Descriptif

Link to the course's web page: click here

Objectives :

There are many contexts in which data have a geometric flavor. For instance, observations given in the form of vectors living in Euclidean or Hilbert spaces, or as a distance or dissimilarity matrix, are inherently geometric. For such data, the quality of the analysis depends essentially on the ability to uncover the geometric structures hidden in the data. Furthermore, the geometry can be leveraged to speed up bottlenecks in the analysis pipeline. This is where techniques coming differential geometry, discrete and computational geometry, algebraic or geometric topology, can help. The goal of this course is to introduce the students to some of these techniques.

Content :

The course is divided into four lectures and four lab sessions. The topics covered include:

• nearest neighbor search,

• Delaunay-based reconstruction,

• metric clustering,

• topological inference.

Language :

The course will be taught either in French or in English, at the students' convenience.

Evaluation :

Oral paper presentation.