The Iris Data Set. The Iris data set is the only data set, on which we test our algorithms, with more than two target classes. The data set contains the sepal and petal length and width of three types of iris plants: Iris Setosa, Iris Versicolour and Iris Virginica. One of the plants is linearly separable from the others using a single attribute and threshold value. The remaining two classes are not linearly separable. All three classes are distributed equally (50 records each). Because of the small number of records and attributes (only 4) the simple gp constructs only 123 internal nodes and 3 terminal nodes for the 3 classes. This results in a search space of size ≈ 1.7 × 1096.
The Iris Data Set. When we consider the results of our new gp algorithms on the Iris data set in Table 3.10 we see that our clustering gp algorithm with k = 3 has a signif- icantly lower misclassification rate than our other gp algorithms. If we look at Table 3.4 we see that the gain ratio gp algorithms all split the domain of the numerical valued attributes into 2 partitions regardless of the maxi- mum allowed number of partitions. This is probably the reason for the bad misclassification rate of these algorithms as both other new top-down atomic representations also classify badly when the domain of the numerical valued attributes is split into 2 partitions or clusters. As a result these algorithms perform significantly worse than the other algorithms. Table 3.10: Average misclassification rates (in %) with standard deviation, using 10-fold cross-validation for the Iris data set. algorithm k average s.d. clustering gp clustering gp clustering gp clustering gp 2345 21.1 2.1 5.2 6.0 9.4 4.2 4.8 5.5 gain gp gain gp gain gp gain gp 2345 29.6 6.3 5.1 6.5 6.3 6.1 6.4 5.6 gain ratio gp gain ratio gp gain ratio gp gain ratio gp 2345 31.7 31.7 31.7 31.7 5.0 5.0 5.0 5.0 simple gp 5.6 6.1 Ltree OC1 C4.5 2.7 7.3 4.7 3.0 6.0 5.0 cefr-miner esia 4.7 4.7 0.0 7.1 default 33.3
The Iris Data Set. In Table 4.7 the results on the Iris data set are displayed. On this data set our clustering gp algorithms using k = 3 is still significantly better than all our other gp algorithms. In the case of the other fuzzy gp algorithms the fuzzy versions are significantly better than the non-fuzzy versions. We already noted above that it seems that fuzzification improves classification performance when the original clusters or partitions result in sub-optimal performance. However, on the Iris data set the performance increase for our non-fuzzy clustering and partitioning gp algorithms is huge. Fuzzification re- duces the misclassificaton rate for our clustering gp algorithm with k = 2 by more than two-thirds, the misclassification rate of our partitioning gp algorithm using the gain criterion and k = 2 by a factor of 5 and the mis- classification rates for our partitioning gp algorithms using the gain ratio criterion also with more than 80%. The differences between our fuzzy gp algorithms and the other algorithms are not statistically significant.
