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.