Though not technically a variant of LLE, Local tangent space alignment (LTSA) is algorithmically similar enough to LLE that it can be put in this category. Rather than focusing on preserving neighborhood distances as in LLE, LTSA seeks to characterize the local geometry at each neighborhood via its tangent space, and performs a global optimization to align these local tangent spaces to learn the embedding. In general, LTSA is less sensitive to the choice of k neighborhoods as compared to LLE. LTSA performs eigen-decomposition on a per point basis, rather than applying on the entire sparse matrix which highly reduces the computational complexity. It is fast as well as adaptive to complex nonlinear manifolds. Hence LTSA has been successfully applied to microarray data analysis[10]and face recognition[11]