Abstract: In this talk, I will describe a generic Topological Data Analysis (TDA) pipeline in machine learning, using persistent homology as an efficient dimension reduction algorithm for image classification. I will first introduce the basic concepts of persistent homology and persistence diagrams and then describe the filtrations that we used on binary images. I will then explain the process of extracting topological features from persistence diagrams and the machine learning application in image classification. Using standard machine learning techniques, I will show how to find and characterise important topological and geometrical features in images. This TDA pipeline is applied on the classical dataset of handwritten digits, the MNIST dataset. This is meant as an introductory talk in TDA and machine learning applications, no prerequisite in persistent homology or machine learning are required.
Note: this talk is in Seminar room 1.37, Hanna Neumann Building, rather than the usual room.