01 Nov 2018

Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing


Lin Yan, Yaodong Zhao, Paul Rosen, Carlos Scheidegger, Bei Wang. Visual Data Science, 2018.


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.