Popular Decision Trees Induction Algorithms - Data Mining with Decision Trees: Theory and Applications - page 79

compares C4.5 with J48 and C5.0 [ Moore et al . (2009) ] indicates that C4.5
performs consistently better (in terms of accuracy) than C5.0 and J48 in
particular on small datasets.

7.4 CART

CART stands for Classification and Regression Trees. It was developed by
Breiman et al . (1984) and is characterized by the fact that it constructs
binary trees, namely each internal node has exactly two outgoing edges.
The splits are selected using the Twoing Criteria and the obtained tree is
pruned by Cost-Complexity Pruning. When provided, CART can consider
misclassification costs in the tree induction. It also enables users to provide
prior probability distribution.
An important feature of CART is its ability to generate regression trees.
In regression trees, the leaves predict a real number and not a class. In case
of regression, CART looks for splits that minimize the prediction squared
error (the least-squared deviation). The prediction in each leaf is based on
the weighted mean for node.

7.5 CHAID
Starting from the early Seventies, researchers in applied statistics developed
procedures for generating decision trees [Kass (1980)].Ch -squared-
Automatic-Interaction-Detection (CHIAD) was originally designed to han-
dle nominal attributes only. For each input attribute a i , CHAID finds

the pair of values in V i that is least significantly different with respect to

the target attribute. The significant difference is measured by the

value
obtained from a statistical test. The statistical test used depends on the type
of target attribute. An

p

test is used if the target attribute is continuous;
a Pearson chi-squared test if it is nominal; and a likelihood ratio test if it
is ordinal.
For each selected pair of values, CHAID checks if the

F

value obtained
is greater than a certain merge threshold. If the answer is positive, it merges
the values and searches for an additional potential pair to be merged. The
process is repeated until no significant pairs are found.
The best input attribute to be used for splitting the current node is
then selected, such that each child node is made of a group of homogeneous
values of the selected attribute. Note that no split is performed if the
adjusted

p

p value of the best input attribute is not less than a certain split