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I read this: enter image description here

But I'm still not sure if I understand what $\Sigma$ is. Does this mean to take the covariance of the entire data set with all classes mixed in, to take the covariance matrix for one class and assume it's the same for the others (even if it isn't), or to average the covariance matrices for the different classes?

I'm playing around with the Iris data set and getting a 98% classification rate with QDA and a 84% classification rate with LDA. I determined $\Sigma$ by doing cov(X) (Matlab) for the entire data set, but now I'm questioning whether I understood correctly.

Austin
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    It is the within-class covariance matrix. If that matrix is same in every class, then the averaged ("pooled") within-class covariance matrix also equals to it. LDA is based on this assumption, QDA is not, http://stats.stackexchange.com/a/190821/3277 – ttnphns Feb 18 '17 at 06:17
  • So if I want to do LDA but I look at each of 3 within-class covariance matrices and they are actually all different rather than equal, what do I do? Then take the average? – Austin Feb 18 '17 at 06:20
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    If they are very different, use QDA. If not very different, you may average them and do LDA. Please read the link I gave, with further links there. – ttnphns Feb 18 '17 at 06:25

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