Uncertainty handling in convolutional neural networks

The performance of convolutional neural networks is degraded by noisy data, especially in the test phase. To address this challenge, a new convolutional neural network structure with data indeterminacy handling in the neutrosophic (NS) domain, named as Neutrosophic Convolutional Neural Networks, is proposed for image classification. For this task, images are firstly mapped from the pixel domain to three sets true (T), indeterminacy (I) and false (F) in NS domain by the proposed method. Then, NCNN with two parallel paths, one with the input of T and another with I, is constructed followed by an appropriate combination of paths to generate the final output. Here, two paths are trained simultaneously, and neural network weights are updated using back propagation algorithm. The effectiveness of NCNN to handle noisy data is analyzed mathematically in terms of the weights update rule. Proposed two paths NS idea is applied to two basic models: CNN and VGG-Net to construct NCNN and NVGG-Net, respectively. The proposed method has been evaluated on MNIST, CIFAR-10 and CIFAR-100 datasets contaminated with 20 levels of Gaussian noise. Results show that two-path NCNN outperforms CNN by 5.11% and 2.21% in 5 pairs (training, test) with different levels of noise on MNIST and CIFAR-10 datasets, respectively. Finally, NVGG-Net increases the accuracy by 3.09% and 2.57% compared to VGG-Net on CIFAR-10 and CIFAR-100 datasets, respectively.