Detect Inflection Point of a Concave Curve (Elbox Method)

This function implements the Elbow (or knee of a curve) method to detect the inflection point of a concave curve. More information on this method: https://en.wikipedia.org/wiki/Elbow_method_(clustering).

elbow(data, plot = TRUE)

Arguments

data	a two-columns data frame (x and y respectively).
plot	a boolean. If TRUE (default) curves are plotted.

Value

This function returns a 2-elements list with:

• the value on x-Axis corresponding to the inflection point

• a data frame with the original data and two additional columns used in the graphic.

Details

This function detects unique inflection point in a simple concave curve. The curve can be concave down/up with a positive/negative slope.

Examples

## Loading dataset ----
data(profiles)
head(profiles)
#>   x concave_down_pos_slo concave_down_neg_slo concave_up_pos_slo
#> 1 0              0.00000                    1       9.313226e-10
#> 2 1              0.50000                    1       1.862645e-09
#> 3 2              0.75000                    1       3.725290e-09
#> 4 3              0.87500                    1       7.450581e-09
#> 5 4              0.93750                    1       1.490116e-08
#> 6 5              0.96875                    1       2.980232e-08
#>   concave_up_neg_slo
#> 1            1.00000
#> 2            0.50000
#> 3            0.25000
#> 4            0.12500
#> 5            0.06250
#> 6            0.03125

## Object returned ----
x <- elbow(profiles[ , c("x", "concave_down_pos_slo")], plot = FALSE)
class(x)
#> [1] "list"
names(x)
#> [1] "x_selected" "data"      
x$"x_selected"
#> [1] 4

## Graphical usage ----
x <- elbow(profiles[ , c("x", "concave_down_pos_slo")])

## The four implemented profiles ----
curves <- colnames(profiles)[-1]
par(mfrow = c(2, 2))
for (i in curves) {
  elbow(profiles[ , c("x", i)])
  title(i)
}