Signal Processing in the Retina: Interpretable Graph Classifier to
  Predict Ganglion Cell Responses
Yasaman Parhizkar Gene Cheung Andrew W. Eckford
It is a popular hypothesis in neuroscience that ganglion cells in the retina
are activated by selectively detecting visual features in an observed scene.
While ganglion cell firings can be predicted via data-trained deep neural nets,
the networks remain indecipherable, thus providing little understanding of the
cells' underlying operations. To extract knowledge from the cell firings, in
this paper we learn an interpretable graph-based classifier from data to
predict the firings of ganglion cells in response to visual stimuli.
Specifically, we learn a positive semi-definite (PSD) metric matrix $\mathbf{M}
\succeq 0$ that defines Mahalanobis distances between graph nodes (visual
events) endowed with pre-computed feature vectors; the computed inter-node
distances lead to edge weights and a combinatorial graph that is amenable to
binary classification. Mathematically, we define the objective of metric matrix
$\mathbf{M}$ optimization using a graph adaptation of large margin nearest
neighbor (LMNN), which is rewritten as a semi-definite programming (SDP)
problem. We solve it efficiently via a fast approximation called Gershgorin
disc perfect alignment (GDPA) linearization. The learned metric matrix
$\mathbf{M}$ provides interpretability: important features are identified along
$\mathbf{M}$'s diagonal, and their mutual relationships are inferred from
off-diagonal terms. Our fast metric learning framework can be applied to other
biological systems with pre-chosen features that require interpretation.