distance: Distance measure from the target

Description

Computes a scalar distance between the target (a set of desirable values for the responses) and the responses values that have been either observed or estimated for each point in the experimental space. Such a distance is used to identify additional experimental points to be investigated.

Usage

distance(xpop, xspace, yspace, weight, opt)

Arguments

xpop

A data frame containing the factor values for the experimental points investigated; the row names uniquely identify each experimental point (ID).

xspace

A data frame containing the factor values for the experimental points defining the entire experimental region; the row names uniquely identify each experimental point (ID).

yspace

A data frame containing the response values (either observed or estimated) for the points in the experimental region.

weight

A numerical vector, of the same length as the number of responses, containing the weights assigned to the each response; the sum of the weights must be equal to 1.

opt

A character vector, of the same length as the number of responses, defining if each response needs to be minimized or maximized. The allowed values are 'mn' (minimize) and 'mx' (maximize).

Value

fit: The scalar distances between the target and the response(s) values for the experimental points in xpop.
obj.nn: Scalar distance from the target for the best experimental point identified by EMMA.

Details

The function normalizes the response values with respect to the estimated limits of the response space, so that the response values lie between 0 and 1. Subsequently, the function identifies the target and computes a scalar distance between the target and the response values.

References

Friedman J. H. (1991) 'Multivariate adaptive regression splines' (with discussion), The Annals of Statistics 19, 1:141.

Villanova L., Falcaro P., Carta D., Poli I., Hyndman R., Smith-Miles K. (2010) 'Functionalization of Microarray Devices: Process Optimization Using a Multiobjective PSO and Multiresponse MARS Modelling', IEEE CEC 2010, DOI: 10.1109/CEC.2010.5586165