International Journal of Science, Engineering and TechnologyAuthors: Dr.Shaista Parveen Shaikh Mohammed
Abstract: Computational topology is an interdisciplinary field of research that connects topological theory with computational algorithms aimed at the analysis of shape and structure within complex data sets. This paper provides an exhaustive overview of mathematical principles that form the basis of computational topology, with a particular focus on persistent homology as the key analytical method. The paper explores the fundamentals of simplicial homology and filtration theory and shows how these mathematical concepts can be used for the extraction of topological features in a multiscale fashion. In our work, we propose a methodology for the use of a new harmonic persistent homology method combined with commutative algebraic structure to solve problems inherent in classical persistence barcodes. Experiments on benchmark data sets prove the efficiency of our approach in terms of improvement of the discriminability of topological features by 23.7%.
DOI: http://doi.org/10.5281/zenodo.22724824
