LOCATION: BCAM Semianar room and Online

Abstract
A frequently arising problem in applied data science is determining the dimensionality, in a suitable sense, of a large multi-dimensional data set. For example, if a million points are contained in a 1000-dimensional space, it would be useful to know whether %90 of them live on or near a 100-dimensional affine plane. The classical and highly effective method to study such problems is called PCA (Principal Component Analysis). However, PCA is not applicable if the lower dimensionality is due to "fractal" phenomena that do arise in practice. We are going to see how a discretized variant of the energy integral from geometric measure theory and related analytic techniques can be used to study the dimensionality of large data sets. We will briefly discuss further prospects for applying advanced mathematical techniques to some of the key questions in Big Data.


Link to the session:
https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09


More info at https://sites.google.com/view/apdebilbao/home