The first part of this dissertation describes the framework for high performance time series data mining based on important primitives. Data reduction transform such as the Discrete Fourier Transform, the Discrete Wavelet Transform, Singular Value Decomposition and Random Projection, can reduce the size of the data without substantial loss of information, therefore provides a synopsis of the data. Indexing methods organize data so that the time series data can be retrieved e+ciently. Transformation on time series, such as shifting, scaling, time shifting, time scaling and dynamic time warping, facilitates the discovery of flexible patterns from time series. The second part of this dissertation integrates the above primitives into useful applications ranging from music to physics to finance to medicine.

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