# Coordinatizing Data With Lens Spaces and Persistent Cohomology

@article{Polanco2019CoordinatizingDW, title={Coordinatizing Data With Lens Spaces and Persistent Cohomology}, author={Luis Polanco and Jose A. Perea}, journal={ArXiv}, year={2019}, volume={abs/1905.00350} }

We introduce here a framework to construct coordinates in \emph{finite} Lens spaces for data with nontrivial 1-dimensional $\mathbb{Z}_q$ persistent cohomology, $q\geq 3$. 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…

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