MDS _polar : A New Approach for Dimension Reduction to Visualize High Dimensional Data

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 method probably leads to good results. 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 datasets. In this paper we present a new approach for dimension reduction to visualize high dimensional data. Our algorithm transforms high dimensional feature vectors into two-dimensional feature vectors under the constraints that the length of each vector is preserved and that the angles between vectors approximate the corresponding angles in the high dimensional space as good as possible, enabling us to come up with an efficient computing scheme.