针对图像识别中传统的嵌入流形算法通常只考虑切线空间却忽略了流形结构以致不能准确建模的问题，提出一种基于关系型发散的黎曼流形分类（RMC）算法。首先从底层黎曼流形建立训练集，并在流形上建立一组表示黎曼点的参考点；然后，借助于最近提出的斯坦因发散计算黎曼点与各个类之间的相似性，从而有效地将流形分类问题转换成寻找合适的相似空间问题；最后，利用经典的线性判别分析进行特征提取，最近邻分类器完成最终的分类、识别。通过纹理分类、人脸识别、人体识别实验验证了所提算法的有效性及高效性。实验结果表明，相比其他几种较为先进的流形算法，提出的算法不仅提高了识别率，同时大大减少了训练、分类所耗时间，有望应用于实时图像识别系统。%For the issue that traditional embedded manifold algorithms usually only consider tangent space but ignoring manifold structure which will cause the inaccurate modelling,we propose a relational divergence-based Riemannian manifold classification (RMC)algorithm. First,it creates the training set from underlying Riemannian manifold on which a group of reference points representing Riemann point will be set up.Then,it calculates the similarities between Riemann point and each class by Stein divergence proposed recently,therefore effectively converts the manifold classification to finding the suitable similarity space.Finally,it uses typical linear discriminant analysis to extract features and uses nearest neighbour classifier to complete the eventual classification and recognition.The effectiveness and high efficiency of the proposed algorithm are verified through experiments on texture classification,face recognition and body identification.Experimental results show that the proposed algorithm improves recognition accuracy and reduces total times consumed in training and classification comparing with several other advanced manifold algorithms,which indicates that it is hopefully to be applied in real-time image recognition systems.
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