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Numerical Exampe of K Nearest Neighbor Algorithm
Here is step by step on how to compute Knearest neighbors KNN algorithm:
 Determine parameter K = number of nearest neighbors
 Calculate the distance between the queryinstance and all the training samples
 Sort the distance and determine nearest neighbors based on the Kth minimum distance
 Gather the category of the nearest neighbors
 Use simple majority of the category of nearest neighbors as the prediction value of the query instance
We will use again the
previous example
to calculate KNN by hand computation. If you want to
download the MS excel companion of this tutorial, click here
Example
We have data from the questionnaires survey (to ask people opinion) and objective testing with two attributes (acid durability and strength) to classify whether a special paper tissue is good or not. Here is four training samples
X1 = Acid Durability (seconds) 
X2 = Strength (kg/square meter) 
Y = Classification 
7 
7 
Bad 
7 
4 
Bad 
3 
4 
Good 
1 
4 
Good 
Now the factory produces a new paper tissue that pass laboratory test with X1 = 3 and X2 = 7. Without another expensive survey, can we guess what the classification of this new tissue is?
1. Determine parameter K = number of nearest neighbors
Suppose use K = 3
2. Calculate the distance between the queryinstance and all the training samples
Coordinate of query instance is (3, 7), instead of calculating the distance we compute square distance which is faster to calculate (without square root)
X1 = Acid Durability (seconds) 
X2 = Strength (kg/square meter) 
Square Distance to query instance (3, 7) 
7 
7 

7 
4 

3 
4 

1 
4 

3. Sort the distance and determine nearest neighbors based on the Kth minimum distance
X1 = Acid Durability (seconds) 
X2 = Strength (kg/square meter) 
Square Distance to query instance (3, 7) 
Rank minimum distance 
Is it included in 3Nearest neighbors? 
7 
7 

3 
Yes 
7 
4 

4 
No 
3 
4 

1 
Yes 
1 
4 

2 
Yes 
4. Gather the category of the nearest neighbors. Notice in the second row last column that the category of nearest neighbor (Y) is not included because the rank of this data is more than 3 (=K).
X1 = Acid Durability (seconds) 
X2 = Strength (kg/square meter) 
Square Distance to query instance (3, 7) 
Rank minimum distance 
Is it included in 3Nearest neighbors? 
Y = Category of nearest Neighbor 
7 
7 

3 
Yes 
Bad 
7 
4 

4 
No 
 
3 
4 

1 
Yes 
Good 
1 
4 

2 
Yes 
Good 
5. Use simple majority of the category of nearest neighbors as the prediction value of the query instance
We have 2 good and 1 bad, since 2>1 then we conclude that a new paper tissue that pass laboratory test with X1 = 3 and X2 = 7 is included in Good category.
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This tutorial is copyrighted .
Preferable reference for this tutorial is
Teknomo, Kardi. KNearest Neighbors Tutorial. http:\\people.revoledu.com\kardi\tutorial\KNN\