The effects of amount of training per reversal on successive reversals of a color discrimination

Three groups of pigeons were trained on a red-green discrimination in which the stimuli were alternately presented in a multiple schedule of reinforcement. The discrimination was reversed 24 times. Groups were given 1, 2, or 4 hr of training on each discrimination. Increasing the length of training had two principal effects on reversal performance: it increased the rate of extinction of responding to one of the stimuli and increased the rate of reacquisition of responding to the other. The latter effect involved both an increase in reacquisition of responding to a positive stimulus within reversals and an increase in recovery of responding to the previous negative stimulus between reversals. Improvements in performance of each group over the series of reversals were qualitatively similar to the two effects of length of training on each discrimination, and were analogous to effects obtained in other studies involving overtraining and successive reversals of simultaneous discriminations.     

Orthogonal rotation algorithms

The quartimax and varimax algorithms for orthogonal rotation attempt to maximize particular simplicity criteria by a sequence of two-factor rotations. Derivations of these algorithms have been fairly complex. A simple general theory for obtaining two factor at a time algorithms for any polynomial simplicity criteria satisfying a natural symmetry condition is presented. It is shown that the degree of any symmetric criterion must be a multiple of four. A basic fourth degree algorithm, which is applicable to all symmetric fourth degree criteria, is derived and applied using a variety of criteria. When used with the quartimax and varimax criteria the algorithm is mathematically identical to the standard algorithms for these criteria. A basic eighth degree algorithm is also obtained and applied using a variety of eighth degree criteria. In general the problem of writing a basic algorithm for all symmetric criteria of any specified degree reduces to the problem of maximizing a trigonometric polynomial of degree one-fourth that of the criteria.This research was supported by the Bell Telephone Laboratories, Murray Hill, New Jersey and NIH Grant FR-3.