  Traditional classification tasks learn to assign samples to given classes
based solely on sample features. This paradigm is evolving to include other
sources of information, such as known relations between samples. Here we show
that, even if additional relational information is not available in the data
set, one can improve classification by constructing geometric graphs from the
features themselves, and using them within a Graph Convolutional Network. The
improvement in classification accuracy is maximized by graphs that capture
sample similarity with relatively low edge density. We show that such
feature-derived graphs increase the alignment of the data to the ground truth
while improving class separation. We also demonstrate that the graphs can be
made more efficient using spectral sparsification, which reduces the number of
edges while still improving classification performance. We illustrate our
findings using synthetic and real-world data sets from various scientific
domains.
