  Metric-based summary statistics such as mean and covariance have been
introduced in neural spike train space. They can properly describe template and
variability in spike train data, but are often sensitive to outliers and
expensive to compute. Recent studies also examine outlier detection and
classification methods on point processes. These tools provide reasonable and
efficient result, whereas the accuracy remains at a low level in certain cases.
In this study, we propose to adopt a well-established notion of statistical
depth to the spike train space. This framework can naturally define the median
in a set of spike trains, which provides a robust description of the 'center'
or 'template' of the observations. It also provides a principled method to
identify 'outliers' in the data and classify data from different categories. We
systematically compare the median with the state-of-the-art 'mean spike trains'
in terms of robustness and efficiency. The performance of our novel outlier
detection and classification tools will be compared with previous methods. The
result shows the median has superior description for 'template' than the mean.
Moreover, the proposed outlier detection and classification perform more
accurately than previous methods. The advantages and superiority are well
illustrated with simulations and real data.
