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, including the efficient computation of proximity queries, reconstruction using Delaunay tessellations, metric-based clustering methods, and topological tools for inference.
Important: bring pens and paper to take notes.
|Session 1: Nearest Neighbor Search (video file)||Slides||TD 1||Sept. 20 2021|
|Session 2: Delaunay-based Reconstruction (video file)||Slides||TD 2||Sept. 27 2021|
|Session 3: Metric Clustering (video file)||Introduction [slides], Hierarchical clustering [slides, notes], Mode seeking [slides, notes 1, notes 2]||TD 3||Oct. 4 2021|
|Session 4: Topological Inference (video file)||Slides [0, 1, 2, 3, 4]||TD 4||Oct. 11 2021|
|Oral presentations: Oct. 18 2021||guidelines|
Feel free to come and ask directly if you are looking for a research internship.