we observe  with the increasing noise level η, thecomputed τi’s get expressed at points with relatively large noise.and we compare between 
colum c, and d that they have same noise levels  η  but deferent    number of neighbors   k   we obsereve  the quality of thecomputed τi’s improved        in hight nombre  neighbors.  In general, k  should  be  chosen to match the sampling density ,noise level and the curvature at each data points so as to extract an accurate local tangent space.It is therefore worthy of considering variable number of neighbors that are adaptively chosen at each data point.
2 nd experience: 
in this test the authors compare between LTSA and LLE with applieing  both LTSA and LLE to the S-curve data set (total data points =2000 uniformly sampled without noise) with different number of neighbors. For d = 2,and k which is chosen from k = 6 to k = 30, LTSA always produces coordinates Tthat has similar geometric structure as the generating coordinates.
they show  the figures :