PCG (Preconditioned Conjugate Gradient) methods are more effective than CG (Conjugate Gradient) methods to solve optimization problems (in machine learning).
So my question is how can I find that if a dataset is ill-conditioned?
Condition number (l) = max value of eigen value divided by min value of eigen value.
If l >> 1 then it we say it is ill-conditioned
If l approx = 1 the well-conditioned.
I think the answer to my question is as follow (can somebody confirm):
Let X (no. of features by number of data points) denotes the dataset then we can roughly estimate whether the dataset is ill-conditioned or not:
- Calculate a = X*X'
- Calculate condition number (in Matlab): b = cond(a)
- If b >> 1 then dataset is ill-conditioned,
if b is near one then well-conditioned
Dear Vinod Kumar Chauhan
I agree and confirm your observation.
For more details, I hope you find the attached chapter is helpful.
Best regards
Dear Issam Kaddoura
Thank you very much for the confirmation and the reference.
Best regards
Vinod
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