Riemannian Manifold Metric Learning Based On Sample Pair Weighting And Selection

With the explosive growth of data and deep learning,data with high-order statistical features play an important role in computer vision tasks.Metric learning is a kind of machine learning algorithms that measures the similarity between samples based on the distance between samples.Traditional metric learning methods focus on the lowdimensional vector features of data samples.However,in recent years,some research works have shown that metric learning algorithms based on higher-order information statistic are generally superior to algorithms based on low-order statistic.Compared to low-order information,methods based on higher-order statistics can better preserve the structural information of the image.The metric learning method based on Riemannian manifold takes advantage of using manifold structure on high-order manifolds to learn a discriminative metric matrix.However,the existing metric learning methods only consider high-order information and ignores low-order information,which not effectively combine low-order information with high-order information.In addition,many algorithms treat the importance of sample pairs as consistent,while ignoring the differences between different sample pairs which the importance of sample pairs should be different.For metric learning,it is still difficult to achieve satisfactory results in the case where samples are insufficient.In order to solve the above problem,methods of metric learning based on Riemannian manifold are proposed from two aspects in this paper:joint metric learning on Riemannian manifold of global Gaussian distributions and a metric learning method based on human-machine cooperation.The main contributions and innovative work of this paper are shown as follows:Firstly,aiming at the Riemannian metric learning on Gaussian distribution,a joint metric learning method based on Gaussian distribution on Riemannian manifold metric learning is proposed.The distance between two Gaussians is defined as the sum of Mahalanobis distance between mean vectors and Log-Euclidean distance between covariance matrices.The model considers the first-order and second-order distance metrics,simultaneously,which effectively fuse the first-order and second-order complementary information.In addition,in order to select the sample pairs,the weights of the sample pairs embedded in the model,which aim to select the samples with the largest amount of information.Finally,method achieved the global closed-form solution by computing matrix geometric mean.Secondly,in order to utilize a large amount of unlabeled data,the model uses a human-machine cooperation strategy for data augmentation to improve the performance of metric learning.In addition,in order to guide the cooperation between expert and machine to label the unlabeled samples,a sample selection strategy based on probability and distance is proposed in this paper.For those samples with high confidence,the machine can label automatically.For samples with low confidence,the distance strategy is used to judge whether to perform manual labeling.Finally,the iterative approach enhance the model continually.Experimental results on five public datasets show that the strategy can effectively enlarge labeled samples from unlabeled samples and improve the effectiveness of the model.