仿射不变的自适应局部线性嵌入

目的: 为将流形学习有效应用于图像的降维与识别中，并消除图像的仿射变换对流形结构产生的影响，本文提出一种仿射不变的自适应局部线性嵌入算法。方法: 该算法在局部线性嵌入的基础上，为适应产生各种仿射变换的图像样本，引入切线距离计算各样本之间的相似程度，以此描述样本空间中的距离，并通过图像相似度函数自适应计算样本空间中每一点的邻域数量。结果: 实验结果表明，该算法能够构造出更合理的低维流形结构，并有效提升统计识别的正确率。结论: 本文算法对仿射变换不敏感，表现出更强的稳健性。

Affine invariant adaptive locally linear embedding

Objectives: In order to apply the manifold learning approach to image dimension reduction and recognition, an affine invariant adaptive locally linear embedding algorithm is proposed. Methods: Tangent distance is introduced and combines with locally linear embedding. In sample space, distance is described by affine invariant image similarity based on tangent distance method. The neighborhood size of every point in sample space is computed adaptively by similarity function. Results: Experimental results show that the proposed algorithm is able to create low dimensional manifold structure more reasonably, and improve the recognition rate. Conclusions: The proposed algorithm is insensitive to affine transformation and performs more robust.