Training and linguistic conclusions

Our goal was to locate and identify groups of individuals having similar opinions to the statements. For each statement category, G, T, S, I, A and N, a separate Self-Organizing Map was trained with the 20 fuzzified variables created from each category (except 16 for N). Several distinct neuron groups could easily be located from these SOMs. There were two obvious groups in most maps: those neurons representing individuals having either positive or negative opinions to all of the five (or four) statements. Additional groups were added as needed (an example can be seen in figure 6: 'Negative attitude to school work, otherwise positive'). There were a total of 16 groups located from the 6 categories.

  
Figure 6: Two snapshots from the SOM for category G, showing three located groups. The average answers are represented by bars inside the neurons.

The final Self-Organizing Map was trained with the grouping information received from the other SOMs using several preprocessing methods. As a result, linguistic conclusions similar to the ones shown in figure 7 were obtained. For example, the neuron at the upper right corner of figure 7 represents a group of 21 students who have a positive attitude to categories G, T, I and A.

  
Figure 7: Linguistic conclusions.

Table 1. presents the classification results obtained from the 4th layer of a TS-SOM [4, 5] (256 neurons) using several group membership functions compared to binary memberships with and without a loss group. Negative exponential functions seem to provide good results with this type of data.

Linear 0.7 70/45

Neg. power 2 0.6 80/41

Neg. power 4 0.5 84/52

Neg. power 6 0.5 84/46

Logsig 0.9 66/1

Binary 0.5 81/33

Binary with loss 0.5 81/44 '95 data set

Linear 0.7 72/56

Neg. power 2 0.6 80/47

Neg. power 4 0.5 83/40

Neg. power 6 0.5 83/34

Logsig 0.9 71/2

Binary 0.5 81/36

Binary with loss 0.5 78/44

Table 1. Classification estimates of the example data sets.