  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.
