Imaging and Computing Seminar

Arthur Szlam , Courant Institute of Mathematical Sciences, NYU

Linear and piecewise linear data analysis

Many data sets arising from signal processing or machine learning problems can be approximately modeled as a union of $K$ low dimensional linear sets. In this talk I will start by discussing the case $K=1$, which remains a surprisingly active area of research, despite more than a hundred years of history and a good understanding of the mathematics of the problem for many notions of ``approximately'' and ``low''.  For larger values of $K$, although heuristic methods have proved succesful in applications, many basic mathematical and computational questions remain open.  I will talk about some regimes where we have made progress, and then give some fun examples in less easy regimes where the math remains murky.