...  ...  @@ 287,7 +287,7 @@ At this point, we have inverted the rotation and scaling in the principal compon 


Previously we mentioned that we will use kurtosis for that purpose but did not explain why. WIth SVD, we assumed that E is zero (first moment). We used second moment, variance above to decorrelate. Next option is the third moment, skewness. Nonetheless, we cannot say anything about the asymmetry in the probability distributions so we need to skip it for a general solution. The next moment (fourth order) is the kurtosis and this is what we will minimize in the objective function. Since we are trying to approximate, we say "fourth order is accurate enough for me". [Kurtosis](https://en.wikipedia.org/wiki/Kurtosis) is given by:






```math



K(\phi)= \sum_{n}^{N} {[\overline{x}_1(n) \overline{x}_2(n)]\begin{bmatrix} cos(phi) \\ sin(phi) \end{bmatrix}}^4



K(\phi)= \sum_{n}^{N} {[x^{'}_1(n) x^{'}_2(n)]\begin{bmatrix} cos(phi) \\ sin(phi) \end{bmatrix}}^4



```






where $`\phi`$ is the rotation applied with U.

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