  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.
