One advantage of LTSA over LLE is that using LTSA we can potentially detect the intrinsic dimension of the underlying manifold by analyzing the local tangent space structure. In particular, we can examine the distribution of singular values of the data matrix \({X_i}\) consisting of the data points in the neighborhood of each data point \({X_i}\). If the manifold is of dimension d, then \({X_i}\) will be close to a rank-d matrix.