making process for the data shown in Figure 3.37(b) can be

ated in Figure 3.38(b). These trees certainly help visualise how

decisions based on the optimised partitioning rules. For instance,

sion-making process shown in Figure 3.38(b) can be written as

hich is very similar to the human intelligence,

y is less than two and x is negative, the object is a triangle.

kind of human-intelligence-alike models may not be easily

using the aforementioned machine learning algorithms such as

MLP for the time being.

he purity measurements

on-making model is a system composed of a set of partitioning

derive an optimal set of partitioning rules as the best decision-

model for a data set is an inductive learning process. For instance,

s certainly not a good partitioning rule compared with the

ng rule y = 2 in Figure 3.37(a). This is because the upper subspace

d by this partitioning rule is highly mixed by two classes of data

hough the lower subspace is very pure to one class of data points.

her hand, each subspace generated by the partitioning rule y = 2

ure to one class of data points.

utomate the discovery of an optimal partitioning rule set, a

ve measurement for measuring the purity or impurity of the

s generated by every partitioning rule is required. Two

ments have been proposed and are still in use. One is called the

x used by CART [Breiman, et al., 1984] and the other is called

mation gain used by both DT and CART [Breiman, et al., 1984;

1986].

Gini index is calculated for each portioning rule. It is the class-

of the products between the probability of correct classification

robability of mis-classification. The product ݌௞ሺ߬ሻሾ1 െ݌௞ሺ߬ሻሿ is