Essays about: "applied algebraic topology"

Found 3 essays containing the words applied algebraic topology.

1. 1. Persistent Homology : A Modern Application of Algebraic Topology in Data Analysis

   University essay from

   Author : Staffan Leijnse; [2023]
   Keywords : Data; Algebraic Topology; Persistent; Homology; Graded; Representation;

   Abstract : Topological data analysis emerged as a field in the 2000s and has proven very useful for examining the shape of data sets. Using persistent homology as their main methodology researchers has succesfully applied the theory presented in this paper to study as varied subjects as robot motion, brain connectivity, network theory, finger print analysis and computer vision. READ MORE

3. 2. From Relations to Simplicial Complexes: A Toolkit for the Topological Analysis of Networks

   University essay from KTH/Matematik (Avd.)

   Author : Johan Lord; [2021]
   Keywords : applied algebraic topology; complex networks; topological data analysis; brain network analysis;

   Abstract : We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. READ MORE

4. 3. 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