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Nearest neighbor rule for static recognition

Lecture



Let be   Nearest neighbor rule for static recognition - the set of objects of the training sequence, that is, the belonging of each of them to one or another pattern is reliably known. Let also   Nearest neighbor rule for static recognition is the object closest to the recognizable   Nearest neighbor rule for static recognition . Recall that in this case the nearest neighbor rule for classification   Nearest neighbor rule for static recognition is that   Nearest neighbor rule for static recognition attributed to the class (image), which belongs   Nearest neighbor rule for static recognition . Naturally, this assignment is random. Probability that   Nearest neighbor rule for static recognition will be referred to   Nearest neighbor rule for static recognition there is a posteriori probability   Nearest neighbor rule for static recognition . If a   Nearest neighbor rule for static recognition very large, it is entirely possible to assume that   Nearest neighbor rule for static recognition located close enough to   Nearest neighbor rule for static recognition so close that   Nearest neighbor rule for static recognition . And this is nothing but a randomized decision rule:   Nearest neighbor rule for static recognition attributed to   Nearest neighbor rule for static recognition with probability   Nearest neighbor rule for static recognition . The Bayesian decision rule is based on the choice of the maximum a posteriori probability, that is,   Nearest neighbor rule for static recognition attributed to   Nearest neighbor rule for static recognition in case if

  Nearest neighbor rule for static recognition .

This shows that if   Nearest neighbor rule for static recognition close to unity, the nearest neighbor rule gives a solution, which in most cases coincides with Bayesian. Recall that these arguments have sufficient grounds only for very large   Nearest neighbor rule for static recognition (the volume of the training sample). Such conditions in practice are not common, but they allow one to understand the statistical meaning of the nearest-neighbor rule.


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Pattern recognition

Terms: Pattern recognition