中文摘要：

局部线性嵌入（Locally linearembedding，LLE）算法通过局部线性来逼近全局的非线性，优点在于可保持降维前后样本点近邻之间的线性结构不变，并且计算速度较快。但是该算法对近邻值的选择十分敏感，不同近邻点数的选择对降维效果影响较大。针对此问题，利用残差作为评价降维前后保持样本距离信息优劣的指标，提出一种改进的可变近邻局部线性嵌入（Variable K-nearest neighbor locally linear embedding, VKLLE）算法，即通过给定一个最大近邻数目值，比较降维前后的残差值，根据较小值选择最优的近邻点数，从而使得每个样本点的近邻点数可据残差值进行调整。通过对手写体数字（Mixing national institute of standards and technology, MNIST）数据集的仿真分析，并与LLE算法进行比较，此方法降维效果更好，计算复杂度也明显降低。最后将该算法运用于轴承状态识别，取得了较好的效果，同时还有效地提高了分类性能和稳定性。

英文摘要：

Locally linear embedding （LLE） can be used to approximate the global non-linearity via local linearity, and it has the advantages of preserving the data structure after dimension reduction, and short time cost for calculation. However, it is sensitive to the number of nearest neighbors, which affects the performance on dimension reduction. Therefore, a variable K-nearest neighbor local linear embedding algorithm is proposed based on the value of residual error before and after dimension reduction, which can be regarded as a measure of data structure preservation. For a given maximum value of the nearest neighbor number, the optimal number of nearest neighbors can be selected according to the smaller residual error, which making the number of nearest neighbors of each sample adjustable. Simulation analysis of the mixing national institute of standards and technology（MNIST） data sets verified the effectiveness and accuracy of the proposed approach, and the computational complexity is decreased. Experiment on bearing vibration signal analysis also demonstrates that the method can provide a better representation after dimension reduction and improve the classification.