This paper extends the co-linearity index and penalty matrix approach (Ransing et al., 2013) for discovering noise free correlations between heterogeneous process variables and responses.
First, a saturated model was fitted to the data to estimate model free correlations between pairs of different genetic and social relatedness, and to test whether correlations between DZ twins differed from correlations between regular siblings.
Specifically, shared weights strategy and a parameter-free correlation layer are exploited to carry out RGB-D-correlated objectness estimation and region-wise recognition in conjunction with RGB-specific and depth-specific procedures.
The model's scale-free correlation degree refers to the fact that the model may have some vital data flow paths that have significant influence on the output of the integrated study, while study enterprise at the end of those flow paths has low correlation degrees.
The pseudo-free correlation coefficient for the correct hand was clearly better than for the other hand (82% vs. 55%), indicating that a correct solution had been found.
We chose this measure as the uncentered correlation coefficient between two orthogonal probability distribution vectors is zero, whereas the normal (mean-free) correlation coefficient would be negative, which is undesirable given the design of the objective function (equation 7).
To alleviate this problem a PCA can be performed on a scale-free correlation matrix rather than a covariance matrix, but outliers could still have a strong influence in defining the direction of the first PC.
In addition, to account for possible skewness in the data, we also employed Kendall's Tau b, which is a distribution-free correlation measure.
Those distribution-free correlations only utilize rank information, and are more robust than the parametric approach.
Thermodynamic data for Th(IV) complexation were used in this study to estimate complexation stability constants for U IV) complexation, using a linear free energy correlation.
When ranked according to total electrostatic binding free energy, correlation with experiment improves (r2 of 0.72); this may be related to underestimated first solvation shell effects by the implicit water models.
