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- W2943667890 abstract "We introduce here a framework to construct coordinates in emph{finite} Lens spaces for data with nontrivial 1-dimensional $mathbb{Z}_q$ persistent cohomology, $qgeq 3$. Said coordinates are defined on an open neighborhood of the data, yet constructed with only a small subset of landmarks. We also introduce a dimensionality reduction scheme in $S^{2n-1}/mathbb{Z}_q$ (Lens-PCA: $mathsf{LPCA}$), and demonstrate the efficacy of the pipeline $PH^1(;cdot; ; mathbb{Z}_q)$ class $Rightarrow$ $S^{2n-1}/mathbb{Z}_q$ coordinates $Rightarrow$ $mathsf{LPCA}$, for nonlinear (topological) dimensionality reduction." @default.
- W2943667890 created "2019-05-09" @default.
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- W2943667890 date "2019-05-01" @default.
- W2943667890 modified "2023-09-27" @default.
- W2943667890 title "Coordinatizing Data With Lens Spaces and Persistent Cohomology" @default.
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