Visualization of High-Dimensional Data with Polar Coordinates

Visualization of High-Dimensional Data with Polar Coordinates

Frank Rehm (German Aerospace Center, Germany), Frank Klawonn (University of Applied Sciences Braunschweig/Wolfenbuettel, Germany) and Rudolf Kruse (University of Magdenburg, Germany)
Copyright: © 2009 |Pages: 6
DOI: 10.4018/978-1-60566-010-3.ch315
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Many applications in science and business such as signal analysis or costumer segmentation deal with large amounts of data which are usually high dimensional in the feature space. As a part of preprocessing and exploratory data analysis, visualization of the data helps to decide which kind of data mining method probably leads to good results or whether outliers or noisy data need to be treated before (Barnett & Lewis, 1994; Hawkins, 1980). Since the visual assessment of a feature space that has more than three dimensions is not possible, it becomes necessary to find an appropriate visualization scheme for such data sets. Multidimensional scaling (MDS) is a family of methods that seek to present the important structure of the data in a reduced number of dimensions. Due to the approach of distance preservation that is followed by conventional MDS techniques, resource requirements regarding memory space and computation time are fairly high and prevent their application to large data sets. In this work we will present two methods that visualize high-dimensional data on the plane using a new approach. An algorithm will be presented that allows applying our method on larger data sets. We will also present some results on a benchmark data set.
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With MDSpolar and POLARMAP we present two approaches to find a two-dimensional projection of a p-dimensional data set 978-1-60566-010-3.ch315.m01. Both methods try to find a representation in polar coordinates 978-1-60566-010-3.ch315.m02, where the length 978-1-60566-010-3.ch315.m03 of the original vector 978-1-60566-010-3.ch315.m04 is preserved and only the angle 978-1-60566-010-3.ch315.m05 has to be optimized. Thus, our solution is defined to be optimal if all angles between pairs of data objects in the projected data set Y coincide as good as possible with the angles in the original feature space 978-1-60566-010-3.ch315.m06. As we will show later, it is possible to transform new data objects without extra costs.

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