Efficient Visualization of High-Dimensional Data with Polar Coordinates

Abstract

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 and 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.