Discriminate predicate-variable

An instantiation of the Discriminate/, predicate-variable tests the values of HX, TX, Y in order to see whether ProcComp/ is applicable. Step 7 yields LA-/ r) by invoking the Proofs-as-Programs Method (see Chapter 9) and generalizing its results via some heuristics. 

Instances of Solve may be defined by fairly complex formulas, including divisions into sub-cases and the corresponding discriminating mechanisms, just as in non-minimal cases. But since this is relatively exceptional, we prefer to keep the schema simple, and always treat such a formula as the instance of a single predicate-variable. 

Second, it is the very focus on structural aspects of the induction parameter (its size, that is) that makes this database approach possible. If semantic aspects of the induction parameter (its value, that is) also have to be taken into account, then a deductive approach reasoning backwards from instances of all other predicate-variables becomes necessary [Smith 85]. We here clearly separate these aspects the size of the induction parameter is analyzed at Step 2 for instantiating Minimal and NonMinimal, and its value is analyzed at Step 7 for instantiating the Discriminate... 

The objective at Step 7 is to instantiate the predicate-variables Discriminate of the divide-and-conquer schema. This amounts to transforming LA r) into LA-j r) such that it is covered by the following schema ... 

Predicate normtest tests/evaluates normality of the given set of data points (corresponding to any variable), while, diaafun performs a linear discriminant analysis on groups of data (maximum of 10 groups) with respect to any selected variables (maximum of 20 variables). ... 

The other commonly alluded to theoretical concern with using PCA for specimen identification is the fact that PCA is predicated on a characterization of the covariance stracture among variables across the entire sample taken as a whole. This differs from the typical discriminant analysis situation where the purpose is to determine the character of structural relations between different... 

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