Alternative Representations

In this slow and gentle walk through the basic ideas of Pattern Recognition, I have concentrated on representing objects by some kind of measuring process which translates them into points in a vector space. There are a few other methods of representation which must be mentioned.

The vector space method of coding a description of the state of affairs runs right through science and is deeply embedded in the psyche of anyone who has survived an undergraduate course in Physics or Engineering. On the other hand, it seems bizarre and unnatural to, say, psychologists or computer scientists.

The power of the system of representation may be judged by what has been accomplished by it: virtually all of modern technology. The biological scientists might think otherwise, but almost all their measuring devices have been supplied by engineers working along lines worked out by physicists and chemists. Without such devices as x-ray diffraction systems and centrifuges, and an understanding of electrophoresis and isotopes, genetics would still be horse and flower breeding. This may sound a strong statement, and indeed it is, but some extended reflection is likely to convince the informed reader of its truth. The spectrum of ideas upon which contemporary science and technology depend, from statistics to electromagnetism, quantum mechanics to fluid mechanics, geology to developmental morphology, very much depends upon describing a system by means of a real or complex vector, sometimes an infinite dimensional one otherwise known as a function. There is a natural prejudice in favour of this representation language in almost all the practioners who come at the subject from a conventional science or engineering background, to the point where it may not occur to them that there is any sane alternative. The success of the language affords sufficient justification for using it, but the reasonable man will want to satisfy himself that the alternatives are not inherently superior.