The computational length of an algorithm for pattern recognition by absolute comparison is a random variable, whose features depend on the probability distribution π∈Rk of the k classes to be discriminated. The Euclidean distance from the uniform probability distribution to any other distribution π is proportional to the greatest lower bound of the total variation of the mean computational length of algorithms used to recognize classes with distribution π. This result is reached by first finding a suitable basis of Rk which allows simple representations of probability distributions and of the functions under study. Furthermore, by using the same basis, the Schwartz inequality easily gives an upper bound of the total variation of the mean computational length.
Inequalities concerning a random computational length of pattern recognizers
VISCOLANI, BRUNO
1982
Abstract
The computational length of an algorithm for pattern recognition by absolute comparison is a random variable, whose features depend on the probability distribution π∈Rk of the k classes to be discriminated. The Euclidean distance from the uniform probability distribution to any other distribution π is proportional to the greatest lower bound of the total variation of the mean computational length of algorithms used to recognize classes with distribution π. This result is reached by first finding a suitable basis of Rk which allows simple representations of probability distributions and of the functions under study. Furthermore, by using the same basis, the Schwartz inequality easily gives an upper bound of the total variation of the mean computational length.
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