UNEQ, SIMCA and related methods

As explained in Section 33.2.1, one can prefer to consider each class separately and to perform outlier tests to decide whether a new object belongs to a certain class or not. The earliest approaches, introduced in chemometrics, were called SIMCA (soft independent modelling of class analogy) [27] and UNEQ [28]. 

UNEQ can be applied when only a few variables must be considered. It is based on the Mahalanobis distance from the centroid of the class. When this distance exceeds a critical distance, the object is an outlier and therefore not part of the class. Since for each class one uses its own covariance matrix, it is somewhat related to QDA (Section 33.2.3). The situation described here is very similar to that discussed for multivariate quality control in Chapter 20. In eq. (20.10) the original variables are used. This equation can therefore also be used for UNEQ. For convenience it is repeated here. 

If care is not taken about the way j is obtained, SIMCA has a tendency to exclude more objects from the training class than necessary. The 5-value should be determined by cross-validation. Each object in the training set is then predicted, using the A- -dimensional PCA model obtained, for the other (n - 1) training set objects. The (residual) scores obtained in this way for each object are used in eq. (33.14) [30]. 

A confidence limit is obtained by defining a critical value of the (Euclidean) distance towards the model. This is given by 

The Euclidean distance from the model is then obtained, similarly to eq. (33.14) 

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