Many neural circuits are composed of numerous distinct cell types that perform different operations on their inputs, and send their outputs to distinct targets. Therefore, a key step in understanding neural systems is to reliably distinguish cell types. An important example is the retina, for which present-day techniques for identifying cell types are accurate, but very labor-intensive. Here, we develop automated classifiers for functional identification of retinal ganglion cells, the output neurons of the retina, based solely on recorded voltage patterns on a large scale array. We use per-cell classifiers based on features extracted from electrophysiological images (spatiotemporal voltage waveforms) and interspike intervals (autocorrelations). These classifiers achieve high performance in distinguishing between the major ganglion cell classes of the primate retina, but fail in achieving the same accuracy in predicting cell polarities (ON vs. OFF). We then show how to use indicators of functional coupling within populations of ganglion cells (cross-correlation) to infer cell polarities with a matrix completion algorithm. This can result in accurate, fully automated methods for cell type classification.