Wavelet Transform in Similarity Paradigm II. Information Systems

摘要

For the majority of data mining applications, there are no models of data which211u001ewould facilitate the tasks of comparing records of time series, thus leaving one 211u001ewith 'noise' as the only description. We propose a generic approach to comparing 211u001enoise time series using the largest deviations from consistent statistical 211u001ebehavior. For this purpose we use a powerful framework based on wavelet 211u001edecomposition, which allows filtering polynomial bias, while capturing the 211u001eessential singular behavior. In particular we are able to reveal scale-wise 211u001eranking of singular events including their scale-free characteristic: the Holder 211u001eexponent. We use such characteristics to design a compact representation of the 211u001etime series suitable for direct comparison, e.g. evaluation of the correlation 211u001eproduct. We demonstrate that the distance between such representations e.g. 211u001eevaluation of the correlation product. We demonstrate that the distance between 211u001esuch representations closely corresponds to the subjective feeling of similarity 211u001ebetween the time series. In order to test the validity of subjective criteria, we 211u001etest the records of currency exchanges, finding convincing levels of (local) 211u001ecorrelation.