Separate Signal Values from Noise let us consider following graph of singular values 



i want to make  some kind of  clustering of these data,namely to  seperate  main components from non main components,let say signal components from noise components,i would like to do like this(any software matlab,etc is great,better matlab)let us start like this  ,first do linear regression  with first point,then do regression analysis with first two point and so on,point is that  one want to  create two group,in first group   coefficients of  regression lines should be  close to each other, also in another group  regression coefficients should be close to each other,but regression  coefficients  in one group must be different then coefficients in another group,that means that we should find such point which separate this group optimally,  in other word i should stop regression analysis at some point which  well separate  two group,and another regression will start from this stop point till other rest points,please help me how to do it programaticaly
I would use the SVD (Singular Value Decomposition).
By looking at the Singular Values I'd determine which vectors spread the data and which spread the noise.

Practically, they both do both, but if we speak which are dominant, this would be a great starting point.