Essays about: "persistence modules"

Found 3 essays containing the words persistence modules.

1. 1. Metrics for Multidimensional Persistence

   University essay from KTH/Matematik (Avd.)

   Author : Daniel Lundin; [2022]
   Keywords : topological data analysis; multidimensional persistence; persistence modules; metrics; noise systems; topologisk dataanalys; multidimensionell persistens; persistensmoduler; metriker; noise system;

   Abstract : A fundamental mathematical object in topological data analysis today is the persistence module. This thesis explores different metrics on multidimensional persistence modules, where spaces are parametrized along multiple dimensions. The focus is especially on metrics constructed by the use of so called noise systems, introduced by Scolamiero et al. READ MORE

3. 2. Classifying RGB Images with multi-colour Persistent Homology

   University essay from Linköpings universitet/Matematiska institutionen

   Author : Wolf Byttner; [2019]
   Keywords : Persistent Homology; Applied Algebraic Topology; Topological Data Analysis; Image Classification; CUB-200-2011;

   Abstract : In Image Classification, pictures of the same type of object can have very different pixel values. Traditional norm-based metrics therefore fail to identify objectsin the same category. Topology is a branch of mathematics that deals with homeomorphic spaces, by discarding length. READ MORE

4. 3. Interactive visualization of community structure in complex networks

   University essay from Umeå universitet/Institutionen för fysik

   Author : Anton Eriksson; [2018]
   Keywords : networks; visualization; clustering; community detection; graph layout;

   Abstract : Several applied sciences model system dynamics with networks. Since networks often contain thousands or millions of nodes and links, researchers have developed methods that reveal and high- light their essential structures. READ MORE