Manifold Regularized Convolutional Neural Network

The state-of-the-art performance of deep learning models is achieved at the expense of large data sets, computational costs, and overcoming the overfitting problem. These requirements may be alleviated by complementing the learning of network parameters with representational features obtained via manifold learning. This paper investigates the effect of regularizing convolutional neural networks (CNN) with a nonlinear embedding of convolutional response features. A locally linear embedding (LLE) is used to learn the manifold of the convolutional features before the fully connected network performs image classification tasks. Our six experimental cases reveal consistent benefits of introducing manifold regularization over using a baseline CNN model in image classification tasks. After several epochs of training, we introduce the manifold regularization in the objective function after stopping the update of the lowest convolutional layer parameters, which yields the best areas under the receiver operating characteristic curves (AVC) with the CIFAR natural image data set (AVC: 0.920) and a medical imaging data set for macular disease classification (AVC: 0.993) when compared to their performances with the baseline CNN model without manifold regularization (AVC: 0.899 and AVC: 0.975), respectively. The performance improvement over the baseline CNN model is observed across all individual object classification, and it additionally recommends an early stopping of the lowest convolutional layer parameter updates during model training. The performance improvement observed in both global shape (object classification) and local disease pattern (medical imaging) classification is promising to guide the development of more efficient alternatives to regular deep parameter learning.