Local coordinates alignment (LCA): a novel manifold learning approach

Manifold learning has been demonstrated as an effective way to represent intrinsic geometrical structure of samples. In this paper, a new manifold learning approach, named Local Coordinates Alignment (LCA), is developed based on the alignment technique. LCA first obtains local coordinates as representations of local neighborhood by preserving proximity relations on a patch, which is Euclidean. Then, these extracted local coordinates are aligned to yield the global embeddings. To solve the out of sample problem, linearization of LCA (LLCA) is proposed. In addition, in order to solve the non-Euclidean problem in real world data when building the locality, kernel techniques are utilized to represent similarity of the pairwise points on a local patch. Empirical studies on both synthetic data and face image sets show effectiveness of the developed approaches