Graph metric learning quantifies morphological differences between two genotypes of shoot apical meristem cells in .

We present a method for learning 'spectrally descriptive' edge weights for graphs. We generalize a previously known distance measure on graphs (graph diffusion distance [GDD]), thereby allowing it to be tuned to minimize an arbitrary loss function. Because all steps involved in calculating this modified GDD are differentiable, we demonstrate that it is possible for a small neural network model to learn edge weights which minimize loss. We apply this method to discriminate between graphs constructed from shoot apical meristem images of two genotypes of specimens: wild-type and triple mutants with cell division phenotype. Training edge weights and kernel parameters with contrastive loss produce a learned distance metric with large margins between these graph categories. We demonstrate this by showing improved performance of a simple -nearest-neighbour classifier on the learned distance matrix. We also demonstrate a further application of this method to biological image analysis. Once trained, we use our model to compute the distance between the biological graphs and a set of graphs output by a cell division simulator. Comparing simulated cell division graphs to biological ones allows us to identify simulation parameter regimes which characterize mutant versus wild-type cells. We find that mutant cells are characterized by increased randomness of division planes and decreased ability to avoid previous vertices between cell walls.