Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing

2018/06/22 by Yan, Lin, Zhao, Yaodong, Rosen, Paul +2 · 1 citation
#Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graphics (cs.GR)

paper · doi:10.48550/arxiv.1806.08460

Abstract

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality reduction: distance preservation and topology preservation. Inspired by recent work in topological data analysis, we are on the quest for a dimensionality reduction technique that achieves the criterion of homology preservation, a generalized version of topology preservation. Specifically, we are interested in using topology-inspired manifold landmarking and manifold tearing to aid such a process and evaluate their effectiveness.

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