Higher Partials of fStress

TL;DR

This paper introduces fDistances and fStress, a generalized framework for fitting dissimilarity data with higher-order derivatives, providing formulas and R code for advanced optimization.

Contribution

It presents a novel generalization of distance measures and derives formulas for higher-order derivatives of the fStress loss function, including implementation details.

Findings

Formulas for derivatives of fStress up to fourth order

R and C code for computing derivatives

Generalization of Euclidean, squared, and log distances

Abstract

We define *fDistances*, which generalize Euclidean distances, squared distances, and log distances. The least squares loss function to fit fDistances to dissimilarity data is *fStress*. We give formulas and R/C code to compute partial derivatives of orders one to four of fStress, relying heavily on the use of Fa\`a di Bruno's chain rule formula for higher derivatives.