  We describe MPSE: a Multi-Perspective Simultaneous Embedding method for
visualizing high-dimensional data, based on multiple pairwise distances between
the data points. Specifically, MPSE computes positions for the points in 3D and
provides different views into the data by means of 2D projections (planes) that
preserve each of the given distance matrices. We consider two versions of the
problem: fixed projections and variable projections. MPSE with fixed
projections takes as input a set of pairwise distance matrices defined on the
data points, along with the same number of projections and embeds the points in
3D so that the pairwise distances are preserved in the given projections. MPSE
with variable projections takes as input a set of pairwise distance matrices
and embeds the points in 3D while also computing the appropriate projections
that preserve the pairwise distances. The proposed approach can be useful in
multiple scenarios: from creating simultaneous embedding of multiple graphs on
the same set of vertices, to reconstructing a 3D object from multiple 2D
snapshots, to analyzing data from multiple points of view. We provide a
functional prototype of MPSE that is based on an adaptive and stochastic
generalization of multi-dimensional scaling to multiple distances and multiple
variable projections. We provide an extensive quantitative evaluation with
datasets of different sizes and using different number of projections, as well
as several examples that illustrate the quality of the resulting solutions.
