The problem with this kind of methods is that they do not consider the explicit form of the differential manifold structure in which our data probably lie. Based on this point a new approach is investigated by representing the data set by a graph which incorporates neighborhood information of the data set, we are talking here about the non-linear dimensionality reduction algorithms like Isomap,  LLE and LE algorithm.
Speaking about The LE approach, the objective is to find a transform that goes from the original n-dimensional space to a k-dimensional space, with k << n, in which the local distances are conserved as much as possible. Use n points {xi}ni =1 to construct a graph G = (V, E)