compute PPMI(digital, result) using data in below table
cherry strawberry digital information
computer
2
0
1670
3325
data
08
1683
3982
result
9
1
85
378
count(context)
4997
5673
473
ple
442
60
5
5
512
sugar
25
19
4
13
61
count(w)
486
80
3447
7703
11716
To compute PPMI (Pointwise Mutual Information) for the words digital and result, we need to calculate the following:
PPMI(digital, result) = max(log2(P(digital, result) / (P(digital) * P(result))), 0)
First, we need to find the probabilities P(digital), P(result), and P(digital, result) using the provided data:
P(digital) = count(digital) / sum(count(w)) = 3447 / 22732 ≈ 0.1516
P(result) = count(result) / sum(count(w)) = 7703 / 22732 ≈ 0.3389
P(digital, result) = count(digital, result) / sum(count(w)) = 85 / 22732 ≈ 0.0037
Now, we can compute PPMI(digital, result):
PPMI(digital, result) = max(log2(P(digital, result) / (P(digital) * P(result))), 0)
= max(log2(0.0037 / (0.1516 * 0.3389)), 0)
= max(log2(0.0037 / 0.0514), 0)
= max(log2(0.072), 0)
= max(-3.845, 0)
= 0
Therefore, PPMI(digital, result) = 0.