Abstract: The pooling operation in convolutional neural networks can achieve the scale invariance of
image transformations, and has better robustness to noise and clutter. In view of the problem that
pooling operation ignores the energy information hidden in the image when it extracts local features for
image recognition, according to the relationship between energy of the image and singular value of the
matrix, and taking into account the image information of the energy mainly concentrates on the larger
singular value, a pooling method based on matrix 2-norm was proposed. The former feature map of
convolutional layer is divided into several non-overlapping sub blocks, and then singular value of the
matrix is calculated. The maximum value is used as the statistical results of each pooling region.
Various numerical experiments has been carried out based on Cohn-Kanade, Caltech-101, MNIST and
CIFAR-10 database using different kinds of pooling method. Experimental results show that the
proposed method is superior in both recognition rate and robustness compared with other methods.

Key words: deep learning, convolutional neural networks, matrix 2-norm, pooling, singular value