogonal Haar wavelet transforms. Multiscale neighborhoods of unknown graphs are estimated by minimizing an average total variation, with a pair matching algorithm of polynomial complexity. Supervised classification with dimension reduction is tested on data bases of scrambled images, and for signals sampled on unknown irregular grids on a sphere.
Xu Chen (Princeton University)
Xiuyuan Cheng (E ́cole Normale Supe ́rieure)
Stephane Mallat (Ecole Polytechnique Paris)
Stéphane Mallat received the Ph.D. degree in electrical engineering from the University of Pennsylvania, in 1988. He was then Professor at the Courant Institute of Mathematical Sciences. In 1995, he became Professor in Applied Mathematics at Ecole Polytechnique, Paris. From 2001 to 2007 he was co-founder and CEO of a semiconductor start-up company. In 2012 he joined the Computer Science Department of Ecole Normale Supérieure, in Paris. Stéphane Mallat’s research interests include signal processing, computer vision, harmonic analysis and learning. He wrote a “Wavelet tour of signal processing: the sparse way”. In 1997, he received the Outstanding Achievement Award from the SPIE Society and was a plenary lecturer at the International Congress of Mathematicians in 1998. He also received the 2004 European IST Grand prize, the 2004 INIST-CNRS prize for most cited French researcher in engineering and computer science, and the 2007 EADS grand prize of the French Academy of Sciences.
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