The Data Processing and Classification team is in the Department d'Informatique of Ecole Normale Superieure, and is a joint research team between École Normale Supérieure de Paris and the Centre National de la Recherche Scientifique : CNRS/ENS UMR 8548.
Our research is devoted to generic mathematical and algorithmic approaches to represent high-dimensional data for classifications. Wide range of applications are studied for speech and music, images and videos, geophysical seismic data, medical data such as ECG and EEG, new sensor output including electromagnetic field signals. Revealing the information carried by these very different high-dimensional data relies on similar principles. They all suffer from a curse of dimensionality, which hides complex structures.
Our approaches are ground on mathematics and algorithms emmerging from harmonic analysis and geometry. They involve wavelet transforms, groups and manifolds, invariant and sparse representations, dictionary and kernel learning, deep neural networks and statistical learning. We also maintain close collaborations with neurophysiological modeling teams, facing similar problems to understand cortical processing of auditory and visual perception.
Data classes suffer from a considerable variability that needs to be reduced without removing discriminative information. We study the construction of stable, informative invariants over groups mainly responsible for the data variability. This topic relies on scattering transforms which iterate on wavelet transforms along deep neural networks. Applications are developed to speech and music , images and medical signal analysis.
Learning representations from unlabeled data amounts to learn important structures in an unknown data world, from examples. Sparsity and dictionary learning are important tool to search for structure that can be modeled as groups or manifolds. Understanding deep neural network structures