Tight Bounds on the Estimation Distance Using Wavelet

Time series similarity search is of growing importance in many applications. Wavelet transforms are used as a dimensionality reduction technique to permit efficient similarity search over high-dimensional time series data. This paper proposes the tight upper and lower bounds on the estimation distance using wavelet transform, and we show that the traditional distance estimation is only part of our lower bound. According to the lower bound, we can exclude more dissimilar time series than traditional method. And according to the upper bound, we can directly judge whether two time series are similar, and further reduce the number of time series to process in original time domain. The experiments have shown that using the upper and lower tight bounds can significantly improve filter efficiency and reduce running time than traditional method.