HCM experiments

In this subsection, the performance of our GGA using the HCM objective function on just the Iris domain will be discussed.

Table 4 shows the J₁ values of the local extrema (and some degenerate partitions) found for many random initializations of HCM applied to the Iris data. Clustering the Iris data can result in 2 degenerate crisp partitions of 1 cluster (J₁ = 680.824) and 2 clusters (J₁ = 152.309) which occur in more than 18% of the 9000 trials. The best two partitions of the Iris data differ by 1 feature vector and have 17 misclassifications (as resubstitution errors of the crisp nearest prototype classifier) and 16 misclassifications, respectively at J₁=78.945 and J₁ = 78.941.

   

Partition J₁ Value Count

1 78.941 2857

2 78.945 3929

3 142.852 18

4 142.859 151

5 142.879 34

6 143.218 1

7 143.454 307

8 145.279 70

9 152.369 1049

10 680.824 584

The GGA was applied 50 times with different random initial populations to the Iris data set with results shown in Table 4. Again, for clarity we report J₁ values even though the equivalent R₁ functional was optimized. Table 5 provides a summary of the results by population size, mutation rate, average J₁ value found, standard deviation and lowest J₁ value found.

The GGA applied to the Iris data finds the two partitions with lowest J₁ values in each of the 50 runs. It finds the best partition 28, 25, 26, 31 and 32 times respectively for the Table 5 entries from top to bottom.

   

Data set Pop. size Gens. Mut. Rate 2c|Average Values Lowest J₁

J₁ st. dv. value found

Iris 30 750 0.0015 78.943 0.002 78.941

Iris 30 750 0.003 78.943 0.002 78.941

Iris 50 550 0.0015 78.943 0.002 78.941

Iris 50 550 0.0015 78.942 0.002 78.941

Iris 75 400 0.0064 78.942 0.002 78.941