A survey on multidimensional persistence theory

Karagüler, Dilan
Persistence homology is one of the commonly used theoretical methods in topological data analysis to extract information from given data using algebraic topology. Converting data to a filtered object and analyzing the topological features of each space in the filtration, we will obtain a way of representing these features called the shape of data. This will give us invariants like barcodes or persistence diagrams for the data. These invariants are stable under small perturbations. In most applications, we need multiscaled analysis of data, which is done by multidimensional persistence. This thesis is a survey that contains how to produce invariants for multiscaled filtration obtained from data and the related stability results.
Citation Formats
D. Karagüler, “A survey on multidimensional persistence theory,” M.S. - Master of Science, Middle East Technical University, 2021.