基于边界检测的多流形学习算法  

Multi-manifold Learning Based on Boundary Detection

作　　者：邹鹏[1] 李凡长[1] 尹宏伟[1] 张莉[1] 张召[1] 

机构地区：[1]苏州大学计算机科学与技术学院,苏州215006

出　　处：《模式识别与人工智能》2016年第11期1037-1047,共11页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.61033013;60775045);苏州大学东吴学者计划(No.14317360)资助~~

摘　　要：已知流形学习算法都假设数据分布于一个单流形,而现实中大部分数据都分布在多流形上,因此限制算法的实际应用.基于此种情况,文中提出基于边界检测的多流形学习算法,通过检测流形的边界处理分布于多流形的数据,并且可以较好地保持流形内、流形间的测地距离.算法首先检测流形边界,再分别降维处理各流形,最后将各低维坐标重置于一个全局坐标系中.在人工数据集和真实数据集上的对比实验表明文中算法的可行性和有效性.In manifold learning algorithms, the data are assumed to be aligned on a single manifold. The application of algorithms is limited due to the general distribution of practical datasets on multiple manifolds. In this paper, multi-manifold learning based on boundary detection （MBD） is proposed. By the proposed method, data of distribution on several manifolds are efficiently learned through boundary detection and intra and inter manifolds geodesic distances can be kept faithfully. Firstly the boundary of data manifolds is detected and then the dimensionality of the manifolds is reduced separately. Finally, low dimensional coordinates are relocated into a global coordinate system. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated through experiments on both synthetic and real datasets.

关 键 词：多流形学习 边界检测 测地距离 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]