6.5.1.3CART algorithm for the analysis of mental functions

As listed in Table 2.16, the WAIS-R dataset has data of 200 people belonging to patient group and 200 sample to healthy control group. The attributes of the control group are data regarding school education, gender, …, DM. Data consist of a total of 21 attributes. It is known that using these attributes of 400 individuals, we can know whether the data patient or healthy group. How can we make the classification as to which individual belongs to which patient or healthy group and those diagnosed with WAIS-R test (based on the school education, gender, …, DM)? D matrix has a dimension of 400 × 21. This means D matrix includes the WAIS-R dataset of 400 individuals along with their 21 attributes (see Table 2.16) for the WAIS-R dataset. For the classification of D matrix CART algorithm, the first step training procedure is to be employed. For the training procedure, 66.66% of the D matrix can be split for the training dataset (267 × 21) and 33.33% as the test dataset (133 × 21). Following the classification of the training dataset being trained with CART algorithm, we can classify the test dataset.

Although the procedural steps of the algorithm may seem complicated at first glance, the only thing you have to do is to concentrate on the steps and grasp them. For this, let us have a close look at the steps provided in Figure 6.31.

How can we classify the WAIS-R dataset in Table 2.16.1 in accordance with the steps of CART algorithm (Figure 6.31)?

Steps (1–3) Let us identify the 66.66% of WAIS-R dataset as the training data (D=267 × 21) and 33.33% as the test data (T= 133 × 21).

2

Steps (4–10) As a result of training the training set (D = 267 × 21) with random forest algorithm, the following results have been obtained: number of nodes –30. Sample decision tree structure is shown in Figure 6.32.

Steps (11–12) Gini index for the attribute is chosen as the splitting subset.

The training of the WAIS-R dataset is done by applying CART algorithm (Steps 1–12 as specified in Figure 6.31). Through this, the decision tree consisting of 20 nodes (the learned tree (N = 20)) has been obtained. The nodes chosen via the CART learned tree nodes ((logical deduction, vocabulary) and some of the rules for the nodes are given in Figure 6.31.

Based on Figure 6.32, some of the rules obtained from the CART algorithm obtained from WAIS-R dataset can be seen as follows.

Figure 6.32(a) and (b) shows WAIS-R dataset sample decision tree structure based on CART, obtained as such; if–then rules are as follows:

…

…

…

Rule 1

IF (logical deduction of test score result < 0.5)

THEN class = healthy

Rule 2

IF ((logical deduction of test score result ≥ 0.5) and

(vocabulary of test score result < 5.5))

THEN class = patient

Rule 3

IF ((logical deduction of test score result ≥ 0.5) and

(vocabulary of test score result ≥ 5.5))

THEN class = healthy

…

…

…

As a result, the data in the WAIS-R dataset with 33.33% portion allocated for the test procedure and classified as patient and healthy individuals have been classified with an accuracy rate of 99.24% based on CART algorithm.

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