A survey on persistence landscape theory

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2022-7

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Gürses, Selçuk

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Topological data analysis (TDA) consists of a growing collection of techniques that reveal the shape of data. These techniques may be especially useful for comprehend ing global features of high-dimensional data that are inaccessible via other methods. The usage of TDA has been constrained by the difficulties of merging the subject’s primary tool, the barcode or persistence diagram, with statistics and machine learning. The persistence landscape is a stable topological summary that is easily combinable with statistical and machine learning technologies. This new summary has various advantages: First, since it is a function, calculations are significantly more quickly than conventional TDA tools. Second, it can be seen as a random variable with values in a Banach space, so it conforms to some statistical theorems such as strong law of large numbers and central limit theorem. Third, it provides a unique average unlike persistence diagrams and barcodes. This thesis is a survey that represents how the persistence landscape is constructed and contributes to the applications.

Subject Keywords

Topological data analysis, Persistence homology, Persistence landscape

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https://hdl.handle.net/11511/98161

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

S. Gürses, “A survey on persistence landscape theory,” M.S. - Master of Science, Middle East Technical University, 2022.