Wavelet Transform in Similarity Paradigm

For the majority of data mining applications, there are no models of data which would facilitate the tasks of comparing records of time series, thus leaving one with `noise'' as the only description. We propose a generic approach to comparing noise time series using the largest deviations from consistent statistical behaviour. For this purpose we use a powerful framework based on wavelet decomposition, which allows filtering polynomial bias, while capturing the essential singular behaviour. In particular we are able to reveal scale-wise ranking of singular events including their scale-free characteristic: the H\older exponent. We use such characteristics to design a compact representation of the time series suitable for direct comparison, e.g. evaluation of the correlation product. We demonstrate that the distance between such representations closely corresponds to the subjective feeling of similarity between the time series. In order to test the validity of subjective criteria, we test the records of currency exchanges, finding convincing levels of (local) correlation.