Fig. 1

Illustrative application of response prediction in latent structure networks on unknown manifolds. Our methodology is applied to the connectome of the right hemisphere of the Drosophila larval mushroom body. Left panel: scatter plot of two dimensions of the estimated latent positions for the 100 Kenyon cell neurons, obtained from spectral embedding of the network; the dot size represents the response variable \(y_i\) (the distance in microns between bundle entry point of neuron i and the mushroom body neuropil). Right panel: plot of responses \(y_i\) against learnt 1-d embeddings \({\hat{z}}_i\) approximating geodesic distances along this curve, for the 100 Kenyon cell neurons, together with the regression line. In the left panel we observe that a one-dimensional curve captures nonlinear structure in the spectral embedding. In the right panel we observe that response regressed against geodesic distance indicates a significant effect (\(p < 0.01\) for \(H_0: a=0\) in \(y_i=a{\hat{z}}_i+b+\eta _i\))