CRITICAL RADIUS IN PERSISTENT HOMOLOGY - Novita Sari, Sri
In this thesis, we will explain how to construct a simlpicial complex from a data by drawing closed ball centered at points from data with radius growing from zero to infinity. Based on this construction we will define a map from the radius of the balls to the rank of 0-th homology group of related simplicial complex. Based on this mapping then we will define critical radius for H0, the smallest critical radius for H0, the biggest critical radius for H0, and the algorithm for finding all of the critical radius for H0.