局部线性嵌入算法及其稳定性实现

局部线性嵌入(locally linear embedding,LLE)算法是一种非常有效的非线性数据降维算法,广泛应用于机器学习、数据挖掘、模式识别等领域。它通过两次局部最小化实现对高维数据的非线性降维。首先给出了LLE算法关键步骤的理论实现,然后对LLE算法降维效果进行验证,最后在非均匀采样数据集上,分别验证了LLE算法的邻域点稳定性和数据点采样稳定性,有效地验证了LLE算法作为非线性降维算法的良好性能。

Local Linear Embedding Algorithm and Its Validations of Stability

The Local Linear Embedding（LLE） is an effective nonlinear dimensional reduction algorithm and is used for machine learning, data mining and pattern recognition. It performs nonlinear dimensional reduction of high dimensional data by twice local minimization. The paper implements the theorem of LLE and then validates the performances of LLE in both uniformed and non-uniformed sampling situations. In the non-uniformed sampling datasets, we validate the robustness of LLE to neighborhood selection and data sampling respectively. All of these indicate the good performance of LLE as a nonlinear dimensional reduction.