Efficient time series matching by wavelets

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 (K-L) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied bl 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 lime series indexing. The major contributions are: (I) we show that Euclidean distance is preserved ill the Haar transformed domain and no false dismissal will occur (2) we show that Haar transform can ourperform 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 rime series databases.