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I have a set of features with the following covariance matrix:

           feature_1   feature_2   feature_3
feature_1  3347        -57         -17
feature_2  -57         2           0.4
feature_3  -17         0.4         53

Each feature is on different scale, thats why the variances magnitude differ that much.

Now, the total "variability" is 3347 + 2.4 + 53 = 3402

According to this post can I say that "feature_1 explains 98% (3347 / 3402) of the total variability" ?

I think this would be unfair, because that feature has that big of a variance only because its scale.

So my question is, would it make more sense to first scale the data (using e.g. the MinMaxScaler) before calculating the covariance matrix ?

quant
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  • You misunderstood the part about total variability, that's only about PCA – Firebug Sep 13 '21 at 15:15
  • But the total variability at that post, is the same both during the PCA and before (in the covariance matrix in the original features), right ? Or do you mean, because the covariances are not 0 ? – quant Sep 13 '21 at 15:17

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