By Alder M.
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Extra info for An Introduction to Pattern Recognition
Tall, it can be found by integrating the function between those values. The gaussian takes only positive values, and the integral from to is 1, so we are simply measuring the area under the curve between two vertical lines, one at 170 and the other at 190. It also follows that there is some fraction of the sample having heights between -50 and -12 cm. This should convince you of the risk of using models without due thought. In low dimensions, the thought is easy, in higher dimensions it may not be.
The hyperplane is a kind of theory. It has its opinions about the category of any new point that may be offered. 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.
Obtained is called the feature space for A little thought suggests that this could be the hard part. One might reasonably conclude, after a little more thought, that there is no way a machine could be made which would be able to always measure the best possible things. Even if we restrict the problem to a machine which looks at the world, that is to dealing with images of things as the objects we want to recognise or classify, it seems impossible to say in advance what ought to be measured from the image in order to make the classification as reliable as possible.