global correlation coefficient

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I hope you guys are doing well. I am working with my adviser on UNFOLDING optimization techniques. Unfolding is a the process of getting true or theoretical data from experimental data, so it is indeed an ill posed inverse problem. There are different unfolding algorithms including, iterative Bayes theorem, and SVD. We are trying to find the best metric to optimize these algorithms. One metric used to optimize the number of iterations in the Bayesian unfolding is the global correlation coefficient which is given by 



**ρ=√(1-〖[(Vxx^(-1))ii (Vxx)ii]〗^(-1) )**


Vxx is the covariance matrix and ii is the element ii in the covariance matrix.So (Vxx) is the element ii in the covariance matrix Vxx.
I tried my best to make the equation clear. Our problem is that we don't know why this metric is used to determine the minimum number of iterations required and we don't know where did this equation come from. So, in brief why is this metric used to optimize the number of iterations although there are other different methods like cross-validation and L-curve, and where is the global correlation coefficient equation come from or how it is derived.



Thanks and Best Regards...




linear-algebra statistics




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    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 28 at 6:18














up vote
-2
down vote

favorite












I hope you guys are doing well. I am working with my adviser on UNFOLDING optimization techniques. Unfolding is a the process of getting true or theoretical data from experimental data, so it is indeed an ill posed inverse problem. There are different unfolding algorithms including, iterative Bayes theorem, and SVD. We are trying to find the best metric to optimize these algorithms. One metric used to optimize the number of iterations in the Bayesian unfolding is the global correlation coefficient which is given by 



**ρ=√(1-〖[(Vxx^(-1))ii (Vxx)ii]〗^(-1) )**


Vxx is the covariance matrix and ii is the element ii in the covariance matrix.So (Vxx) is the element ii in the covariance matrix Vxx.
I tried my best to make the equation clear. Our problem is that we don't know why this metric is used to determine the minimum number of iterations required and we don't know where did this equation come from. So, in brief why is this metric used to optimize the number of iterations although there are other different methods like cross-validation and L-curve, and where is the global correlation coefficient equation come from or how it is derived.



Thanks and Best Regards...




linear-algebra statistics




share|cite|improve this question

















  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 28 at 6:18












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











I hope you guys are doing well. I am working with my adviser on UNFOLDING optimization techniques. Unfolding is a the process of getting true or theoretical data from experimental data, so it is indeed an ill posed inverse problem. There are different unfolding algorithms including, iterative Bayes theorem, and SVD. We are trying to find the best metric to optimize these algorithms. One metric used to optimize the number of iterations in the Bayesian unfolding is the global correlation coefficient which is given by 



**ρ=√(1-〖[(Vxx^(-1))ii (Vxx)ii]〗^(-1) )**


Vxx is the covariance matrix and ii is the element ii in the covariance matrix.So (Vxx) is the element ii in the covariance matrix Vxx.
I tried my best to make the equation clear. Our problem is that we don't know why this metric is used to determine the minimum number of iterations required and we don't know where did this equation come from. So, in brief why is this metric used to optimize the number of iterations although there are other different methods like cross-validation and L-curve, and where is the global correlation coefficient equation come from or how it is derived.



Thanks and Best Regards...




linear-algebra statistics




share|cite|improve this question













I hope you guys are doing well. I am working with my adviser on UNFOLDING optimization techniques. Unfolding is a the process of getting true or theoretical data from experimental data, so it is indeed an ill posed inverse problem. There are different unfolding algorithms including, iterative Bayes theorem, and SVD. We are trying to find the best metric to optimize these algorithms. One metric used to optimize the number of iterations in the Bayesian unfolding is the global correlation coefficient which is given by 



**ρ=√(1-〖[(Vxx^(-1))ii (Vxx)ii]〗^(-1) )**


Vxx is the covariance matrix and ii is the element ii in the covariance matrix.So (Vxx) is the element ii in the covariance matrix Vxx.
I tried my best to make the equation clear. Our problem is that we don't know why this metric is used to determine the minimum number of iterations required and we don't know where did this equation come from. So, in brief why is this metric used to optimize the number of iterations although there are other different methods like cross-validation and L-curve, and where is the global correlation coefficient equation come from or how it is derived.



Thanks and Best Regards...





linear-algebra statistics





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 28 at 9:30









Bernard

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asked Jul 28 at 5:54









Saif

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1







  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 28 at 6:18












  • 1




    Please see math.meta.stackexchange.com/questions/5020
    – Lord Shark the Unknown
    Jul 28 at 6:18







1




1




Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Jul 28 at 6:18




Please see math.meta.stackexchange.com/questions/5020
– Lord Shark the Unknown
Jul 28 at 6:18















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