标架丛上的多流形联络学习算法

Multi-manifold Connection Learning Algorithm Based on Frame Bundle

传统的流形学习算法通常需要较多的训练样本,将所有样本看作一个流形进行学习,并提取判别特征以进行后续的分类等具体应用.然而在很多实际问题中,并不能获得大量的训练样本,因此存在很多只有一个训练样本的情况.文中提出标架丛上联络学习算法,构建出多流形结构,提取出流形与流形间以及单一流形内的判别信息处理样本少的情形.在处理多流形结构数据集时,利用标架丛上的横空间和纵空间学习模型,将高维空间数据投影到横空间以最大化流形与流形间的间隔,同时又在纵空间中保持同一流形内数据的相关结构.最后通过实例验证了本文算法的有效性.

Traditional manifold learning methods need a large number of training samples. All samples are regarded as a manifold and then discriminative features are extracted for practical application such as classification. But in many situations, only one sample is existed during the training phase since there are not enough training samples. Therefore, frame bundle connection learning method is presented and a multi-manifold structure is constructed. Besides, intermanifold and intramanifold features are extracted to get more discriminative information to solve the problem. When dealing with the multi-manifold structure, learning models of two subspaces based on frame bundle are used to project the data in high-dimensional space to horizontal space for maximizing margins of different manifolds. Simultaneously, the data structure is maintained with the same manifold in the vertical space. Finally, a simulation experiment is presented to prove the validity of the proposed algorithm.