Question

How to calculate entropy in Artificial Intelligence?

Answer 1

Answer:

Suppose you have data:

color height quality

===== ====== =======

green tall good

green short bad

blue tall bad

blue short medium red tall medium red short medium

To calculate the entropy for quality in this example:

X = {good, medium, bad}

x1 = {good}, x2 = {bad}, x3 = {medium}

Probability of each x in X:

Probability of each x in X:p1 = 1/6 = 0.16667

p2 = 2/6 = 0.33333

p3 = 3/6 = 0.5

for which logarithms are:

log2(p1) = -2.58496

log2(p2) = -1.58496

log2(p3) = -1.0

and therefore entropy for the set is:

H(X) = - (0.16667 * -2.58496) - (0.33333 * -1.58496) - (0.5 * -1.0) = 1.45915

by the formula in the question.

Remaining tasks are to iterate this process for each attribute to form the nodes of the tree.

Answer 2

Answer:

Description of entropy breaks down the formula, but I still don't know how to determine the values of X and p(x), defined as "The proportion of the number of elements in class x to the number of elements in set S".

Explanation:

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