We address the handling of time series search based on two important distance definitions: Euclidean distance and time warping distance. The conventional method reduces the dimensionality by means of a discrete Fourier transform. We apply the Haar wavelet transform technique and propose the use of a proper normalization so that the method can guarantee no false dismissal for Euclidean distance. We found that this method has competitive performance from our experiments. Euclidean distance measurement cannot handle the time shifts of patterns. It fails to match the same rise and fall patterns of sequences with different scales. A distance measure that handles this problem is the time warping distance. However, the complexity of computing the time warping distance function is high. Also, as time warping distance is not a metric, most indexing techniques would not guarantee any false dismissal. We propose efficient strategies to mitigate the problems of time warping. We suggest a Haar wavelet-based approximation function for time warping distance, called Low Resolution Time Warping, which results in less computation by trading off a small amount of accuracy. We apply our approximation function to similarity search in time series databases, and show by experiment that it is highly effective in suppressing the number of false alarms in similarity search.

Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases.