A random model for multidimensional fitting method

TL;DR

This paper introduces a stochastic extension to the multidimensional fitting (MDF) method, incorporating random effects into the modification vectors to better model uncertainties in multivariate data analysis.

Contribution

It extends the MDF method by modeling modification vectors as random variables, enhancing its ability to handle real-world data variability.

Findings

Incorporates random effects into MDF, improving flexibility.

Demonstrates application in the sensometric domain.

Provides a probabilistic framework for data fitting.

Abstract

Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the distances between the same points. The idea of MDF is to modify the coordinates through modification vectors in order to fit the new distances calculated on the modified coordinates to the given distances. In the previous works, the modification vectors are taken as deterministic variables, so here we want to take into account the random effects that can be produce during the modification. An application in the sensometric domain is also given.