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A Structure-Based Distance Metric for High-Dimensional Space Exploration with Multidimensional Scaling
March 2014 (vol. 20 no. 3)
pp. 351-364
Jenny Hyunjung Lee, Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Kevin T. McDonnell, Dept. of Math. & Comput. Sci, Dowling Coll., Oakdale, NY, USA
Alla Zelenyuk, Pacific Northwest Nat. Lab., Richland, WA, USA
Dan Imre, Imre Consulting, Richland, WA, USA
Klaus Mueller, Dept. of Comput. Sci., Stony Brook Univ., Stony Brook, NY, USA
Although the euclidean distance does well in measuring data distances within high-dimensional clusters, it does poorly when it comes to gauging intercluster distances. This significantly impacts the quality of global, low-dimensional space embedding procedures such as the popular multidimensional scaling (MDS) where one can often observe nonintuitive layouts. We were inspired by the perceptual processes evoked in the method of parallel coordinates which enables users to visually aggregate the data by the patterns the polylines exhibit across the dimension axes. We call the path of such a polyline its structure and suggest a metric that captures this structure directly in high-dimensional space. This allows us to better gauge the distances of spatially distant data constellations and so achieve data aggregations in MDS plots that are more cognizant of existing high-dimensional structure similarities. Our biscale framework distinguishes far-distances from near-distances. The coarser scale uses the structural similarity metric to separate data aggregates obtained by prior classification or clustering, while the finer scale employs the appropriate euclidean distance.
Index Terms:
Layout,Euclidean distance,Correlation,Indexes,Data visualization,Extraterrestrial measurements,visual analytics,Information visualization,multivariate visualization,clustering,high-dimensional data
Citation:
Jenny Hyunjung Lee, Kevin T. McDonnell, Alla Zelenyuk, Dan Imre, Klaus Mueller, "A Structure-Based Distance Metric for High-Dimensional Space Exploration with Multidimensional Scaling," IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 3, pp. 351-364, March 2014, doi:10.1109/TVCG.2013.101
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