How to calculate the threshold value for numeric attributes in Quinlan's C4.5 algorithm?

Question

I am trying to find how the C4.5 algorithm determines the threshold value for numeric attributes. I have researched and can not understand, in most places I\'ve found this i

Answer 1

As your generated tree image implies, you consider attributes in order. Your 75 example belongs to outlook = sunny branch. If you filter your data according to outlook = sunny, you get following table.

outlook temperature humidity    windy   play
sunny   69           70         FALSE   yes
sunny   75           70         TRUE    yes
sunny   85           85         FALSE   no
sunny   80           90         TRUE    no
sunny   72           95         FALSE   no

As you can see, threshold for humidity is "< 75" for this condition.

j4.8 is successor to ID3 algorithm. It uses information gain and entropy to decide best split. According to wikipedia

The attribute with the smallest entropy 
is used to split the set on this iteration. 
The higher the entropy, 
the higher the potential to improve the classification here.

Answer 2

I'm not entirely sure about J48, but assuming its based on C4.5 it would compute the gain for all possible splits (i.e., based on the possible values for the feature). For each split, it computes the information gain and chooses the split with the most information gain. In the case of {70,85,90,95} it would compute the information gain for {70|85,90,95} vs {70,85|90,95} vs {70,85,90|95} and choose the best one.

Quinlan's book on C4.5 book is a good starting point (https://goo.gl/J2SsPf). See page 25 in particular.