Seminaria w Instytucie Podstaw Informatyki PAN

Streszczenie (autorskie):

In this talk I will present a general introduction to topological data analysis suitable for the use in practical statistics. There are two aspects in which topology can contribute to statistical learning; in data visualization, for exploratory data analysis and for feature extraction, to make the existing statistical techniques potentially more efficient in practice. We will start from data visualization methods and present a number of topological visualization tools, including mapper, ball mapper and ClusterGraph. Subsequently we will discuss some basic data features, focusing on concepts originating from Euler characteristics. We will show how it can be utilized for topological goodness-of-fit tests as well as as a tool to extract information from various branches of sciences, including image analysis and dynamical systems.