Parameter Regimes

There are two parameters associated with the chunking UpWrite as described so far, one is the resolution radius and the other is the order of the moments used to compute the UpWrite symbol assigned to each chunk. It is natural to wonder how one can pick the best values for these parameters.

A choice of resolution radius amounts to a decision that smaller scale variation will be treated as noise and averaged over. The decision as to what constitutes noise and what signal is seldom clear cut in the real world.

The problem is not well-posed: in order to decide what is the optimum resolution one must know what one is trying to perceive in the image, and there may be structure at many levels. The following example was suggested to me by Richard Thomas of the University of Western Australia:

  

Figure 8.10: A bit of a page of handwritten text.

Look at a page of handwritten text, as in fig. 8.10.

If we choose a resolution radius bigger than the mean distance between lines of text, we get an image, after chunking, which looks like the region in fig. 8.11.

  

Figure 8.11: The page at low resolution.

If we had used a smaller radius, we should have still got the same outcome, until the resolution falls below a certain value, whereupon we should have got fig. 8.12 briefly, before getting more details of the word level.

  

Figure 8.12: The page at intermediate resolution.

It is clear that there are stable regimes for the parameter values, and that between them there are fairly fast transitions. It depends rather on what we are trying to do which of these regimes matter to us most.

I shall often observe that a problem is solvable by the general means outlined in this chapter, by simply noting that there are stable parameter regimes which solve them. A purist might grumble that I do not give procedures for finding them which are practicable on present day computing equipment, and that investigating a large sample of parameter values concurrently requires specialised hardware of colossal power. This is correct. In a later section I shall discuss what we are here regarding simply as a more sophisticated pattern recognition system, in the different and significant context of a new class of neural models, and the suggestion will be made that neural implementations would proceed at many different scales or parameter values concurrently, and would also infer the regime structure, and correlations between regimes.

In particular applications, we may cheat and use the human eye to decide on a suitable scale value. This is generally more convenient than trying a range of values, when it is possible to do it at all.

The situation with respect to order of UpWrite is, I suspect somewhat different, but I shall go into that below when I discuss neural implementations of the UpWrite process.