Signed Difference Analysis
A pedestrian guide to a new analytical tool
John Dunn and Ralph James
University of Western Australia
What's this all about?
Signed difference analysis (SDA) is a technique to investigate the relative structure of an arbitrary set of datapoints or of a quantifiable theoretical model.
What use is that?
Two important applications follow directly.
Two competing models can be compared in this way, and further distinguishing experiments flagged. Other useful outcomes are described below.
- A dataset can be checked for consistency with a proposed model
- An empirical model may be determined on the basis of the data alone.
What's special about this approach?
Being non-metric it can be easily applied to nonlinear or ill-determined processes. Limited only by computing power (not really relevant in practice) it can handle arbitrary dimensional data-spaces with arbitrary sub-dimensional structure.
Still in preparation:
The core of the matter...
The relationship between any two points in an n-dimensional space can be characterised by ranking the points on each measure. This can be represented as an n-component signed vector whose entries are either "+", "0" or "-". This forms the basis of an analytical technique to investigate all inter-relationships in an arbitrary dataset. Particular structures have a recognisable signature that allows identification of an appropriate parametrisation of the data. This can be in the form of a matrix of constant (or variable) coefficients or as a collection of relational equations.
Alternatively the allowed relationships inherent in a proposed numerical model can be routinely verified with respect to the totality of all available relevant data.