一种基于局部保持的子流形可视化方法

A VISUALISATION METHOD FOR SUBMANIFOLDS BASED ON LOCALITY PRESERVING

针对多数流形学习算法是基于单一流形的假设,当高维数据集中存在多个流形,流形学习算法可视化效果差问题,借鉴流形曲面在二维平面空间展开的思想提出基于局部保持的的子流形可视化方法。利用奇异值分解和k均值聚类方法将流形数据划分为多块子流形,计算第一流形切块中心与其余切块中心的拓扑结构关系,在目标低维空间保持上述中心间拓扑结构下逐一对流形切块投影展开,最后在人脸数据集上进行实验。实验结果表明:该方法较好保持了子流形内的数据间的拓扑结构。

Majority of the manifold learning algorithm are based on the assumption of single manifold,when the high dimensional data con-centrate in more than one manifold,the visual effect of the manifold learning algorithm becomes worse.Aiming at this problem and learningfrom the idea of expanding the manifold surfaces in two-dimensional flat space,we propose a locality preserving-based submanifold visualisa-tion method.It divides the manifold data into multi-block submanifolds using singular value decomposition and k-means clustering method,calculates the topology relationship between the centre of the first diced manifold block and the centres of the remaining blocks,and projectsthe diced manifold blocks one by one followed by expansion while maintaining the above topology structure between the centres in targeted low-dimension and targeted space;at last,the experiment is conducted on face data-sets.Experimental results demonstrate that this method betterkeeps the topology structure between the data in submanifolds.