By Alder M.
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9. Don't shoot the author, he's doing his best. 9: Two dimensional (bivariate) normal or gaussian distribution This time the gaussian function is of two variables, say x and y, and its parameters now are more complicated. html (2 of 6) [12/12/2000 4:04:14 AM] has become changed rather Parametric more radically. Casting your mind back to your elementary linear algebra education, you will recall that quadratic functions of two variables may be conveniently represented by symmetric matrices, for example the function given by may be represented by the matrix and in general for quadratic functions of two variables we can write for the function usually written ax2 + 2bxy + cy2.
We are, of course, conducting a leisurely survey of the basic concepts at present, rather than getting down to the nitty-gritty and the computational, because it is much easier to get the sums right when you can see what they are trying to accomplish. The framework discussed so far, however, has concentrated on recognising things which just sit there and wait to be recognised; but many things change in time in distinctive ways. As an example, if we record the position and possibly the pressure of a stylus on a pad, we can try to work out what characters are being written when the user writes a memo to himself.
A good theory has to be right when tested on new data, and the theory given by line B does not look promising. Another serious drawback of the ANN described by B is that an object weighing in at 50 Kg. and having a height of three metres is unequivocally theorised to be a man. Modifying the ANN so that it admits that it has never seen anything like it before and consequently doesn't have the foggiest idea what class a new point belongs to, is not particularly easy. Next: Statistical Methods Up: Decisions, decisions..
An Introduction to Pattern Recognition by Alder M.