Geometric graphs from data to aid classification tasks with graph convolutional networks

Classification is a classic problem in data analytics and has been approached from many different angles, including machine learning. Traditionally, machine learning methods classify samples based solely on their features. This paradigm is evolving. Recent developments on Graph Convolutional Networks have shown that explicitly using information not directly present in the features to represent a type of relationship between samples can improve the classification performance by a significant margin. However, graphs are not often immediately present in data sets, thus limiting the applicability of Graph Convolutional Networks. In this paper, we explore if graphs extracted from the features themselves can aid classification performance. 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 separation in 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.