How to select an appropriate similarity measure: Towards a symmetry-based approach

Abstract

When practitioners analyze the similarity between time series, they often use correlation to gauge this similarity. Sometimes this works, but sometimes, this leads to counter-intuitive results, in which case other similarity measures are more appropriate. An important question is how to select an appropriate similarity measures. In this paper, we show, on simple examples, that the use of natural symmetries – scaling and shift – can help with such a selection.