基于流形学习的泛化改进的LTSA算法

在数据稀疏、数据非均匀分布和数据流形具有较大曲率的情况下，传统的局部切空间方法不能够有效地揭示流形结构。提出了一种泛化的ILTSA（GILTSA）流形学习方法，该方法以改进的局部切空间排列算法（ILTSA）为基础，在解决流形结构问题的同时，不仅能够获得用于人脸识别更好的低维特征，而且能有效地处理日益增加的数据集的问题。该方法首先基于样品间距离选择近邻集，实现训练集的低维流形，为每个新样本寻找最近的样本训练集。然后结合ILTSA算法，根据其最近样本投影距离计算低维流形。在ORL的人脸图像数据库的实验、Swiss roll和手书的“2”等实验结果表明，与局部线性嵌入和局部切空间排列算法等相比，GILTSA方法增加了整体精度。

Generalized improvement of LTSA algorithm based on manifold learning

In the case of data sparse and data non-uniform distribution and data manifold with large curvature, the conventional local tangent space arrangement method can not reveal the manifold structure effectively. In this paper, a Generalized ILTSA（GILTSA）manifold learning is proposed. The method is based on the Improved Local Tangent Space Arrangement（ILTSA）algorithm. In solving the problem of manifold structure, it can not only obtain the low dimensional feature for face recognition, but also can deal with the problem of increasing data set. Firstly, on the basis of the nearest distance between the neighbor sets to select sample, the proposed method can get the low dimensional manifold of the training set to search for the nearest training sample set of each new sample. Then combined with ILTSA algorithm, it calculates low-dimensional manifolds according to its nearest sample projection distance. The experiments are tested on face database ORL, Swiss roll and the handwritten “2” images. The results show that the proposed GILTSA method increases the overall accuracy in comparison with correlated local linear embedding and local tangent space alignment algorithm.