Procedures for controlling reference frame effects in the measurement of multidimensional processes

Abstract

A wide array of perceptual mapping techniques have been developed which make it possible to describe the dissimilarities relations among datapoints as spatial arrays. While most of these present advantages and disadvantages for representing any single dataset, special difficulties arise when time-ordered data are available. These difficulties arise from the fact that the directional orientation of such techniques are (necessarily) arbitrary. When multiple datasets are scaled, therefore, the arbitrary orientations of each of the maps representing each of the time points render the description of motion and change difficult or impossible.

This problem can be solved by choosing a set of stable points within the process to serve as anchoring reference points for controlling the orientation of the individual “frames”. A worked through example is provided, in which the positions of the end points of the hands of a clock are mapped over ten intervals of time using conventional methods and the method proposed. Results indicate that a satisfactory choice of stable referent points, along with a suitable choice of rotation and translation rules, can overcome the original difficulty.