关键词: 维数约简, 黎曼流形学习, 低维嵌入, 法坐标, 权值

Abstract: An improved algorithm of preserving global and local properties based on Riemannian Manifold Learning (RML) was proposed, which could solve the problem that RML cannot reserve the local geometry property of neighbor data. In the algorithm, all points were projected by Principal component analysis (PCA) firstly, and then a neighbor graph was constructed. The most important step was that all data points were classified into two parts, for the k neighboring nodes of a base point, it adopted a weight which can preserve local property of the base point and neighboring nods to get the low-dimensional embedding coordinates. As for the other points, the RML algorithm was still used. Thus the new algorithm could both preserve the metrics at all scales and keep the geometrical property of local neighbor to the maximum. The experimental results demonstrate the validity and real-time quality.

Key words: dimensionality reduction, Riemannian Manifold Learning (RML), low-dimensional embedding, normal coordinate, weight