[en] In this paper, we introduce a functional wavelet based semi-distance for comparing curves with sharp patterns that might not be well aligned from one curve to another. This semi-distance is data-driven and highly adaptive to the curves being studied. Its main originality is its ability to consider simultaneously horizontal and vertical variations of patterns, which proofs highly useful when used together with clustering algorithms or visualization method. We also develop statistical tools for detecting and localizing differences between groups of curves using this semi-distance. Finally, we apply this methodology to H-NMR spectrometric curves and solar irradiance time series.
