An Introduction to Pattern Recognition

Footnotes . . . . ...long. The reason for allowing infinitely long sequences is not that anybody expects to meet one and be able to say with satisfaction, `wow, that was infinitely long', it is more of a reluctance to specify the longest case one expects to get. In other words, it is done to simplify things; the infinitude of the natural numbers is a case in point. There may be some grounds for reasonable doubt as to whether this in fact works: sometimes one merely defers the difficulties to a later stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...end. Grammarians used to believe that high levels of inflection showed a highly evolved language, probably because Latin was regarded as morally superior to English, German or French. Then it was discovered that Chinese used to be inflected a few thousand years ago but the chinese very http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (57 of 66) [12/12/2000 4:05:28 AM]

Footnotes sensibly gave it up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...level. Past a certain point it is called `plagiarism'. . . . . . . . . . . . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (58 of 66) [12/12/2000 4:05:28 AM]

Footnotes . . . . . . . . . . . . . . . . . . ...is. As Herod said to the three wise men. . . . . . . . . . . . . . . . . . . . . . . . . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (59 of 66) [12/12/2000 4:05:28 AM]

Footnotes . . . . . ...methods Or whatever is the pet method favoured by the audience. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...world. To a geometer, it looks as though the algebraists have gotten into the cookie-jar when everyone knows they are there to tidy things up and nit-pick about details, not go around being creative. Or, even worse than algebraists, gasp, logicians. When logicians go around being creative, universes totter and crumble. . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (60 of 66) [12/12/2000 4:05:29 AM]

Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...calculation mere singularity is unimportant; to have one eigenvalue collapsing to zero may be regarded as a misfortune, to have both collapse seems like carelessness . . . . . . . . . . . . . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (61 of 66) [12/12/2000 4:05:29 AM]

Footnotes . . . . . . . . . . . . . . . . ...world. As when one's progeny want one to switch off the Bach so they can concentrate on the Heavy Metal, or vice versa. . . . . . . . . . . . . . . . . . . . . . . . . . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (62 of 66) [12/12/2000 4:05:29 AM]

Footnotes . . . . ...group. A Topological Group is a collection of invertible transformations such that the composite (do one then another) of any two is a third, and also having the property that the multiplication operation and the inversion operation are continuous. A Lie Group (pronounced `Lee') is a topological group where the operations are also differentiable and the set forms a manifold, which is a higher dimensional generalisation of a curve or surface. This definition is sloppy and intended to convey a vague and intuitive idea which is adequate for present purposes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...group The term is from differential topology, and may be found in any of the standard texts. It is not necessary to expand upon its precise meaning here, and an intuitive sense may be extracted from http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (63 of 66) [12/12/2000 4:05:29 AM]

Footnotes the context. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...book. But watch out for the sequel. . . . . . . . . . . . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (64 of 66) [12/12/2000 4:05:29 AM]

Footnotes . . . . . . . . . . . . . . . . . . ...cognition. Blakemore conjectured it in the paper cited, but it probably struck a lot of people that this was a variant of a Hebbian learning rule. . . . . . . . . . . . . . . . . . . . . . . . . http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (65 of 66) [12/12/2000 4:05:29 AM]

Footnotes . . . . . . ...preference. There is a belief in some quarters that God is a mathematician, or why did He make Physics so mathematical? And in particular, He must be a geometer, because most of Physics uses geometry. This is like wanting the Sun to shine at night when we need it and not in the daytime when it's light anyway. The fact is that the most powerful languages allow you to say more interesting and important things. That is why I use geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mike Alder 9/19/1997 http://ciips.ee.uwa.edu.au/~mike/PatRec/footnode.html (66 of 66) [12/12/2000 4:05:30 AM]

About this document ... Up: An Introduction to Pattern Previous: Bibliography About this document ... An Introduction to Pattern Recognition: Statistical, Neural Net and Syntactic methods of getting robots to see and hear. This document was generated using the LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997) Copyright © 1993, 1994, 1995, 1996, 1997, Nikos Drakos, Computer Based Learning Unit, University of Leeds. The command line arguments were: latex2html PatRec.tex. The translation was initiated by Mike Alder on 9/19/1997 Mike Alder 9/19/1997 http://ciips.ee.uwa.edu.au/~mike/PatRec/node221.html [12/12/2000 4:34:46 AM]