Thursday, December 15, 2011

Implementation of Mallat's Scattering transform

A year ago, I mentioned the work of Stephane Mallat ( Mallat's Invariants). It looks he and his co-authors (Joan Bruna and Joakim Anden) released an implementation of their scattering transform that allows different signals featuring the same object and its translated/rotated companion to be compared to each other using the Euclidian norm Here is the video presentation of a year ago 

High dimensional classification by recursive interferometry
envoyé par Sciences_Maths_Paris. - Vidéos des dernières découvertes technologiques.

From the webpage:
A Scattering transform defines a signal representation which is locally invariant to translations and potentially to other groups of transformations such as rotations or scaling. It linearizes deformations and is thus well adapted to signal classification. A scattering transform is implemented with a convolutional network architecture, iterating over wavelet decompositions and complex modulus. This web page provides articles and softwares on scattering transforms and classification applications.

[1] Mathematical introduction of scattering operators for group invariant representations (78 pages): "Group Invariant Scattering" S. Mallat.
[2] Scattering transform review with an image classification algorithm (6 pages) : Classification with Scattering Operators" J. Bruna and S. Mallat. Proceedings of the IEEE CVPR 2011 conference.
[3] Scattering transform applied to audio signals and musical classification (6 pages) : Multiscale Scattering for Audio Classification" Joakim Andén and S. Mallat. Proceedings of the ISMIR 2011 conference. For Matlab code and reconstruction examples, see the audio section.
 The implementation is here.

Of interest, there is also this abstract : Convolution Networks with Stable Invariants by Joan Bruna and Stephane Mallat.

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