Axes Bundling and Brushing in Star Coordinates

Abstract

Visual analysis of multidimensional data commonly involves dimensionality reduction to project the data samples into a lowerdimensional visual space. Star coordinates (SC) provide a means to explore the multidimensional data distribution by interactively changing the linear projection matrix. While SC have the advantages of being intuitive, allowing for relating the data samples to their original dimensions, having low computation costs, and scaling well with the number of data samples, they have the disadvantages of not scaling well to larger number of dimensions and being restricted to linear projections. We address these short-comings by introducing novel SC interactions. First, interactive bundling of axes is proposed to reduce the number of dimensions. While bundles are fully customizable, the bundling interactions are supported by visualizations of correlation matrices and hierarchical axes clustering dendrograms. Second, we enhance classical region brushing in SC projections with axes brushing, which allows for multidimensional cluster selection, even if two (separable) clusters are projected to the same area of the visible space. Axes brushing is supported by visualizing 1D histograms of data distributions along the SC axes. Our brushing interactions alleviate the restriction of SC to linear projections. The integration of histograms into SC also eases other interactions such as moving axes to change the projection matrix. A user study evaluates how analysis tasks for labeled and unlabeled multidimensional data can benefit from our extensions.