. The second part consisted of comparing
the results of doing this on a new object,
with some set of data where we know the category
to which the object belongs, thus comparing
vectors with vectors.
The second chapter looked at ways of measuring objects- mostly pixel arrays, since these arise from pointing cameras at the world. In this chapter and the next, I shall start on the task of doing the actual recognition using statistical methods. In the following chapter I shall discuss neural nets, and in later chapters I shall treat syntactic methods.
We assume then that the robot has sensed the world, maybe by pointing a camera at it, possibly by other means, and that some measuring process has been applied to obtain a vector of real numbers. The robot has seen other such vectors in the past and has also been told what category of object they describe: now it has to make up its own mind about the latest vector. An industrial robot looking at something to be sorted, or possibly welded, may easily be in this situation.
I find myself, yet again, in a difficult position. It is not hard to give recipes which are easy to implement in programs, and to pass lightly over the issues concerning why they work, or indeed if they work. This goes against the grain; it is necessary to give a survey of what is standard practice, but it is also necessary to look at standard practice with a cold, critical and careful eye if there is to be any progress. The situation is particularly acute in Statistics. Statistics is often taught as recipes, with the deplorable consequences I have mentioned in chapter one, and it is about time this repellent habit was abandoned.
On the other hand, sorting out fundamental ideas in Probability theory carefully is a very technical business indeed, and many issues are still in dispute. So this chapter starts off somewhere between Scylla and Charybdis, trying to get fundamental ideas examined in informal language. This may show more courage than judgement; you can decide whether or not you feel illuminated.
I shall in this chapter, then, go into foundational issues with more enthusiasm than is common in Pattern Recognition texts. When we come to investigate Syntactic Pattern Recognition we shall come up against conceptual difficulties related to the kinds of models of neural processing which these methods imply. We might as well start the way we intend to continue and clear away the undergrowth from the beginning. In the spirit of critical reflection which I propose to stimulate, I shall draw attention to the underlying assumptions and conceptual underpinnings of contemporary practice. It is hard to change your own ideas, and even harder if you don't know what they are. Those who feel uncomfortable with theoretical issues should appreciate that there is nothing so practical as a good theory, and nothing so dangerous as a bad one.
The present chapter then is about the general ideas of statistics and probability theory which have a bearing on pattern recognition; the next chapter will give the recipes. I have broken the material up in this way because painful experience has compelled me to recognise that many people who claim to be of a practical disposition object to generalities and find ideas confusing. `Don't give me all that blather, just give me the formulae', they say. Thought hurts their heads and gives them doubts about their certainties, so they want nothing to do with it. I have taken pity on them; this chapter therefore, may be skipped by those for whom thinking is an unnatural act. They may, of course, regret the decision later.