Construct a decision tree for the following dataset using...

Construct a decision tree for the following dataset using ID3 algorithm. Calculate the values of Overall Information Gain, Entropy and Gains for each attribute. Justify the branching in the final decision tree structure. The classes are indicated by last column named 'Inference'. Cycle Doc_Sub Category Inference Third Yes Layer 0 Third No Layer 0 Third No Rock 0 Second Yes Layer 0 Second Yes Rock 0 Second No Rock 1 Second No Layer 1 First Yes Layer 1 First No Rock 1 First No Layer 1

Transcript

00:01 So we can start with the entropy has equal to negative 0 .5, log 2, 0 .5, minus 0 .5, log 2, 0 .5, log 2, 0 .5 .5.

00:39 This is equal to 1.

00:44 So that would satisfy the initial entropy.

00:54 So next, we have to calculate the information gain for each.

00:57 Each attribute.

01:03 So we could use the gain cycle, gain of cycle made equal to entropy s, oops, entropy s, there we go, minus.

01:40 So if we look at 0 .3, so we're at a function of 10, so we use three tenths entropy of the third cycle plus three tenths, entropy second, plus four tenths, entropy first.

02:47 So this will become gain cycle equal to 1 minus 0 plus 0 .274 plus 0 .4 plus 0 .4.

03:14 So this is 0 .320.

03:18 So this is 0 .3254.

03:20 So that satisfies the gain for each attribute consolidated.

03:34 And then we can go to the doc sub yes.

03:39 So that's five instances, correlating with two inference equal zero, three inference equal one.

03:48 And then doc sub no is five instances, correlating with three inference equals zero, and two in inference equaling 1.

04:05 So if we represent entropy with yes, we have entropy, entropy represented by s of yes, and then entropy of no.

04:28 So if we correlate these simultaneously, we have negative two -fifths for yes, negative three -fifths for no.

04:47 Log 2, 2 5ths, 3 5ths.

05:03 Difference from 3 5ths and 2 5ths, log 2, 3 5ths, 2 5ths.

05:29 So both should have equal values in both do.

05:38 All right, so now we can go to the gain dock sub.

05:44 This becomes one minus, see we have half on 10, so we can go five -tenths, entropy, yes, plus five -tenths, entropy, no.

06:22 So this becomes one minus 0 .971, 0 .029.

06:33 So we got our gain doc sub evaluation satisfied.

06:42 Now we go to category.

06:44 So category is equal to layer and category is equal to rock.

06:50 So layer would be five instances, which correlates the three inference equal zero, two inference equal one.

06:59 And then for category rock, five instances correlates the two inference equal zero and three inference equal one.

07:08 So we'll just do the entropy simultaneously for layer.

07:20 And so this is negative and negative.

07:35 So 0 .6 and 0 .4.

07:38 So we go 3 5ths, 2 5ths.

07:47 Log 2, log 2, 3 5ths, 2 5ths.

08:02 It would be minus both approximately equal to 971 .971.

08:36 So this gain category is equal to 1 minus 5 tenths...

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