To demonstrate the working of the recall algorithm, it was tested on two synthetic pattern distributions, a noisy sine wave and a noisy circle. For both distributions, the mixture of local PCA was gained by using the algorithm MPPCAext (section 3.3). However, the alternative algorithm NGPCA (section 3.2) could have been also used; the results were similar.
The sinewave distribution is composed of 800 points. The mixture model contained nine ellipses with two principal components each. Figure 4.3 shows the result of the recall if the xcoordinate was given. The recall is locally linear and discontinuities occur between the changes from one ellipse to the next. On a global scale, the sinewave is correctly restored.

The second test illustrates the two advantages over feedforward networks, like multilayer perceptrons. The distribution consists of 1000 points arranged in a noisy circle with radius 1.0 (figure 4.4). It was approximated by six ellipses with two eigenvectors each. Figure 4.4 shows the results of the recall for two different directions ( x y and y x) using the same mixture of local PCA. The mapping in both directions is redundant (onetomany). Nevertheless, the algorithm finds a valid solution that lies on the distribution of training patterns for input values in the training domain. Here, the solution jumps between the two semicircles. In contrast, a multilayer perceptron would average over redundant solutions, and thus, it would learn to produce a line going through the middle of the circle.
