Question

Given the training data in Question 1 below| (on buying RRSP8), predict the class of the following new example using k-nearest-neighbor classification fork = 5: sector = oil industry, income = medium, self-employed = yes, credit-rating fair. For distance measure, use the following similarity measure: similarity(tupleAtupleB)-4-.(w"S(ab/4), where S(ab) is 1 if parameter a equals parameter b and o otherwise The parameters atand biare either Sector, income, self-employed, or credit-rating. The weights wiare all 1, except for income, which is 2. Please show your calculations or explain the steps. Note: the similarity measure is the opposite of the distance measure. Sector of activity Self-Employed Credit-rating Person ID Class: Buys-RRSP Income farming medium fair 1 no no farming fair low 2 yes no oil industry medium fair no no oil industry low fair yes 4 yes oil industry medium excellent 5 yes yes banking medium excellent yes no oil industry high fair 7 no no oil industry high excellent no no banking high fair yes no farming low excellent 10 yes yes banking low excellent 11 yes yes farming medium fair 12 yes no high banking fair 13 yes yes farming medium excellent 14 no yes

Answer 1

Given K =5

And We have to predict for : sector = oil industry, income = medium, self-employed = yes, credit-rating fair

Also the similarity measure is given as : Similarity(tupleA, tupleB)=

Wi (S(ai, b)) i=1

where S(a, b) =1 if parameter "a" equals parameter "b" and =0 otherwise The parameters a(i), b(i) are either Sector, income, self-employed, or credit-rating. The weights w(i) are all 1, except for income, which is 2

NOTE: For calculating similarity measure we just use the given formula and corresponding value of S and W, depending on the case if they match our training set and the query or not.

Person ID	Sector of Activity	Income	Self-employed	Credit Rating	Similarity Measure Value
1	farming	medium	No	Fair	0+2+0+1 = 3
2	farming	low	yes	Fair	0+0+1+1 = 2
3	oil industry	medium	No	Fair	1+2+0+1 = 4
4	oil industry	low	yes	fair	1+0+1+1 = 3
5	oil industry	medium	yes	excellent	1+2+1+0 = 4
6	banking	medium	no	excellent	0+2+0+0 = 2
7	oil industry	high	no	fair	1+0+0+1 = 2
8	oil industry	high	no	excellent	1+0+0+0 = 1
9	banking	high	no	fair	0+0+0+1 = 1
10	farming	low	yes	excellent	0+0+1+0 = 1
11	banking	low	yes	excellent	0+0+1+0 = 1
12	farming	medium	yes	fair	0+2+1+1 = 1
13	banking	high	yes	fair	0+0+1+1 = 2
14	farming	medium	no	excellent	0+2+0+0 = 2

Person ID	Sector of Activity	Income	Self- employed	Credit Rating	Similarity Measure Value	Rank Highest Similarity Measure	Can we include it in (K=5) Nearest Neighbour	Y=Category Of Nearest Neighbour
1	farming	medium	No	Fair	0+2+0+1 = 3	3	YES	No
2	farming	low	yes	Fair	0+0+1+1 = 2	5	YES	No
3	oil industry	medium	No	Fair	1+2+0+1 = 4	1	YES	No
4	oil industry	low	yes	fair	1+0+1+1 = 3	4	YES	Yes
5	oil industry	medium	yes	excellent	1+2+1+0 = 4	2	YES	Yes
6	banking	medium	no	excellent	0+2+0+0 = 2	6	NO	Yes
7	oil industry	high	no	fair	1+0+0+1 = 2	8	NO	No
8	oil industry	high	no	excellent	1+0+0+0 = 1	10	NO	No
9	banking	high	no	fair	0+0+0+1 = 1	11	NO	Yes
10	farming	low	yes	excellent	0+0+1+0 = 1	12	NO	Yes
11	banking	low	yes	excellent	0+0+1+0 = 1	13	NO	Yes
12	farming	medium	yes	fair	0+2+1+1 = 1	14	NO	No
13	banking	high	yes	fair	0+0+1+1 = 2	8	NO	Yes
14	farming	medium	no	excellent	0+2+0+0 = 2	9	NO	Yes

So we can see that we have 3 No and 2 yes so our final answer class label will be "No".

(Note: here we had to choose one among several choices for the fifth neighbour so we selected one randomly. and there will be a change of answer if we had chose another one. So in such case we just select a random one and make our decision of the class)