Localized Persistence Diagram and Applications

Student: Boykov Aleksey

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 8

Year of Graduation: 2024

This paper presents a new brand method for analyzing simplicial complexes with filtration functions on it. Standard algorithms that use a basic persistence diagram do not utilize any information about persistent homologies' positions. Our proposed method enhances these approaches by adding eigenvectors from the discrete Laplace operator spectrum that appear and disappear with corresponding persistent homology. To prove effectiveness, we will conduct some experiments with object classification and object-distincting tasks on both real and artificial datasets using non-topology methods, methods with basic diagrams, and methods with augmented (localized) diagrams. The results will be compared. This work can contribute a lot in such data analysis fields as graph and topology deep learning.

Full text (added May 20, 2024)

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