The following dataset contains eight items representing colored points on the x-y plane: х y color
1 1 red
1 3 green
2 5 blue
3 5 green
4 1 blue
4 4 red
5 3 blue
5 4 green
Using this data as the training set, run the k-nearest-neighbors classification algorithm (k=1) using square distance and choose the color for a new item with x = 3 and y = 3.

Solution :

According to the question, the following datasheet contains eight items representing the colored points o the x-y plane.

We have to use this data as training set to run the k-nearest classification algorithm to decide most likely color for a new item with x = 3 and y = 3.

The distance between the points is actual distance on x-y plane, called as Eucledian distance.

We will make a data table, by calculating distance from (3, 3) of each point. By using formula :

Distance,

x      y    Color       Distance from point (3, 3)

1       1     Red        

1      3    Green                    

2     5    Blue              

3     5   Green      

4     1    Blue          

4     4   Red          

5     3   Blue        

5     4   Green    

Now, we will do sorting of colors with distance in ascending order.

We get, [ Red, Green, Green, Blue, Blue, Blue, Green, Red]  

Now if we run the algorithm with k = 1, then we pick only 1 color having the shortest distance that will be assigned to the given point.

Therefore the color is RED.

If we run the algorithm with k = 4, we will pick up with shortest distance which are . Since, now we know, Green has the greatest frequency among 4, hence the answer is Green.

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