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Fig. 18.12
Group centroids for three systolic blood pressure groups in discriminant analysis
with two discriminant functions
operate with fuzzy rule bases and inference engines. Instead of functions, in the
fuzzy case we now construct one fuzzy model for each cluster.
The switching regression approach has an interesting analogy to analysis of co-
variance (ANCOVA) when we examine the data groups of a test variable with its
covariates. Since we now consider whether these groups have similar means when
the effects of the covariates are excluded, we do not use the original group means
directly, but rather their “corrected” values. In statistics we thus specify (usually
linear) fitting functions for these groups and then we evaluate the distances, the
corrected groups distinctions, between these fittings (Fig. 18.16).
We notice that ANCOVA modeling is in a sense a special case of switching re-
gression modeling. In both cases we first specify the sufficiently good fittings to our
data clusters, but in the former case we usually evaluate the distances between these
fittings, whereas the latter aims at finding for good fittings. Hence, we could also
apply fuzzy modeling and switching regression technique to ANCOVA, even when
nonlinear correlations prevail between the covariates and the test variable. Given
the fittings based on fuzzy models, we may evaluate the distances between these
fittings, and these distances would be the correct distinctions between the groups.
As above, we may aim at minimizing the errors within the clusters and maximizing
the distances between the cluster fittings. However, we still expect more extensive
studies on this topic (Fig. 18.17).
