Controlling the Location of Errors

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Controlling the Location of Errors

In a simple case the model space allows for as many positions in two-dimensional space as there are nodes in your data. Most likely under the given constraints this will not make it possible for each node to take a position where its overall distance in the model space (to all nodes to which it is linked directly) is minimal.

While this is the basic problem of trading simplicity for exactness, we are willing to sacrifice exactness to a certain degree if we force the solution into a constrained space. A pragmatic solution to this problem is to try to get as much exactness as possible under the given circumstances: for the visual inspection it is often sufficient if the most important elements are placed best, i.e. are located in the most central positions available in a model space.

This also means that we are willing to accept errors if they occur to structurally less important elements: if not possible we are willing to have them misplaced to a certain degree.

The general idea of controlling where the errors are placed in the model space means using the optimization criterion itself to specify priorities for misspecification: if the structurally most important elements are placed first, less important elements are forced to the remaining positions under more restricted alternatives for positioning.

Depending on the quality of your data, such a strategy might save you from interpreting white noise contained in your data, if you expect noise to affect mainly the periphery of the underlying structure.

Lothar Krempel
Fri Mar 31 13:14:02 MET DST 1995