Topological Vector Spaces II

During the last twenty years the problem of pattern recognition (specifically, image recognition) has been studied intensively by many investigators, yet it is far from being solved. The number of publications increases yearly, but all the experimental results-with the possible exception of some dealing with recognition of printed characters-report a probability of error significantly higher than that reported for the same images by humans. It is widely agreed that ideally the recognition problem could be thought of as a problem in testing statistical hypotheses. However, in most applications the immediate use of even the simplest statistical device runs head on into grave computational difficulties, which cannot be eliminated by recourse to general theory. We must accept the fact that it is impossible to build a universal machine which can learn an arbitrary classification of multidimensional signals. Therefore the solution of the recognition problem must be based on a priori postulates (concerning the sets of signals to be recognized) that will narrow the set of possible classifications, i.e., the set of decision functions. This notion can be taken as the methodological basis for the approach adopted in this book.