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Full-Text Articles in Statistical Methodology
Statistical Computational Topology And Geometry For Understanding Data, Joshua Lee Mike
Statistical Computational Topology And Geometry For Understanding Data, Joshua Lee Mike
Doctoral Dissertations
Here we describe three projects involving data analysis which focus on engaging statistics with the geometry and/or topology of the data.
The first project involves the development and implementation of kernel density estimation for persistence diagrams. These kernel densities consider neighborhoods for every feature in the center diagram and gives to each feature an independent, orthogonal direction. The creation of kernel densities in this realm yields a (previously unavailable) full characterization of the (random) geometry of a dataspace or data distribution.
In the second project, cohomology is used to guide a search for kidney exchange cycles within a kidney paired …