Before revision:  First, we show that constructing optimal geometric graphs directly from data features can aid classification tasks on both synthetic and real-world data sets from different domains. Second, we introduce two metrics to characterize optimal graphs: i) by measuring the alignment between the subspaces spanned by the features convolved with the graph and the ground truth ; and ii) ratio of class separationin the output activations of Graph Convolutional Networks: this shows that the optimal graph maximally separates classes. Finally, we find that sparsifying the optimal graph can potentially improve classification performance .
After revision:  First, we show that constructing optimal geometric graphs directly from data features can aid classification tasks on both synthetic and real-world data sets from various scientific domains .