By Alder M.
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Extra info for An Introduction to Pattern Recognition
Of course, one number or the other might easily be zero if the ball is too small, but if the ball is too big it might measure only the total number of points in each category. Oh well, life wasn't meant to be easy. An alternative is to take, for some positive integer k, the k nearest neighbours of the new point, and count those in each category. Again, the bigger number is the best guess. This is called the k nearest neighbours algorithm. It looks rather like the metric method with which we started the quest to get sensible answers to the pattern recognition problem, but is making different assumptions about the nature of the process producing the data.
2. will give a second gaussian hill sitting over the female points. The two hills will intersect in some curve, but we shall imagine each of them sitting in place over their respective data points- and also over each others. Let us call them gm and gf for the male and female gaussian functions respectively. If a new data point is provided, we can calculate the height of the two hills at that point, and respectively. It is intuitively appealing to argue that if the male hill is higher than the female hill at the new point, then it is more likely that the new point is male than female.
The normal or is often written N( ) for short. All this may be found explained and justified, to some extent, in the undergraduate textbooks on statistics. See Feller, An Introduction to Probability Theory and Applications volume 2, John Wiley 1971, for a rather old fashioned treatment. Go to Information Theory for a more modern explanation. html (3 of 6) [12/12/2000 4:04:14 AM] Parametric have the problem of working out which of the numerical values to select. The parameter space of possible values allows an infinite family of possible gaussian hills.
An Introduction to Pattern Recognition by Alder M.