The corrections are as follows:
1. Page 7783, 17 change to 27 in step 2.
2. Page 7783, in eq 32 and text thereafter, change Dn to DnT.
3. Page 7783, in eq 33c, change P to P̅.
4. Page 7784, change N to I in eq 36.
5. Page 7787: The correct ref 28 for the paper by the author S. Joe Qin and the team on kernel independent component analysis should be updated to: Lee, J-M.; Qin, S. J.; Lee, I-B. Fault Detection of Nonlinear Processes Using Kernel Independent Component Analysis. Can. J. Chem. Eng. 2007, 85, 526-536. DOI: 10.1002/cjce.5450850414. Section 3 was taken largely from Lee and Qin et al. in our research group. We should have included a citation to that article and indicated that section 3 was being presented as a review for the reader.