Local linear Laplacian eigenmaps: A direct extension of LLE

The local linear embedding (LLE) and Laplacian eigenmaps are two of the most popular manifold learning approaches since they can perform much faster than the other approaches. However, the LLE is sensitive to local structure and noises and the Laplacian eigenmaps, though more robust, cannot model and retain local linear structures. In this paper, a direct extension of LLE, called local linear Laplacian eigenmaps (LLLE), is proposed. Unlike the LLE, LLLE finds multiple local linear structures. Unlike the Laplacian eigenmaps, the LLLE uses P artificial neighbors to construct the adjacency graph for reconstruction. The LLLE is as efficient as the LLE and Laplacian eigenmaps. The experimental results indicate that it can model the local linear structures and is robust.