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Accueil du site > Séminaires > Mathématiques des systèmes complexes > Dimensionality reduction : from PCA to recent nonlinear techniques.

Vendredi 29 mai 2009 à 11h00

Dimensionality reduction : from PCA to recent nonlinear techniques.

John Lee (Université Catholique de Louvain, Belgique)

Résumé : Dimensionality reduction is an old yet unsolved problem, with many applications in data visualization, knowledge discovery, and machine learning in general. Our aim in this talk will be to review several developments in the field of dimensionality reduction, with a particular focus on nonlinear methods.

As an introduction, we will point out some weird properties of high dimensional spaces, which will motivate the use of dimensionality reduction.

Next, we will go back in time and start our review with a short reminder about well known techniques such as principal component analysis and multidimensional scaling. Our travel into time will also bring us to visit Sammon mapping and other methods based on distance preservation. Next, we will come across self-organizing maps and auto-encoders with bottleneck neural networks. Some spectral methods such as Isomap and locally linear embedding will be reviewed as well. A glance at recent methods based on similarity preservation such as stochastic neighbor embedding will close the survey. Finally, we will try to identify the relationships between the different approaches, and say a few words about quality criteria for dimensionality reduction techniques.

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