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Using table in Appendix C, Create classification model using decision-tree and hence classify following tuple. Very High, Old?
No. Income Age Own House
1 Very High Young Yes
2 High Medium Yes
3 Low Young Rented
4 High Medium Yes
5 Very High Medium Yes
6 Medium Young Yes
7 High Old Yes
8 Medium Medium Rented
9 Low Medium Rented
10 Low Old Rented
11 High Young Yes

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P (Very High) = 2/11

P (High) = 4/11

P (Low) = 3/11

P (Medium) = 2/11

Own House has only two values Yes and Rented.

Total Number of Very High Income = 2

Total Number of High Income = 4

Total Number of Low Income = 3

Total Number of Medium Income = 2

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Use above values to classify new tuple as very High.

Consider new Tuple as t = {Yes, Very High, Old}

P (t l Very High) = 1*0=0

P (t l High) = 1* ¼ = 1/4

P (t l Medium) = ½ *0=0

P (t l Low) = 0 * 1/3=0

Therefore likelihood of being Very High = P (t l Very High) * P (Very High) = 0* 2/11=0

Similarly,

Likelihood of being High = P (t l High) * P (High) = ¼*4/11=0.09

Likelihood of being Medium = P (t l Medium) * P (Medium) = 0*2/11=1

Likelihood of being Low = P (t l Low) * P (Low) = 0*3/11=0

Then estimate P (t) by adding individual likelihood values since t will be very high, high, medium or low P (t) = 0+0+0+0.09=0.09

Finally Actually Probability of each event

P (Very High) = (P (t l Very High) * P (Very High)) /P (t) = 0

Similarly,

P (High) = (P (t l High) * P (High)) /P (t) = (1/4 * 4/11) /0.09=1

P (Medium) = (P (t l Medium) * P (Medium)) /P (t) = 0

P (Very High) = (P (t l Low) * P (Low)) /P (t) = 0

New Tuple is a High as it has the highest Probability.

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