Visualization of High-Dimensional Data with Relational Perspective Map

This paper introduces a method called relational perspective map (RPM) to visualize distance information in high-dimensional spaces. Like conventional multidimensional scaling, the RPM algorithm aims to produce proximity preserving 2-dimensional (2-D) maps. The main idea of the RPM algorithm is to simulate a multiparticle system on a closed surface: whereas the repulsive forces between the particles reflect the distance information, the closed surface holds the whole system in balance and prevents the resulting map from degeneracy. A special feature of RPM algorithm is its ability to partition a complex dataset into pieces and map them onto a 2-D space without overlapping. Compared to other multidimensional scaling methods, RPM is able to reveal more local details of complex datasets. This paper demonstrates the properties of RPM maps with four examples and provides extensive comparison to other multidimensional scaling methods, such as Sammon Mapping and Curvilinear Principle Analysis.

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