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Open AccessArticle

Upsampling for Improved Multidimensional Attribute Space Clustering of Multifield Data

Department of Mathematics and Informatics, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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This paper is an extended version of our paper published in the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, Funchal, Portugal, 27–29 January 2018.
Information 2018, 9(7), 156; https://doi.org/10.3390/info9070156
Received: 11 May 2018 / Revised: 15 June 2018 / Accepted: 20 June 2018 / Published: 27 June 2018
(This article belongs to the Special Issue Selected Papers from IVAPP 2018)
Clustering algorithms in the high-dimensional space require many data to perform reliably and robustly. For multivariate volume data, it is possible to interpolate between the data points in the high-dimensional attribute space based on their spatial relationship in the volumetric domain (or physical space). Thus, sufficiently high number of data points can be generated, overcoming the curse of dimensionality for this particular type of multidimensional data. We applies this idea to a histogram-based clustering algorithm. We created a uniform partition of the attribute space in multidimensional bins and computed a histogram indicating the number of data samples belonging to each bin. Without interpolation, the analysis was highly sensitive to the histogram cell sizes, yielding inaccurate clustering for improper choices: Large histogram cells result in no cluster separation, while clusters fall apart for small cells. Using an interpolation in physical space, we could refine the data by generating additional samples. The depth of the refinement scheme was chosen according to the local data point distribution in attribute space and the histogram’s bin size. In the case of field discontinuities representing sharp material boundaries in the volume data, the interpolation can be adapted to locally make use of a nearest-neighbor interpolation scheme that avoids averaging values across the sharp boundary. Consequently, we could generate a density computation, where clusters stay connected even when using very small bin sizes. We exploited this result to create a robust hierarchical cluster tree, apply our technique to several datasets, and compare the cluster trees before and after interpolation. View Full-Text
Keywords: multi-dimensional data visualization; multi-field data; clustering multi-dimensional data visualization; multi-field data; clustering
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Molchanov, V.; Linsen, L. Upsampling for Improved Multidimensional Attribute Space Clustering of Multifield Data. Information 2018, 9, 156.

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