Comparison of fault detection techniques: problem and solution

Haar Wave-Net (HWN) and Projection Pursuit Regression (PPR) are two useful modeling tools for pattern classification. In this case study, the two methodologies are compared with respect to the problem of misclassification close to class boundaries with sparse training data. A variety of examples were specifically tailored to elucidate their respective properties. It is observed that PPR locates the class boundaries at the midline of two classes of training data, which is a logical choice for the class boundary location, in the absence of sufficient information. For HWN, both the initial positioning of receptive fields and the density of training data near the class boundary may both have great impact on the definition of the class boundary. To solve the problem of insufficient training data, the data void can be filled with artificial data according to their nearest neighborhood. PPR propagates the effect of noisy data to a distance determined by the midpoint between the noisy data and the good data, in the projected input space. On the other hand, the orthonormal and localized properties of the Haar basis functions enable a HWN to limit the noise effect within its local receptive fields. This is a major advantage, which the HWN has over the PPR.