Multi-Perspective, Simultaneous Embedding

Md Iqbal Hossain, Vahan Huroyan, Stephen Kobourov, Raymundo Navarrete

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Article number9241407
Pages (from-to)1569-1579
Number of pages11
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number2
StatePublished - Feb 2021


  • Dimensionality reduction
  • Graph visualization
  • Mental map preservation
  • Multidimensional scaling

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

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