Variations in neuronal morphology among cell classes, brain regions, and animal species are thought to underlie known heterogeneities in neuronal function. Thus, accurate quantitative descriptions and classification of large sets of neurons is important for functional characterization. However, unbiased computational methods to classify groups of neurons are currently scarce. We introduce an unbiased method to study neuronal morphologies. We develop mathematical descriptors that assign to each Neuron an invariant depending on distance from the soma, and taking values in real numbers or other suitable metric spaces (including a metric space of persistence diagrams). Such descriptors can include tortuosity, branching pattern, “energy”, wiring, TMD, etc. Using detection and metric learning algorithms, we can then provide efficient clustering and classification schemes for neurons. This is joint work with Reem Khalil, Ahmad Farhat and Pawel Dlotko