b-Locally Linear Embedding : is approach which address the problem of nonlinear dimensionality reduction by computing low dimensional, neighborhoods preserving embedding of high dimensional data. ""so his aims is to find a mapping to preserve local linear relationship between neighbors. And he preserve the local regression weights that reconstruct the original data with the new data .\ref{contribution}"".
Minimizing the cost function taken into account that each sample  is reconstructed using its neighbors we obtain the weights for each case as a matrix, knowing that the sum of all weights of the same row must be equals to 1. So in the final step we can compute the cost function, basing on locally linear reconstruction errors, using the low dimensional vector  obtained from the corresponding  that represents the global coordinates of the manifold