Manifold learning and manifold alignment based on coupled linear projections

Traditional manifold learning mainly deals with data dimensionality reduction problems from a single manifold.Through further development,manifold learning focusing on the multi-manifold has drawn the attention of many scholars.An algorithm of manifold alignment based on coupled projections was proposed.The proposed method using the coupled linear projections dealt with an out-of-sample data set without re-training.Compared to other linear methods,it handled some real problems of manifold alignment with flexibility since the proposed method did not need any assumptions about the relationship of affine transformation between the manifolds.