The back-propagation (BP) algorithm is usually used to train convolutional neural networks (CNNs) and has made greater progress in image classification. It updates weights with the gradient descent, and the farther the sample is from the target, the greater the contribution of it to the weight change. However, the influence of samples classified correctly but that are close to the classification boundary is diminished. This paper defines the classification confidence as the degree to which a sample belongs to its correct category, and divides samples of each category into dangerous and safe according to a dynamic classification confidence threshold. Then a new learning algorithm is presented to penalize the loss function with danger samples but not all samples to enable CNN to pay more attention to danger samples and to learn effective information more accurately. The experiment results, carried out on the MNIST dataset and three sub-datasets of CIFAR-10, showed that for the MNIST dataset, the accuracy of Non-improve CNN reached 99.246%, while that of PCNN reached 99.3%; for three sub-datasets of CIFAR-10, the accuracies of Non-improve CNN are 96.15%, 88.93%, and 94.92%, respectively, while those of PCNN are 96.44%, 89.37%, and 95.22%, respectively.
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