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

 uik R Documentation

## Implementation of Unit Invariant Knee (UIK) method for finding the knee point of a curve

### Description

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

### Usage

```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

`check_curve` and `d2uik`

### Examples

```## 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 15, 2022, 5:07 p.m.