Manifold Structure Neural Network Methods And Application Research

Traditional deep neural networks implicitly assume that the input data is in Euclidean space,but in many practical application scenarios,more data is in non-Euclidean high-dimensional space.In order to explore the inherent geometric structure in the data,geometric deep learning starts from the two directions of graph and manifold,and extends the traditional deep neural network from Euclidean space to non-Euclidean space.Research on deep neural networks based on graphs has received widespread attention in recent years,while research on deep neural networks based on manifolds is relatively rare.Based on these,this paper explores the structure of the deep manifold network,and conducts algorithms verification research on different tasks.The main contributions of this paper are:(1)An end-to-end manifold structure neural network model based on second-order pooling is proposed and applied to the tasks of smoke image classification and clothing image sets classification.This model is different from the step-by-step structure of existing methods,and can automatically convert Euclidean data into non-Euclidean Riemannian manifold data.This model first uses convolutional neural network to extract the feature information of smoke image and clothing image sets,then uses second-order pooling to model the feature information of Euclidean space as SPD manifold,and finally use Riemannian manifold network based on symmetric positive definite matrix to perform data classification.In this designed method,each process of data processing simultaneously optimizes parameters,and has achieved better results in comparison with multiple existing algorithms.(2)Aiming at the task of face verification based on image sets,a pseudo-Siamese manifold structure neural network model is proposed,which combines a Riemannian manifold network based on a symmetric positive definite matrix and a Riemannian manifold network based on a Grassmannian manifold to form the complementary between these two heterogeneous information.Through the metric learning of heterogeneous manifold data,the model can obtain better discrimination ability of face image sets.Firstly,the face image sets are modeled as symmetric positive definite manifold and Glassman manifold respectively.Then,the features of heterogeneous manifolds are learned by Riemannian manifold network based on symmetric positive definite matrix and Riemannian manifold network based on Grassmannian manifold.Then,the learned manifold features are mapped into Euclidean space respectively.Finally,the contrast loss function is applied to perform metric learning of the face image sets in the Euclidean space.Compared with other manifold methods,the proposed method achieves better results on two different face verification datasets,which provides a new idea for exploring the network structure of Riemannian manifold.