基于双度量约束的拉普拉斯特征映射

Laplace Characteristic Mapping Based on Double Measure Constraint

针对传统的拉普拉斯特征映射(LE:Laplacian Eigenmaps)算法采用欧氏距离度量样本点之间的位置关系只适用于线性数据集,但实际工程中的数据常表现出强烈的非线性导致最终的嵌入结果难以反映出原始数据的本质特征问题,提出了一种基于双度量约束的拉普拉斯特征映射(D-LE:Double metric constraint Laplace Eigenmaps)的算法。该算法采用余弦相似性评估样本间的相似性,并融合样本间以及样本与局部流形的度量关系,构建降维模型。通过在3个轴承数据集上进行实验,实验结果表明,该方法对处理非线性数据集能明显提高降维效果。

The traditional LE(Laplacian Eigenmaps)algorithm uses Euclidean distance to measure the position relationship between sample points,which is only applicable to linear data sets.However,the data in practical engineering often show strong non-linearity,which makes the final embedding results difficult to reflect the essential characteristics of the original data.An algorithm for D-LE(Double metric constraint Laplace Eigenmaps)based on Double metric constraint is proposed.The algorithm uses cosine similarity to evaluate the similarity between samples,and combines the measurement relations between samples and between samples and local manifolds to build dimensionality reduction model.Experiments on three bearing datasets show that this method can significantly improve the dimensionality reduction effect for processing nonlinear datasets.