Composite Pairwise Loss Function — composite_pair

Computes the total loss across all pairwise combinations of rows in a matrix.

Usage

composite_pair_loss(x, fun, trans = identity, rescale = "df", ...)

Arguments

x: A numeric vector, matrix, or data frame. If not a matrix, it will be coerced to one after applying the transformation function.
fun: A function to compute the loss for each pairwise difference. The package supports the alignment loss (alf) and the approximate L0 penalty (l0a), but users can provide custom functions as well.
trans: A transformation function to apply to x before computing pairwise differences. Default is identity (no transformation).
rescale: Either "df" (default) to rescale the total loss by the degrees of freedom (number of rows - 1), or a numeric value (likely between 0 and 1) to multiply the total loss by.
...: Additional arguments passed to the loss function fun.

Value

A numeric scalar representing the sum of losses across all pairwise combinations of rows.

Details

The function works by:

Applying the transformation function trans to the input x
Converting the result to a matrix
Generating all possible pairwise combinations of row indices
Computing the difference between each pair of rows
Applying the loss function fun to each difference
Summing all the individual losses

Examples

# Example with a simple matrix
x <- matrix(runif(12), nrow = 4)
composite_pair_loss(x, fun = alf)
#> [1] 5.148134

# Example with log transformation and L2 loss
composite_pair_loss(x, fun = function(x) x^2, trans = log)
#> [1] 36.73551