The CUNY Data Science and Applied Topology Reading Group is joint between the Mathematics and Computer Science programmes. We meet Fridays 11.45 -- 12.45 in GC 4419. You can contact us at firstname.lastname@example.org.
Our plan is to primarily read and discuss seminal papers in data science, in applied topology and in topological data analysis. Each seminar one participant takes the responsibility to present a paper and prepare items for discussion. We expect occasionally to be able to invite external speakers.
Current schedule can be found here.
We will be sending out announcements through a mailing list; you can subscribe here.
- Mikael Vejdemo-Johansson, Computer Science Programme, CUNY Graduate Center; Department of Mathematics, CUNY College of Staten Island
- Azita Mayeli, Mathematics Programme, CUNY Graduate Center; Department of Mathematics, CUNY Queensborough Community College
We have compiled a list of papers that might be interesting to present.
Singularity in Data Analysis
Statistical data by their very nature are indeterminate in the sense that if one repeated the process of collecting the data the new data set would be somewhat different from the original. Therefore, a statistical method, f, taking a data set x to a point in some space F, should be stable at x: Small perturbations in x should result in a small change in f(x). Otherwise, f is useless at x or -- and this is important -- near x. So one doesn't want f to have "singularities", a data set x such that the the limit of f(y) as y approaches x doesn't exist. (Yes, the same issue arises elsewhere in applied math.)
However, broad classes of statistical methods have topological obstructions of continuity: They must have singularities. In this talk I will show why and give lower bounds on the Hausdorff dimension, even Hausdorff measure, of the set of singularities of such methods. I will give examples.