Extrema features for global-localization and pattern matching of time-series data.

摘要

This dissertation describes the use of extrema features for the purposes of localization and pattern matching in time-series data. One of the principle contributions of this work is to develop a wavelet-based framework to extract extrema features from raw data. The utility of these features is then demonstrated through different applications in pitch and acceleration-based localization. Another major contribution is the formulation of the filter optimization problem to obtain robust extrema as an eigenvalue problem with a tractable solution. This optimization framework which was conceived and formulated in a 'deterministic' sense was finally extended to the stochastic domain. This extension resulted in interesting theoretical results that show that the filters of the Discrete Sine Transform are the optimal filters for extracting extrema from Gaussian random walk data. Finally, the nature of the optimal filters for the case of general random walk data was also explored.