Generalisation of the LP norm for time series and its application to Self-Organizing Maps

Lee, John Aldo [UCL] Verleysen, Michel [UCL]

Time series are often encoded in vectors and analyzed using standard vectorial tools (distances, inner products, etc.). Most of them neglect the temporal structure of time series. This paper proposes a generalization of the Lp norm that takes the temporal structure into account. This norm remains computationally simple and keeps useful properties, like e.g. differentiability, which allow integrating the new norm into Self-Organizing Maps to analyze sets of time series. Experiments on artificially generated data show the advantages and specificities of the proposed norm.