In the Fig 3, it showed that different neighborhood size k produced different embedding results. Few neighbors used may result a rank-deficient tangent space and leads to over-fitting, while a large neighborhood introduced too much bias and the computed tangent space would not much the local geometry well. Hence it is worthy of considering variable number of neighbors that are adaptively chosen at each data point. Fortunately, our LTSA algorithm seems to be less sensitive to the choice of k than LLE does as will be shown later.