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k-simplex volume optimizing projection algorithms for high-dimensional data sets




Stiverson, Shannon J., author
Kirby, Michael, advisor
Peterson, Chris, advisor
Adams, Henry, committee member
Hess, Ann, committee member

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Many applications produce data sets that contain hundreds or thousands of features, and consequently sit in very high dimensional space. It is desirable for purposes of analysis to reduce the dimension in a way that preserves certain important properties. Previous work has established conditions necessary for projecting data into lower dimensions while preserving pairwise distances up to some tolerance threshold, and algorithms have been developed to do so optimally. However, although similar criteria for projecting data into lower dimensions while preserving k-simplex volumes has been established, there are currently no algorithms seeking to optimally preserve such embedded volumes. In this work, two new algorithms are developed and tested: one which seeks to optimize the smallest projected k-simplex volume, and another which optimizes the average projected k-simplex volume.


2021 Spring.
Includes bibliographical references.

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