How to perform KNN regression

Hi,

I have data as below:

X:
1
2
3
4
9
11
13
17
19
20

y:
0.1
0.3
0.4
0.65
1.5
2.5
2.7
2.9
3.2
3.6

I want to compute y values for at x values at 6.3, 15.5&21.5

1. for each value of x, I want to take 4 nearest points in my calculation and choose most reasonable one as the final y
2. In the second method, compare minkowski & chebychev distances and choose most reasonable one

Many thanks in advance,

[Jan]

There is no "most reasonable" in maths. You want a valus for x=21.5, but the original data stop at x=20. There is an infinite number of possible ways to extrapolate. Without any further information like "the data follow a polynomial of order 3" it is not possible to prefer any method or even to measure the degree or reasonability. Perhaps a linear interpolation is fair, and the extrapolated values should be simply NaN.

[Image Analyst]

"In the second method, compare ....." sounds like a homework problem,

Is it?

Answer 1

[Royi Avital]

At each point you want to calculate the value (x, y) find the K closest point (For x).

Then average them to create the new value.