Data Mining - Information Gain

Information theory was find by Claude Shannon. It has quantified entropy. This is key measure of information which is usually expressed by the average number of bits needed to store or communicate one symbol in a message.

Information theory measure information in bits

<math> entropy(p_1,p_2,\dots,p_n)=-{p_1}log(p_1)-{p_2}log(p_2)-\dots-{p_n}log(p_n) </math>

Information gain is the amount of information gained by knowing the value of the attribute

<math> \text{Information gain} = \text{(Entropy of distribution before the split)} – \text{(entropy of distribution after it)} </math>

Information gain is the amount of information that's gained by knowing the value of the attribute, which is the entropy of the distribution before the split minus the entropy of the distribution after it. The largest information gain is equivalent to the smallest entropy.

With the Weather data set

14 records, 9 are “yes”

The outlook attribute contains 3 distinct values:

• overcast: 4 records, 4 are “yes”

• rainy: 5 records, 3 are “yes”

• sunny: 5 records, 2 are “yes”

Expected new entropy:

Expected new entropy:

Expected new entropy:

Consider every possible binary partition; choose the partition with the highest gain

Expected new entropy:

The highest information gain is with the outlook attribute.

• Bill Howe University of Washington, Coursera, Introduction to data science