Programme :
Programme :

The objective of this course is to familiarize PhD candidates and Master students in electrical engineering with unsupervised linear and non-linear dimensionality reduction methods. We will start by studying spectral dimensionality reduction techniques such as principal component analysis (PCA) canonical correlation analysis (CCA), and multi-dimensional scaling (MDS) that operate on either covariance or Gram (dot-product) matrices built over the observed data. We will then turn our attention to non-linear extensions of these methods, or graph-based methods, such as ISOMAP, Laplacian eigenmaps (LE) or locally-linear embedding (LLE), and more generally kernel methods such as kernel PCA, kernel CCA, and graph kernels. Finally, we will study probabilistic dimensionality reduction methods such as probabilistic PCA and factor analysis. The course will be illustrated with numerous examples from various applications such as:
- Visual computing (images, image collections, and videos)
- Graphical and animation methods (voxels, meshes, 3D scans),
- Robotics (2D and 3D point clouds, multi-sensory data, inverse kinematics)
- Audio signal processing (auditory scene analysis, speech recognition, audio-visual interpretation),
- Medical analysis (MRI and fMRI data), and
- Data mining (text, multimedia documents, social

Pré-requis :
Bases en signal, image et analyse de données