Topo-Loss: A Novel Loss Function for Learning Multiple Manifold Structures in Image Classification with Deep Neural Networks

abstract-The real data distribution of a specific category tends to approach a low-dimensional manifold in the Riemannian space, and the manifolds of different categories do not intersect in high-dimensional space. However, existing loss functions used for image classification ignore the inherent manifold structure between samples, resulting in limited network performance. In this paper, we reveal that maintaining the manifold structure between samples while extracting features can significantly improve the efficiency of neural networks in image classification tasks and propose a novel loss function called Topo-Loss. Topo-Loss is calculated by a dual-branch structure network. One of the branches is used to calculate the cross-entropy loss, and the other branch is used to get the cosine loss between the local geodesic distance of samples in the feature space and it in the original space. The optimization goal of the network is to minimize the weighted sum loss of the two branches, thus allows the neural network to maintain the manifold structure between samples during the feature extraction. The visualization experiments show that the DNN gains the ability to learn multiple manifolds with Topo-Loss simultaneously, significantly improving the network’s performance in image classification. Meanwhile, our work outperforms other similar works.