MDSQ – Quality Assessment of Distance-Preserving Projections

Theoretical (Analytical):

Practical (Implementation):

Literature Work:


Distance-preserving projections such as multi-dimensional scaling (MDS) or t-distributed stochastic neighborhood embedding (t-SNE) are popular methods to analyze high-dimensional data. The general idea is to project original data into a 2D layout by preserving the original similarities as well as possible. The analysis assumption is that close objects in the 2D projection correspond to similar objects in the high-dimensional space.

Problem Statement

The visual patterns in 2D projections are often interpreted without questioning the quality of the projection. MDS, for example, optimizes the 2D layout by preserving all pair-wise similarities of the original data. Depending on the (dis-)similarity distribution, the MDS projection can reflect the original structures or not. The goal of this project is to develop methods for the quality assessment of such projections.


  • Literature review for existing quality measures for projections.
  • Development of quality criteria.
  • Development of novel quality measures for distance-preserving projections.
  • Development of a visual-interactive tool for the quality assessment of distance-preserving projections.


  • Knowledge in information visualization.
  • Good programming skills in Java and Web-Technologies (JavaScript, d3.js, etc.).


  • Scope: Bachelor/Master
  • 6 Month Project, 3 Month Thesis (Bachelor) / 6 Month Thesis (Master)
  • Start: immediately



  • Probing Projections: Interaction Techniques for Interpreting Arrangements and Errors of Dimensionality Reductions [Stahnke et al., 2016]
  • ProxiViz: an Interactive Visualization Technique to Overcome Multidimensional Scaling Artifacts [Heulot et al., 2012]
  • IPCA: An interactive system for PCA-based visual analytics [Jeong et al., 2009]
  • Data-driven Evaluation of Visual Quality Measures [Sedlmair and Aupetit, 2015]
  • Data Visualization With Multidimensional Scaling [Buja et al., 2008]
  • Modern multidimensional scaling [Borg and Groenen, 2005]
  • Visualizing Data using t-SNE [Maaten and Hinton, 2008]