Similarity Assessment

Choosing experiments for validation is widely based upon the similarity indices such as $c_k$, $E$, and $G$. They allow numerically quantifying how much two systems are similar and finding the amount of shared information. The most accepted index is $c_k$, the correlation coefficient, defined as:

$$c_k=\frac{S_aCS^T_e}{\sqrt{S_aCS_a^T}\sqrt{S_eCS_e^T}}$$

where $S_a$ is the application sensitivity vector; $S_e$ is the application sensitivity vector; $C$ is the covariance matrix.

The second index is $E$ and defined as the cosine between two vectors:

$$E=\frac{S_aS^T_e}{|S_a||S_e|}$$

The $G$ similarity index is intended to quantify the coverage of the application by an experiment and defined as follows:

$$G=1-\frac{\sum_{n,x,g}|S_{a,n,x,g}-S_{e',n,x,g}|}{\sum_{n,x,g}|S_{a,n,x,g}|}$$

where $S_{a,n,x,g}$ is the application sensitivity to group $g$ of reaction $x$ of nuclide $n$; $S_{a,n,x,g}$ is the experimental sensitivity to group $g$ of reaction $x$ of nuclide $n$;

$S_{e',n,x,g}=S_{e,n,x,g}$ if $|S_{a,n,x,g}|\geq |S_{e,n,x,g}|$ and $S_{a,n,x,g}/|S_{a,n,x,g}|=S_{e,n,x,g}/|S_{e,n,x,g}|$;

$S_{e',n,x,g}=S_{a,n,x,g}$ if $|S_{a,n,x,g}|\lt |S_{e,n,x,g}|$ and $S_{a,n,x,g}/|S_{a,n,x,g}|=S_{e,n,x,g}/|S_{e,n,x,g}|$;

$S_{e',n,x,g}=0$ otherwise.