针对非连通流形数据降维的过渡曲线方法

针对位于非连通流形上的数据的特征提取是流形学习领域的一个公开问题,分解-整合算法是目前处理此问题的最有效的方法.然而,此算法的最大局限是边缘问题,即当不同类间的最短距数据对位于相应类内而非类边缘时,算法往往表现异常.针对这一关键问题,提出了一种解决方法——过渡曲线方法.其主要思想为,通过构建连接不同类边缘最短距数据对间的平滑过渡曲线以使流形类间的连接关系更为有效,进而使得数据的全局形态在低维空间中能够更好地保持.一系列人工与图像数据集上的实验结果表明,过渡曲线方法的表现明显优于分解-整合算法,特别是,边缘问题得到了解决,这极大地扩展了分解-整合算法的应用范围.

Transition Curve Method for Dimensionality Reduction of Data on Disconnected Manifold

Feature extraction of data lying on disconnected manifold is an open problem in the field of manifold learning, and decomposition-composition (D-C) algorithm is the most effective method so far to deal with this problem. However, the biggest limitation of D-C method is edge problem, that is when the nearest data points of different clusters are located in the inner part instead of the edge part of the corresponding cluster, D-C method always behaves poorly. To tackle this key issue, a method, called transition curve method, is presented in this paper. The main idea of the method is to make all clusters on the underlying manifold connect more effectively by constructing smooth transition curves which connect the nearest edge points of different clusters, and in this way the global shape of the data can be preserved better in the low-dimensional space. Experimental results on a series of synthetic and image data sets verify that the transition curve method performs evidently better than D-C method. Particularlly, the edge problem is alleviated. In this way, the application scope of D-C method is expanded remarkably.