基于随机投影的正交判别流形学习算法

Manifold Learning Algorithms of Orthogonal Discriminant Based on Random Projection

提出一种基于流形距离的局部线性嵌入算法,以流形距离测度数据间的相似度,选择各样本点的近邻域,解决了欧氏距离作为相似性度量时对邻域参数的敏感性.在MDLLE算法中引入最大边缘准则(maximum margin criterion,MMC)来构建最优平移缩放模型,使得算法在保持LLE局部几何结构的同时,具有MMC准则判别能力.通过正交化低维特征向量可消除降维过程中的噪声影响,进而提高算法的监督判别能力.由实验结果得到,所提出的方法具有良好的降维效果,能有效避免局部降维算法对邻域参数的敏感.随机投影独立于原始高维数据,将高维数据映射到一个行单位化的随机变换矩阵的低维空间中,维持映射与原始数据的紧密关系,从理论上分析证明了在流形学习算法中采用随机投影可以高概率保证在低维空间保持高维数据信息.

A kind of locally linear embedding algorithms based on manifold distance,MDLLE was proposed. The similarity between data can be could measured based on the manifold distance and the neighbor domain of the sample points can be selected. This could solve the neighborhood parameter sensitivity of the Euclidean distance in similarity measure. The maximum margin criterion（ MMC） is introduced in the MDLLE algorithm for constructing the optimal translation and scaling model. Thus,the algorithm both can both maintain local geometric structure of LLE and have discriminant ability of Maximum margin criterion. The low-dimensional feature vector of orthogonalization can eliminate noise effects in the process of dimension reduction,and improve the supervision and discriminant ability of the algorithm. The experimental result showed that this method had good dimension reduction effect and can effectively avoid sensitivity. Random projection is independent of the original high-dimensional data,which mapped the highdimensional data to a low-dimensional space of the random transformation matrix of line normalized. The theoretical analysis proved that the manifold learning algorithm of taking random projection could maintain high-dimensional data in low-dimensional space in high probability.