基于鲁棒等度规特征映射的非线性降维算法

摘要

Isomap is one of the representative techniques of nonlinear dimensionality reduction.It extends classical multidimensional scaling by considering approximate geodesic distance. However,Isomap is sensitive to noise because the approximate geodesic distance is constructed on the basis of Euclidean distance. In this paper,a kernel-induced distance metric defined in the feature space is introduced instead of the Euclidean distance to evaluate the geodesic distance and construct the corresponding neighborhood graph. The resulting algorithm is robust against noise. Numerical experimental results with noisy Swiss roll data and face image set confirm the validity and high performance of this kernel-induced distance Isomap.%采用核方法在特征空间推导出一类异于欧氏距离的新度量,代替等度规特征映射 (Isomap)中的对噪声敏感的欧式距离,用新度量构造测地距离和相应的最小近邻图,提高Isomap算法的抗噪声能力.利用含噪声的Swiss roll数据和人脸图像数据进行实验验证,结果表明这种基于核特征空间的测地距离具有较强的鲁棒性.