Wavelet-based data reduction and mining for multiple functional data

Advance technology such as various types of automatic data acquisitions, management, and networking systems has created a tremendous capability for managers to access valuable production information to improve their operation quality and efficiency. Signal processing and data mining techniques are more popular than ever in many fields including intelligent manufacturing. As data sets increase in size, their exploration, manipulation, and analysis become more complicated and resource consuming. Timely synthesized information such as functional data is needed for product design, process trouble-shooting, quality/efficiency improvement and resource allocation decisions. A major obstacle in those intelligent manufacturing system is that tools for processing a large volume of information coming from numerous stages on manufacturing operations are not available. Thus, the underlying theme of this thesis is to reduce the size of data in a mathematical rigorous framework; and apply existing or new procedures to the reduced-size data for various decision-making purposes. This thesis, first, proposes Wavelet-based Random-effect Model which can generate multiple functional data signals which have wide fluctuations (between-signal variations) in the time domain. The random-effect wavelet atom position in the model has locally focused impact which can be distinguished from other traditional random-effect models in biological field. For the data-size reduction, in order to deal with heterogeneously selected wavelet coefficients for different single curves, this thesis introduces the newly-defined Wavelet Vertical Energy metric of multiple curves and utilizes it for the efficient data reduction method. The newly proposed method in this thesis will select important positions for the whole set of multiple curves by comparison between every vertical energy metrics and a threshold (Vertical Energy Threshold; VET) which will be optimally decided based on an objective function. The objective function balances the reconstruction error against a data reduction ratio. Based on class membership information of each signal obtained, this thesis proposes the Vertical Group-Wise Threshold method to increase the discriminative capability of the reduced-size data so that the reduced data set retains salient differences between classes as much as possible. A real-life example (Tonnage data) shows our proposed method is promising.