Data reduction for multiple functional data with class information

The term ‘functional data’ (or ‘curve’) refers to an analog or digital signal measured during each operational cycle of a manufacturing process. Functional data contain rich information concerning the process condition and product quality for quality improvement. We propose a vertical group-wise threshold (VGWT) procedure for the reduction of multiple high-dimensional functional data containing class information. The proposed method selects important wavelet coefficients for the whole set of multiple curves by a comparison between every vertical energy metric and a threshold (VGWT). The VGWT increases the class separability with a reasonably small loss in data-reduction efficiency. A real-life example is presented to illustrate the proposed method, and a Monte Carlo simulation is performed to study the impact of different levels of class variation and noise.

[1]  Jionghua Jin,et al.  Automatic feature extraction of waveform signals for in-process diagnostic performance improvement , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[2]  Adedeji Badiru,et al.  On-line prediction of motor shaft misalignment using fast fourier transform generated spectra data and support vector regression , 2006 .

[3]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[4]  Di Chen,et al.  Wavelet-Based Data Reduction Techniques for Process Fault Detection , 2006, Technometrics.

[5]  Jionghua Jin,et al.  Feature-preserving data compression of stamping tonnage information using wavelets , 1999 .

[6]  Arun K. Sikder,et al.  Wavelet-based identification of delamination defect in CMP (Cu-low k) using nonstationary acoustic emission signal , 2003 .

[7]  Uk Jung.  Wavelet-based Data Reduction and Mining for Multiple Functional Data , 2004 .

[8]  Bhavik R. Bakshi,et al.  Multiscale analysis and modeling using wavelets , 1999 .

[9]  Gary W. Rubloff,et al.  Dynamic rate and thickness metrology during poly‐Si rapid thermal chemical vapor deposition from SiH4 using real time insitu mass spectrometry , 1996 .

[10]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Anestis Antoniadis,et al.  Model selection using wavelet decomposition and applications , 1997 .

[12]  Nouna Kettaneh,et al.  Statistical Modeling by Wavelets , 1999, Technometrics.

[13]  Jye-Chyi Lu,et al.  Equipment fault detection using spatial signatures , 1997 .

[14]  Jye-Chyi Lu,et al.  A Vertical-Energy-Thresholding Procedure for Data Reduction With Multiple Complex Curves , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Jye-Chyi Lu,et al.  In situ selectivity and thickness monitoring during selective silicon epitaxy using quadrupole mass spectrometry and wavelets , 2005, IEEE Transactions on Semiconductor Manufacturing.

[16]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[17]  Andrei V. Gribok,et al.  Information complexity-based regularization parameter selection for solution of ill conditioned inverse problems , 2002 .

[18]  Jye-Chyi Lu,et al.  Thresholded scalogram and its applications in process fault detection , 2003 .

[19]  Y. Ueno,et al.  Prediction of spalling on a ball bearing by applying the discrete wavelet transform to vibration signals , 1996 .

[20]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[21]  Emily K. Lada,et al.  A wavelet-based procedure for process fault detection , 2002 .