By William S. Meisel

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13 illustrates this point. In Fig. 13a, note that the A’s are transformed into points in feature space near one another and the letter B is distinguishable by distance in pattern space. In Fig. 13b, the A’s are transformed into points close to one another despite the fact that they appear in radically different forms in terms of rotation and size in the physical pattern; the characteristic to be recognized is not relevant to size or rotation. Of course, irrelevant differences may be reflected 26 I Basic Concepts and Methods A Physlcol Patterns ( 0 ) Transference of Similority ( b ) Similarity in Terms of Chorocteristic to be Recognized FIG.

I) Noting Eq. 2). we can write this more simply ast AF (x")) % VF * Ax. 4) We are looking for the direction of Ax which will maximize (or minimize) AF for Ax of constant length. 5) implies by Eq. 4) that - jlVF I/ IlAxlI I VF. 6) AF will be maximized (minimized) for Ax such that the right-hand (lefthand) inequality holds. This is the case for AX = + K VF, - (z:= t The expression x y is the dofproditcl (or innerproduct) of x and y: x y = 1 The norm of x is \ / x i /= I xiZ)"' in this chapter. 7) 7 - 1xty;.

Sanimon, J. , and Proctor, A,, Considerations of Dimensionality versus Sample Size, IEEE Synip. Adaptive Processes, Austin, Texas, December 1970. 35. , Decision-Making Processes in Pattern Recognition,” Macmillan, New York, 1962. 36. Tou, J. T. ), “Computer and Information Sciences-11,” Academic Press, New York, 1967. ’ Selected Bibliography 37 37. Ullnian, J. , Experiments with the N-Tuple Method of Pattern Recognition, IEEE Trans. Comput. 18, 1135-1137 (1969). 38. , “Knowing and Guessing,” Wiley, New York, 1969.

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Computer-Oriented Approaches to Pattern Recognition by William S. Meisel
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