Implicit Data Augmentation On Grassmann Manifolds And Its Applications

Action recognition has wide application in our life,and recognition method based on Grassmann manifolds is a classification method utilizing linear subspaces on Grass-mann manifolds to represent action sequences,which has achieved success in variant action-recognition tasks.To handle subspace data,different metrics have been proposed to describe the similarity between subspaces and are used with different classifiers in action recognition,e.g.,support vector machines with projection metric.Although ex-isting Grassmann-based methods could recognize actions accurately,they mostly ig-nore the instability of subspaces in representing action sequences,which might cause the learning of classifiers to be misled by the disturbances of subspaces.Besides,in learning,there exist cases when few action data are available for training or significant testing noise is encountered.They will cause classifiers fail to sufficiently learn or accu-rately predict data patterns through limited training.These problems will finally lower action-recognition accuracy.To address this problem,this paper extends the data augmentation method in lin-ear spaces to Grassmann manifolds,increasing noise samples in training,keeping a low computation complexity,and improving the robustness of classifiers with respect to noise.Concerning the nonlinear characteristics of Grassmann manifolds,this paper makes use of the projection mapping to obtain an isometric expression of subspaces.It,therefore,makes the extensions of previous implicit data augmentation to Grass-mann manifolds straight.However,when the data dimensionality is high,the efficiency of using projection mapping is relatively low.Thus,through the dual optimization of subspace-disturbance-involved objective function,a disturbance Grassmann kernel method is proposed in this paper,which owns lower computation costs,when applying the same projection mapping.The major contributions of this paper are summarized as:(1)Distinguished from traditional discriminative learning on Grassmann manifolds,this paper considers subspace disturbances of variant Grassmann manifolds,im-plicitly add such disturbances in learning to improve the accuracy of action recog-nition,and utilize the properties of subspace representations to choose disturbance parameters automatically by Bayesian method.(2)According the idea of implicit data augmentation methods and dual optimization,a novel disturbance Grassmann kernel is proposed in this paper which has an analytic form depending on the characteristics of kernel functions the forms of disturbance distributions.(3)According to disturbance distributions on the Grassmann manifold(pseudo-Gaussian and Dirichlet distributions)and Grassmann kernels(projection kernels and tan-gent bundle kernels)simple disturbance Grassmann kernels are derived,and the connection between the two subspace disturbances and data noise are analyzed.(4)Experiments on different data sets under different hardness and noise are done in this paper,which demonstrates the robustness of the proposed methods in general,low-latency,multiple-view or noise-action-appended cases.