# uik: Implementation of Unit Invariant Knee (UIK) method for... In inflection: Finds the Inflection Point of a Curve

## Description

It finds the UIK estimation for elbow or knee point of a curve, see  for details.

## Usage

 `1` ```uik(x, y) ```

## Arguments

 `x` The numeric vector of x-abscissas, must be of length at least 4. `y` The numeric vector of y-abscissas, must be of length at least 4.

## Details

Given the x, y numeric vectors it first checks the curve by using `check_curve` and classifies it as convex, concave or convex/concave, concave/convex.

## Value

It returns the x-abscissa which is the UIK estimation for the knee point.

## Author(s)

Demetris T. Christopoulos

## References

 Christopoulos, Demetris T., Introducing Unit Invariant Knee (UIK) As an Objective Choice for Elbow Point in Multivariate Data Analysis Techniques (March 1, 2016). Available at SSRN: https://ssrn.com/abstract=3043076 or http://dx.doi.org/10.2139/ssrn.3043076

## See Also

`check_curve` and `d2uik`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## Lets create a convex data set x=seq(1,10,0.05) y=1/x plot(x,y) knee=uik(x,y) knee ##  3.15 abline(v=knee) ## Lets add noise to them now set.seed(20190625) x=seq(1,10,0.05) y=1/x+runif(length(x),-0.02,0.02) plot(x,y) knee=uik(x,y) knee ##  3.3 abline(v=knee) ```

inflection documentation built on June 28, 2019, 5:03 p.m.