Existing manifold learning algorithms use Euclidean distance to measure the proximity of data points. However, in high-dimensional space, Minkowski metrics are no longer stable because the ratio of distance of nearest and farthest neighbors to a given query is almost unit. It will degrade the performance of manifold learning algorithms when applied to dimensionality reduction of high-dimensional data. We introduce a new distance function named shrinkage-divergence-proximity (SDP) to manifold learning, which is meaningful in any high-dimensional space. An improved locally linear embedding (LLE) algorithm named SDP-LLE is proposed in light of the theoretical result. Experiments are conducted on a hyperspectral data set and an image segmentation data set. Experimental results show that the proposed method can efficiently reduce the dimensionality while getting higher classification accuracy.
© 2008 Chinese Optics Letters
Qin Luo, Zheng Tian, and Zhixiang Zhao, "Shrinkage-divergence-proximity locally linear embedding algorithm for dimensionality reduction of hyperspectral image," Chin. Opt. Lett. 6, 558-560 (2008)