基于鲁棒的全局流形学习方法

非线性降维在数据挖掘、机器学习、图像分析和计算机视觉等领域应用广泛。等距映射算法(Isomap)是一种全局流形学习方法，能有效地学习等距流形的“低维嵌入”，但它对数据中的离群样本点缺乏鲁棒性。针对这种情况，该文提出一种离群点检测方法，基于Isomap的基本思想，给出一种鲁棒的全局流形学习方法，提高Isomap处理离群样本点的能力。数值实验表明了该方法的有效性。

Global Manifold Learning Approach Based on Robust

Nonlinear dimensionality reduction is applied to many research fields, including data mining, machine learning, image analysis, and computer vision. Isomap is a global manifold learning approach. It is effective for learning the embedding results of the Isometric manifold, but it is not robust against outliers in the data. This paper proposes an outlier detection algorithm, and gives a global manifold learning approach based on the basic idea of Isomap to make Isomap more robust against outliers. Numerical experiments show the method is effective.