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Branching and Circular Features in High Dimensional Data
Stanford University, USA.ORCID iD: 0000-0001-6322-7542
2011 (English)In: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 17, no 12, 1902-1911 p.Article in journal (Refereed) Published
Abstract [en]

Large observations and simulations in scientific research give rise to high-dimensional data sets that present many challenges and opportunities in data analysis and visualization. Researchers in application domains such as engineering, computational biology, climate study, imaging and motion capture are faced with the problem of how to discover compact representations of highdimensional data while preserving their intrinsic structure. In many applications, the original data is projected onto low-dimensional space via dimensionality reduction techniques prior to modeling. One problem with this approach is that the projection step in the process can fail to preserve structure in the data that is only apparent in high dimensions. Conversely, such techniques may create structural illusions in the projection, implying structure not present in the original high-dimensional data. Our solution is to utilize topological techniques to recover important structures in high-dimensional data that contains non-trivial topology. Specifically, we are interested in high-dimensional branching structures. We construct local circle-valued coordinate functions to represent such features. Subsequently, we perform dimensionality reduction on the data while ensuring such structures are visually preserved. Additionally, we study the effects of global circular structures on visualizations. Our results reveal never-before-seen structures on real-world data sets from a variety of applications.

Place, publisher, year, edition, pages
IEEE Computer Society, 2011. Vol. 17, no 12, 1902-1911 p.
Keyword [en]
Dimensionality reduction, circular coordinates, visualization, topological analysis
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-150361DOI: 10.1109/TVCG.2011.177ScopusID: 2-s2.0-80855156200OAI: diva2:742592

QC 20140908

Available from: 2014-09-02 Created: 2014-09-02 Last updated: 2014-09-08Bibliographically approved

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Vejdemo-Johansson, Mikael
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