4 - Contribution :

In this paper  the authors propose an algorithme to solve  this problem via local tangent space alignement(LTSA).it use it for nonlinear dimension reduction.
compared with other dimention reduction is to reduce the computation complexity of the algorithm and improve the performance and precision    .

5-Expériences:

In this parte i will presente somme experience of LTSA so :
1/- in the first experience:
f(τ) = 3τ 3 + 2τ 2 − 2τ, τ ∈ [−1.1, 1] , The data set is generated by adding noise in a relative fashion :
xi= xi = f(τi∗) (2+ η * ei )     with   with normally distributed ei           .
we  increase the noise levls from  η =0.01,    0.03 and 0.05 for three colum a, b , and arespectively.and we use same number of neighbors k=10.
for colum d   η =0.05  and   k=20.