The handwritten numbers were obtained from an online database provided by National Institute of Standards and Technology(NIST). Some examples of the data are shown in Figure 1.
Figure 1: Some examples of the preprocessed data obtained from the
MNIST numeral set
Acquiring and preprocessing the images are no small tasks; the possibility and success of the classification methods is quite dependent on the quality of these steps. We used a 10 000-sample subset of the whole NIST database. 5 000 of the digits were obtained from Census Bureau employees and the rest were collected from high-school students. The data contained many different writing styles, which stemmed from the disparity of the sources. Numbers first had to be segmented; this is complicated by the fact that not all written digits are separated from their neighbors.
As can be seen from Figure 1, the final images are normalized to fixed size from the range that written numbers initially span. Final numbers are 28x28-pixel, 256 gray level images. Even in the limited set of examples shown, the variety of written numbers is apparent. This variety is the root of one of the challenges of automatic handwriting recognition. A measure such as the mean-squared error between two images would not be very informative because differences that should not affect the classification end up having a bad influence on the performance. Conversely, meaningful differences might end up not having enough influence. The classification methods used try to circumvent these problems by ``training'' on a large number of samples containing the various forms that numbers can appear in, for example the number ``2'' with a variety of lengths and angles of its lower horizontal line. Then, hopefully, if the training sample set was large enough and the learning system of sufficient complexity, we can induce or ``generalize'' to classify unseen examples.
The 28x28 number samples were reshaped into 784-element vectors, and the gray-scale values were normalized to lie in the range [-1,1].