The resulting classification set class

Using the SRT obtained in the example above, we can demonstrate how we would attempt to classify a new instance of the Iris data into one of the classes—Setosa, Versicolor, or Virginica. If the new instance is (4.4 2.9 1.4 0.2), then its template (Tnew) after discretization is (1 1 1 1 ?). The corresponding probabilities for each attribute, stored in the GPV, are (.1.2.3.3). The first step fails to find an exact match. The next step replaces the most typical attribute value by a wild card ("?") which yields the template (1 1 ? ?). However there are still no matching templates. The next step is to turn the next most typical attribute (in this case the third attribute) into a wild card, but again there are no matching templates. As the general probabilities of PL = 1 and PW = 1 are the same (0.3), the first template was chosen arbitrarily over the second. But as we shall see later, this choice may turn to be important and ambiguity in such cases can be met by applying a classification with certainty degrees. Only on the third partial-matching cycle, when the second attribute is turned into a "?," a matching RT is found. The matching RT is (1 2 1 1 1 1), which belongs to classl. The classification for this example would be (classl/1, class2/0, class3/0).

In the case of Tnew = (3 2 4 3), the template (3 2 4 ?) matches class2's RT with a PC = 1 and the template (3 2 ? 3) matches class3's RT with a PC = 3. The resulting classification set is (class 1/0, class2/0.25, class3/0.75).

1. Derive the Ncl class centers, a class center being an RT with the highest probability coefficient, PC, that is, representing most of the examples. In this case three centers, C1 = (2 2 1 1), C2 = (3 1 4 2), and C3 = (3 2 5 3), are chosen from the RTs in SRT1. Their corresponding probability vectors are (.2 .8 .3 .3), (.6 .2 .3 .3) and (.6 .8 .4.4).

2. Match C1, C2, and C3 against SRT1. All RTs are matched using the wild-carding of attributes, based on typicality, and associated with one of the classes. Figure 2.39 illustrates an implementation of the unsupervised learning algorithm to the data set above when the number of classes is given (Ncl = 3).

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