Analysis and prediction of wavelet and filter-bank frames performance for machine learning/scattering networks

Réf. 2018_R11_AC03

Stage - Data / Mathématiques Appliquées

Localisation : Hauts-de-Seine

Début : entre aujourd'hui et mai 2018
Durée : 5 mois
Indem. : Oui

IFP Energies nouvelles - Technologie, Informatique et Mathématiques appliquées

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Analysis and prediction of wavelet and filter-bank frames performance for machine learning/scattering networks


We wish to study large datasets of experimental data (e.g. physico-chemical spectral signals, microscopy or geophysical subsurface images) toward clustering, classication and learning. When data satisfy regularity properties, they often admit sparse or compressible representations in a judicious transformed domain: a few transformed coecients provide accurate data approximation. Such representations, like multiscale or wavelet transforms, are benecial to subsequent processing, and they form the core of novel data processing methodologies, such as Scattering networks/transforms or Functional Data Analysis.

Due to the variety of such transforms, without prior knowledge, it is not evident to find the most suitable representation for a given set of data. The aim of this subject is to investigate potential relations between transform properties and data compressibility on the one hand, and classication/clustering performance on the other hand, especially with respect to the robustness to shifts/translations or noise in data features, with matters in experimental applications.


Rooting on a recent work, the first objective is to develop a framework to allow the use of different sparsifying transformations (bases or frames of wavelets and multiscale transformations) at the input of reference SN algorithms. This will permit to evaluate the latter on a variety of experimental datasets, with the aim of choosing the most appropriate, both in terms of performance and usability, since the redundancy in transformations may hinder their application to large datasets. A particular interest could be laid on complex-like transformations, that may improve either the sparsication or "invariance properties" in the transformed data. Their importance has been underlined recently for deep convolutional

Then, starting from real data, the trainee will develop realistic models reproducing the expected behaviors in the data, for instance related to shifts or noise. Finally, the relative clustering/classication performances will be assessed with respect to different transformation choices, and their impact on both realistic models and real data. A particular interest could be laid on either transform properties (redundancy, frame bounds, asymptotic properties) or the resulting data multiscale statistics.


Second/third year engineering school and/or master of science with strong skills and curiosity in signal/image processing, statistics, machine learning, applied mathematics.

Applicants should provide a resume and a motivation letter emphasizing prior knowledge related to the subject (esp. learning and sparsifying transforms).

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