Speaker: Leo Liberti CNRS & LIX, Ecole Polytechnique, France

Abstract:
Many problems in data science are addressed by mapping entities of various kind to vectors in a Euclidean space of some dimension. Most of these methods (e.g. Multidimensional Scaling, Principal Component Analysis, K-means clustering, random projections) are based on the proximity of pairs of vectors. In order for the results of these methods to make sense when mapped back, the proximity of entities in the original problem must be well approximated in the Euclidean space setting. If proximity were known for each pair of original entities, this mapping would be a good example of isometric embedding. Usually, however, this is not the case, as data are partial, wrong and noisy. I shall survey some of the methods above from the point of view of Distance Geometry. Time permitting, I will also showcase some code examples.
Location: Aula “Piano Terra”, via dei Taurini 19, Roma
First lecture:  September 3, 2018  time 11.30
Second lecture:  September 4, 2018 time 11.30
Slides available upon request to Claudio Gentile