In this project, we have examined how handwritten number recognition could be performed with neural networks and PCA. The data were obtained from an online database collected by the NIST; the pre-processing and segmentation allowed us to focus on the classification methods. A 50-unit neural network trained with the conjugate-gradient method was found to have the best overall performance (6.95% test error, 2.85% training error). Contrary to our prediction of better accuracy of larger networks (150 and 300 units) on the training data, the big units performed relatively poorly overall because prohibitively long training times prevented the networks from converging to output low error values.
The PCA method, which was implemented as a reference to the NNs, did best when greater than 23 principal eigenvectors were used (14% test error); the performance was probably limited due to the inability of our clustering method to take the between-class overlap into account. We expect that improving this should help PCA achieve the same quality as the neural nets did.
One modification which could be added to both systems is a rejection mechanism designed to eliminate overly ambiguous data. For the neural nets, this could be done by imposing threshold limits on the outputs and not accepting images which do not meet the thresholds. For the PCA, the distance to the closest mean could be used as a threshold, so that if an image is ``far'' from all the centroids it is not classified.