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Confusion about principal component and major axis of the ellipse corresponding to the covariance matrix

You are right, the ellipse given by $\mathbf x^T\Sigma\mathbf x = 1$ has the largest axis along the smallest eigenvalue. So it is kind of the "opposite" of the curves from contour plots of e....
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Factor analysis and Dimensional Reduction difference

You can use the principal components (PCs) in PCA in the same way as the factors in factor analysis (FA). If you express the PCs as linear combinations of the features, you can see how the features ...
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Which has more mutual information with a multivariate Gaussian: its first principal component, or its first factor?

I realize this question is three years old, but I just came across this during my own Googling, so here goes! The simple answer is that, mutual information is not really the metric you want here, ...
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Interpretation of "low variance" in PCA

can it be said that no predictor has a strong influence on the system no. You could have strong influence, but in a way that cannot be well approximated linearly. Imagine a situation where controls ...
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Interpretation of "low variance" in PCA

Based on your comment, I believe there could be two, not necessarily related, things at play: Your principal components do not explain enough of the variance; and Your groups cannot be distinguished ...
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Interpretation of "low variance" in PCA

If the variance is "low" in every PC then you can conclude that no linear combination of variables can explain much variability, and this does include individual variables also since if you ...
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Categorising the PCA Method

Dimensionality reduction techniques such PCA occupy a somewhat unusual position, as John Madden points out. It's fair to think of them as algebraic building blocks to be used in statistical and ...
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Scaling Variables in PCA, yet all on the same scale

This a good question, and one that I’ve encountered a number of times at work. The short answer is it cannot hurt to scale even when input variables are all on same scale (in your case 0-100). When ...
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Arrows of underlying variables in PCA biplot in R

The biplot() function following a PCA using prcomp() is minimal in functionality. As we all (should) know, ...
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