Similarity Measure for Vector Field Learning

Vector data containing direction and magnitude information other than position information is different from common point data only containing position information. Those general similarity measures for point data such as Euclidean distance are not suitable for vector data. Thus, a novel measure must be proposed to estimate the similarity between vectors. The similarity measure defined in this paper combines Euclidean distance with angle and magnitude differences. Based on this measure, we construct a vector field space on which a modified locally linear embedding (LLE) algorithm is used for vector field learning. Our experimental results show that the proposed similarity measure works better than traditional Euclidean distance.