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Find Elbow Point in a Curve (Perpendicular Distance Method)

Source: R/elbow.R
find_elbow.Rd

Identifies the "elbow" point in a metric-vs-H curve using the perpendicular distance method. Useful for model selection when fitting multiple H values (e.g., identifying the optimal H by finding where RMSE or variance improvements plateau).

Usage

find_elbow(x, y, minimize = TRUE)

Arguments

x

Numeric vector of x-values (typically H values).

y

Numeric vector of y-values (typically RMSE or variance).

minimize

Logical. If TRUE (default), assumes lower y is better (e.g., RMSE). If FALSE, assumes higher y is better (e.g., likelihood).

Value

Numeric. The x-value (H) at the identified elbow point.

Details

The elbow method finds where the curve transitions from steep to flat. The algorithm:

  1. Identifies the decreasing region of the curve

  2. Normalizes x and y to 0,1 scale

  3. Draws a line from the start to the end of the decreasing region

  4. Calculates perpendicular distance from each point to this line

  5. Returns the x-value (H) with maximum perpendicular distance

This is particularly useful for model selection when the optimal H is unclear from the metric alone.

Examples

if (FALSE) { # \dontrun{
# Find elbow in RMSE curve
H_values <- 2:7
rmse_values <- c(0.85, 0.42, 0.38, 0.36, 0.35, 0.35)
elbow_h <- find_elbow(H_values, rmse_values, minimize = TRUE)
print(elbow_h) # Likely returns H around 3-4
} # }