Multi-Perspective, Simultaneous Embedding

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. Finally, we provide a functional prototype which implements both settings.