基于几何距离摄动的局部切空间排列算法

LTSA algorithm based on geometric distance perturbation

局部切空间排列算法(Local Tangent Space Alignment)是一种具有严格数学推理的流形学习算法,能有效地学习出高维数据的低维嵌入坐标,但也存在一些不足,如对近邻点的选取依赖性较强、不适应处理高曲率分布、稀疏分布数据源。针对这些缺点,提出了一种基于几何距离摄动的局部切空间排列算法。利用几何摄动条件把样本空间划分为一组线性分块的组合,在每一个线性块上应用LTSA算法完成降维。实验结果表明了该算法的有效性。

LTSA（Local Tangent Space Alignment） is a manifold learning algorithm with strict mathematical reasoning.It is et＇- ficient for many nonlinear dimension reduction problems but unfit for sparse and high curvature source data.In order solve the problem, an LTSA algorithm based on geometric distance perturbation is presented.The original datasets have been set into some maximal linear patch according to the geometric distance perturbation.The LTSA will be applied to this maximal linear patch to complete the embedding dimensional-reduction.Experiment result validates the effectiveness of the algorithm.