Fisher Discriminant Analysis

Abstract

In the pattern classification approach to fault diagnosis outlined in Chapter 3, it was described how the dimensionality reduction of the feature extraction step can be a key factor in reducing the misclassification rate when a pattern classification system is applied to new data (data independent of the training set). The dimensionality reduction is especially important when the dimensionality of the observation space is large while the numbers of observations in the classes are relatively small. A PCA approach to dimensionality reduction was discussed in the previous chapter. Although PCA contains certain optimality properties in terms of fault detection, it is not as well-suited for fault diagnosis because it does not take into account the information between the classes when determining the lower dimensional representation. Fisher Discriminant Analysis (FDA), a dimensionality reduction technique that has been extensively studied in the pattern classification literature, takes into account the information between the classes and has advantages over PCA for fault diagnosis.