Finally 2.1 Face and Orientation Discrimination 2 the Factor Analysis Network

, we have shown that this method is appropriate for clustering face data when such a data set is taken from a number of individuals in a number of diierent poses. The network learns to create lters of the data set such that both the identity of the individual can be recognised and his/her pose also identiied. Future work will investigate larger data sets and diierent numbers of lters per person. References 1] D. Charles and C. Fyfe. Modelling multiple cause structure using rectiica-tion constraints. 9 Figure 6: The test results when a network of 5 output neurons were tested on 1 set of 20 images of 1 face. The third row shows the lters found when using the-insensitive training rule with =0.05 the fth row shows the lters found when =0.1, and the seventh when =0.3. We see that the last nds the most complete lters, however unlike the results based on the quadratic cost function, some interference from non-similar poses is found. The top row shows the image used to test the network's reactions. Rows 2, 4 and 6 show the neurons activations in each case when presented with this face. 8 Figure 5: The test results when a network of 50 output neurons were tested on 10 faces. The top row shows 3 images not used in training, the middle row shows the outputs' responses to these inputs and the bottom row shows the weight vectors of the highest responding neurons. In each case, the individual was correctly identiied as was his/her pose. each case when presented with this face; again the identiication is less clear cut. Now this is not to say that the noise on the face data is Gaussian, however the assumption of Gaussian noise from which the quadratic cost function may be derived, is suuciently robust that the derived rules perform well on all data sets. 3 Conclusion In this paper, we have derived a new learning rule based on knowledge of the probability density function of the noise in the data set. The new rule is extremely simple and performs well on the data set for which it was speciically designed. We have compared the use of two diierent cost functions on both real and artiicial data; on the artiicial data, the-insensitive learning rule performs well since the pdf of the noise approximates that pdf to which this learning rule is best …