Improved N-dimensional data visualization from hyper-radial values

Abstract

Higher-dimensional data, which is becoming common in many disciplines due to big data problems, are inherently difficult to visualize in a meaningful way. While many visualization methods exist, they are often difficult to interpret, involve multiple plots and overlaid points, or require simultaneous interpretations. This research adapts and extends hyper-radial visualization, a technique used to visualize Pareto fronts in multi-objective optimizations, to become an n-dimensional visualization tool. Hyper-radial visualization is seen to offer many advantages by presenting a low-dimensionality representation of data through easily understood calculations. First, hyper-radial visualization is extended for use with general multivariate data. Second, a method is developed by which to optimally determine groupings of the data for use in hyper-radial visualization to create a meaningful visualization based on class separation and geometric properties. Finally, this optimal visualization is expanded from two to three dimensions in order to support even higher-dimensional data. The utility of this work is illustrated by examples using seven datasets of varying sizes, ranging in dimensionality from Fisher Iris with 150 observations, 4 features, and 3 classes to the Mixed National Institute of Standards and Technology data with 60,000 observations, 717 non-zero features, and 10 classes.