Respuesta :
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, [tex]$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$[/tex]
x y Color Distance from point (3, 3)
1 1 Red [tex]$\sqrt{(3-1)^2+(3-1)^2} = 2.82$[/tex]
1 3 Green [tex]$\sqrt{(3-1)^2+(3-3)^2} = 2$[/tex]
2 5 Blue [tex]$\sqrt{(3-2)^2+(3-5)^2} = 2.23$[/tex]
3 5 Green [tex]$\sqrt{(3-3)^2+(3-5)^2} = 2$[/tex]
4 1 Blue [tex]$\sqrt{(3-4)^2+(3-1)^2} = 2.23$[/tex]
4 4 Red [tex]$\sqrt{(3-4)^2+(3-4)^2} = 1.41$[/tex]
5 3 Blue [tex]$\sqrt{(3-5)^2+(3-3)^2} = 2$[/tex]
5 4 Green [tex]$\sqrt{(3-5)^2+(3-4)^2} = 2.23$[/tex]
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 [tex]$4 \text{ colors}$[/tex] with shortest distance which are [tex]$\text{red, green, green, blue}$[/tex]. Since, now we know, Green has the greatest frequency among 4, hence the answer is Green.
