  In ordinary Dimensionality Reduction (DR), each data instance in a high
dimensional space (original space), or on a distance matrix denoting original
space distances, is mapped to (projected onto) one point in a low dimensional
space (visual space), building a layout of projected points trying to preserve
as much as possible some property of data such as distances, neighbourhood
relationships, and/or topology structures, with the ultimate goal of
approximating semantic properties of data with preserved geometric properties
or topology structures in visual space. In this paper, the concept of
Multi-point Dimensionality Reduction is elaborated on where each data instance
can be mapped to (projected onto) possibly more than one point in visual space
by providing the first general solution (algorithm) for it as a move in the
direction of improving reliablity, usability and interpretability of
dimensionality reduction. Furthermore by allowing the points in visual space to
be split into two layers while maintaining the possibility of having more than
one projection (mapping) per data instance , the benefit of separating more
reliable points from less reliable points is dicussed notwithstanding the
effort to improve less reliable points. The proposed solution (algorithm) in
this paper, named Layered Vertex Splitting Data Embedding (LVSDE), is built
upon and extends a combination of ordinary DR and graph drawing techniques.
Based on the experiments of this paper on some data sets, the particular
proposed algorithm (LVSDE) practically outperforms popular ordinary DR methods
visually (semantics, group separation, subgroup detection or combinational
group detection) in a way that is easily explainable.
