Manifold Learning of Vector Fields

In this paper, vector field learning is proposed as a new application of manifold learning to vector field. We also provide a learning framework to extract significant features from vector data. Vector data containing position, direction and magnitude information is different from common point data only containing position information. The algorithm of locally linear embedding (LLE) is extended to deal with vector data. The learning ability of the extended version has been tested on synthetic data sets and experimental results demonstrate that the method is very helpful and promising. Manifold features of vector data obtained by learning methods can be used for next work such as classification, clustering, visualization, or segmentation of vectors.