Shape-Driven Coordinate Ordering for Star Glyph Sets via Reinforcement Learning

We present a neural optimization model trained with reinforcement learning to solve the coordinate ordering problem for sets of star glyphs. Given a set of star glyphs associated to multiple class labels, we propose to use shape context descriptors to measure the perceptual distance between pairs of glyphs, and use the derived silhouette coefficient to measure the perception of class separability within the entire set. To find the optimal coordinate order for the given set, we train a neural network using reinforcement learning to reward orderings with high silhouette coefficients. The network consists of an encoder and a decoder with an attention mechanism. The encoder employs a recurrent neural network (RNN) to encode input shape and class information, while the decoder together with the attention mechanism employs another RNN to output a sequence with the new coordinate order. In addition, we introduce a neural network to efficiently estimate the similarity between shape context descriptors, which allows to speed up the computation of silhouette coefficients and thus the training of the axis ordering network. Two user studies demonstrate that the orders provided by our method are preferred by users for perceiving class separation. We tested our model on different settings to show its robustness and generalization abilities and demonstrate that it allows to order input sets with unseen data size, data dimension, or number of classes. We also demonstrate that our model can be adapted to coordinate ordering of other types of plots such as RadViz by replacing the proposed shape-aware silhouette coefficient with the corresponding quality metric to guide network training.

1 Introduction

Since the beginning of information visualization, radial plots have been used for showing multi-dimensional data points in complex data sets. Already in 1858, Florence Nightingale [1] applied them to depict mortality causes for the months of a year. Star glyphs are a type of radial plot that show data points in a compact representation since the coordinate axes are circularly arranged around a central point. Variants such as RadViz [2] and ArcVis [3] also enable to visualize multiple dimensions in 2D radial plots. An overview of radial visualization methods and glyph-based plots is given by Behrisch et al. [4] and Borgo et al. [5].