Data Mining - Information Gain
Table of Contents
1 - About
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.
2 - Articles Related
3 - Overfitting
4 - Steps to calculate the highest information gain on a data set
With the Weather data set
4.1 - Entropy of the whole data set
14 records, 9 are “yes”
4.2 - Expected new entropy for each attribute
4.2.1 - outlook
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:
4.2.2 - temperature
| Distinct value | Yes records | Entropy |
|---|---|---|
| cool | 4 records, 3 are “yes” | 0.81 |
| rainy | 4 records, 2 are “yes” | 1.0 |
| sunny | 6 records, 4 are “yes” | 0.92 |
Expected new entropy:
4.2.3 - humidity
4.2.3.1 - discrete values
| Distinct value | Yes records | Entropy |
|---|---|---|
| normal | 7 records, 6 are “yes” | 0.59 |
| high | 7 records, 2 are “yes” | 0.86 |
Expected new entropy:
4.2.3.2 - continues values
Consider every possible binary partition; choose the partition with the highest gain
4.2.4 - windy
| Distinct value | Yes records | Entropy |
|---|---|---|
| TRUE | 8 records, 6 are “yes” | 0.81 |
| FALSE | 5 records, 3 are “yes” | 0.97 |
Expected new entropy:
4.3 - Gain
| Attribute | Information Gain |
|---|---|
| outlook | 0.94 - 0.69 = 0.25 |
| temperature | 0.94 - 0.91 = 0.03 |
| humidity | 0.94 - 0.72 = 0.22 |
| windy | 0.94 - 0.87 = 0.07 |
The highest information gain is with the outlook attribute.
5 - Documentation / Reference
- Bill Howe University of Washington, Coursera, Introduction to data science