An Analytical Mapping for LLE and Its Application in Multi-Pose Face Synthesis

Locally Linear Embedding (LLE) is a nonlinear dimensionality reduction method proposed recently. It can reveal the intrinsic manifold of data, which can’t be provided by classical linear dimensionality reduction methods. The application of LLE, however, is limited because of its lack of a mapping between the observation and the low-dimensional output. In this paper, we propose a method to establish an analytical mapping for LLE and validate its efficiency with the application in multi-pose face synthesis. Furthermore, through learning the similarity for the same kind of pose change mode of different persons, we generalize our method to small set cases with methods of statistical learning theory. The experiments of multi-pose face synthesis on small sets prove that our idea and method are correct.