ANALYSIS AND RESULTS
Both the definition of the clusters extracted from each set of data and the clustering process itself were achieved using TRH-32 software, which implements the neural gas algorithm. The TRN model introduced under the name of Topology Representing Network by Martinetz and Schulten, in 1994, employs the competitive learning principle in which the prototypes rival one another in attempting to approximate the frequency distribution of empirical data; however, unlike other networks, “the training rule adjusts not only the winning prototype but all prototypes according to the rank of distances between data point and the first winner, second winner, etc” (Mazanec, p.49).
This method of analysis, adapted by Mazanec, consisted of three distinct phase. In the first phase, the optimum number of clusters to be formed from the two sets of data was decided; in the second, the networks were trained to form homogenous segments, allocate the weight of the variables to the prototypes and identify the clusters of each one of the respondents; in the last phase clusters were typified according to the identified between the preponderant values and opinion in each of the clusters.
The decision regarding the number of clusters was based both on statistical criteria and on interest, since the techniques for deciding the “correct” number of clusters generally have their limitations. The statistical criterion used was the percentage of uncertainty reduction (%UR), based on the repeated quantization of the data (30 rounds), recommended as a good reference for decision. As a result of this process four clusters were suggested for the values and three for the positioning, as shown in Table 1.
Nevertheless, if positioning data were restricted to only three clusters, 98 percent of the respondents would be concentrated into just two of them, which would greatly reduce the explanatory power. Thus, the option to include five clusters seemed reasonable, both in terms of the more uniform distribution of the respondents (table omitted) and for the gain in density (mean/standard deviation) obtained (0.38). Of the 36 values in the Rokeach Scale, only 14 (four terminal and 10 instrumental) had discriminant loads and for this reason were treated as distinct values. The remainder loaded (or not) indistinctly in all the clusters. The characterization of the respondents from the different groups, according to the predominant values, can be found in Table 2(L).
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