Ability of the complex backpropagation algorithm to learn similar transformation

It has been discovered by computational experiments that the “complex-BP” algorithm can transform geometrical figures (e.g. rotation, similar transformation and parallel displacement), and reported that this ability can be successfully applied to computer vision. In this paper, the ability of the “complex-BP” algorithm to learn similar transformation of geometrical figures is analyzed. A complex-BP network which has learned similar transformation, has the ability do generalize the similitude ratio with a distance error which, is represented by the sine of the difference between the argument of the test pattern and that of the training pattern