Accounting for non-linear dependence using function driven component analysis

Majority of practical multivariate statistical analyses and optimizations model interdependence among random variables in terms of the linear correlation among them. Though linear correlation is simple to use and evaluate, in several cases non-linear dependence between random variables may be too strong to ignore. In this paper, We propose polynomial correlation coefficients as simple measure of multivariable non-linear dependence and show that need for modeling non-linear dependence strongly depends on the end function that is to be evaluated from the random variables. Then, we calculate the errors in estimation which result from assuming independence of components generated by linear de-correlation techniques such as PCA and ICA. The experimental result shows that the error predicted by our method is within 1% error compared to the real simulation. In order to deal with non-linear dependence, we further develop a target function driven component analysis algorithm (FCA) to minimize the error caused by ignoring high order dependence and apply such technique to statistical leakage power analysis and SRAM cell noise margin variation analysis. Experimental results show that the proposed FCA method is more accurate compared to the traditional PCA or ICA.