Locally linear embedding: a survey

As a classic method of nonlinear dimensional reduction, locally linear embedding (LLE) is more and more attractive to researchers due to its ability to deal with large amounts of high dimensional data and its non-iterative way of finding the embeddings. However, several problems in the LLE algorithm still remain open, such as its sensitivity to noise, inevitable ill-conditioned eigenproblems, the lack of how to deal with the novel data, etc. The existing extensions are comprehensively reviewed and discussed classifying into different categories in this paper. Their strategies, advantages/disadvantages and performances are elaborated. By generalizing different tactics in various extensions related to different stages of LLE and evaluating their performances, several promising directions for future research have been suggested.