The University of Arizona
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Multi-Perspective, Simultaneous Embedding

TRIPODS Seminar

Multi-Perspective, Simultaneous Embedding
Series: TRIPODS Seminar
Location: ENR2 S210
Presenter: Raymundo Navarrete, TRIPODS PostDoc, University of Arizona Mathematics

We describe a method for simultaneous visualization of multiple
pairwise distances in 3 dimensional (3D) space. Given the distance
matrices that correspond to 2 dimensional projections of a 3
dimensional object (dataset) the goal is to recover the 3 dimensional
object (dataset). We propose an approach that uses 3D to place the
points, along with projections (planes) that preserve each of the
given distance matrices. Our multi-perspective, simultaneous embedding
(MPSE) method is based on non-linear dimensionality reduction that
generalizes multidimensional scaling. We consider two versions of the
problem: in the first one we are given the input distance matrices and
the projections (e.g., if we have 3 different projections we can use
the three orthogonal directions of the unit cube). In the second
version of the problem we also compute the best projections as part of
the optimization. We experimentally evaluate MPSE using synthetic
datasets that illustrate the quality of the resulting solutions.

(Pizza, coffee & tea will be provided at 11:20am)