融合LLE和ISOMAP的非线性降维方法

Nonlinear dimensionality reduction method by fusing LLE and ISOMAP

局部线性嵌入(LLE)和等距映射(ISOMAP)在降维过程中都只单一地保留数据集的某一种特性结构,从而使降维后的数据集往往存在顾此失彼的情况。针对这种情况,借助流形学习的核框架,提出融合LLE和ISOMAP的非线性降维方法。新的融合方法使降维后的数据集既保持着数据点间的局部邻域关系,也保持着数据点间的全局距离关系。在仿真数据集和实际数据集上的实验结果证实了该方法的优越性。

LLE（local linear embedding） and ISOMAP （Isometric map） only preserved one specific feature of the data sets during the dimensionality reduction process, and ignored other meaningful features. So the features of the original data sets could not be preserved as well as possible after dimensionality reduction. This paper proposed a new method that could better solve this problem. This method could preserve both the neighborhood relationships and the global pairwise distances of the high-dimensional data sets. Experiments on both artificial and real data sets prove effectiveness of the proposed method.