Wavelet-Based Methodology in Data Mining for Complicated Functional Data

Abstract

To handle potentially large size and complicated nonstationary functional data, we present the wavelet-based methodology in data mining for process monitoring and fault classification. Since traditional wavelet shrinkage methods for data de-noising are ineffective for the more demanding data reduction goals, this thesis presents data reduction methods based on discrete wavelet transform. Our new methods minimize objective functions to balance the tradeoff between data reduction and modeling accuracy. Several evaluation studies with four popular testing curves used in the literature and with two real-life data sets demonstrate the superiority of the proposed methods to engineering data compression and statistical data de-noising methods that are currently used to achieve data reduction goals. Further experimentation in applying a classification tree-based data mining procedure to the reduced-size data to identify process fault classes also demonstrates the excellence of the proposed methods. In this application the proposed methods, compared with analysis of original large-size data, result in lower misclassification rates with much better computational efficiency. This thesis extends the scalogram's ability for handling noisy and possibly massive data which show time-shifted patterns. The proposed thresholded scalogram is built on the fast wavelet transform, which can effectively and efficiently capture non-stationary changes in data patterns. Finally, we present a SPC procedure that adaptively determines which wavelet coefficients will be monitored, based on their shift information, which is estimated from process data. By adaptively monitoring the process, we can improve the performance of the control charts for functional data. Using a simulation study, we compare the performance of some of the recommended approaches.