Matching event sequences approach based on Weyl's discrepancy norm

Abstract

A novel approach for matching event sequences, that result from threshold-based sampling, is introduced. This approach relies on Hermann Weyl's discrepancy norm, which plays a central role in the context of stability analysis of threshold-based sampling. This metric is based on a maximal principle that evaluates intervals of maximal partial sums. It is shown that minimal length intervals of maximal discrepancy can be exploited, in order to efficiently cluster spikes by means of approximating step functions. In contrast to ordinary spikes, these spike clusters can not only be shifted, deleted or inserted, but also stretched and shrinked, which allows more flexibility in the matching process. A dynamic programming approach is applied in order to minimizing an energy functional of such deformation manipulations. Simulations based on integrate-and-fire sampling show its potential above all regarding robustness.