Depth-based statistical analysis in the spike train space

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 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 'template' of the observations. It also provides a principled method to identify 'outliers' and classify data from different categories. We systematically compare the new median, outlier detection and classification tools with state-of-the-art competing 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.