On the Relevance of Discrepancy Norm for Similarity-Based Clustering of Delta-Event Sequences

摘要

In contrast to sampling a signal at equidistant points in time the on-delta-send sampling principle relies on discretizing the signal due to equidistant points in the range. On-delta-send sampling is encountered in asynchronous event-based data acquisition of wireless sensor networks in order to reduce the amount of data transfer, in event-based imaging in order to realize high-dynamic range image acquisition or, via the integrate-and-fire principle, in biology in terms of neuronal spike trains. It turns out that the set of event sequences that result from a bounded set of signals by applying on-delta-send sampling can be characterized by means of the ball with respect to the so-called discrepancy norm as metric. This metric relies on a maximal principle that evaluates intervals of maximal partial sums. It is discussed how this property can be used to construct novel matching algorithms for such sequences. Simulations based on test signals show its pontential above all regarding robustness.