The Regression of MNIST Dataset Based on Convolutional Neural Network.

The MNIST dataset of handwritten digits has been widely used for validating the effectiveness and efficiency of machine learning methods. Although this dataset was primarily used for classification and results of very high accuracy (99.3%+) on it have been obtained, its important application of regression is not directly applicable, thus substantially deteriorates its usefulness and the development of regression methods for such types of data. In this paper, to allow MNIST to be usable for regression, we firstly apply its class/label with normal distribution thereby convert the original discrete class numbers into float ones. Modified Convolutional Neural Networks (CNN) is then applied to generate a regression model. Multiple experiments have been conducted in order to select optimal parameters and layer settings for this application. Experimental results suggest that, optimal outcome of mean-absolute-error (MAE) value can be obtained when ReLu function is adopted for the first layer with other layers activated by the softplus functions. In the proposed approach, two indicators of MAE and Log-Cosh loss have been applied to optimize the parameters and score the predictions. Experiments on 10-fold cross-validation demonstrate that, desired low values of MAE and Log-Cosh error respectively at 0.202 and 0.079 can be achieved. Furthermore, multiple values of standard deviation of the normal distribution have been applied to verify the applicability when data of label number at varied distributions is used. The experimental results suggest that a positive correlation exists between the adopted standard deviation and the loss value, that is, the higher concentration degree of data will contribute to the lower MAE value.