Abstract: Locally Linear Embedding（LLE） algorithm is one of the nonlinear data dimensionality reduction approaches based on manifold learning. Considering the distribution of data points mostly present the heterogeneity, there will result in large amounts of information loss when LLE selects neighboring points. This paper proposes a novel locally linear embedding algorithm based on tightness of data points, named tLLE, which can reduce dimensionality effectively for the datasets that present the non-uniform distribution. And, it has better effects of dimensionality reduction than LLE. The embedding and classification results on synthetic and real data show that tLLE is very effective.

摘要： 局部线性嵌入算法（LLE）是流形学习中非线性数据降维的重要方法之一。考虑数据点分布大多呈现不均匀性，LLE对近邻点的选取方式将会导致大量的信息丢失。根据其不足，提出一种基于数据点松紧度的局部线性嵌入改进算法——tLLE算法，针对数据点分布不均匀的数据集，tLLE算法能有效地进行维数约简，且具有比LLE更好的降维效果。在人造数据和现实数据上的嵌入以及分类识别结果表明了tLLE算法的有效性。