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Imagine you have some multivariate data (1000s of variables) which approximately follows the Gaussian distribution.

You can generate various PCA Scores plots from this data, of course. One option is to extract variables from the Gaussian (such as the max height of the distribution or its full width at half maximum and so on) and use this as input for creating your PCA scores plot. I did this and I also plotted the PCA scores plot using just the original data as it was. Something unusual happened: the axes remained on the same scale and these plots were a flip of each other about x = 0. That is, the left-most point became the right-most point on the other plot and so on. So like a mirror reflection.

What could this mean?

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Absolutely nothing.

A PCA decomposition maps the original variables into new dimensions which capture the highest amount of variability. Note that the directionality of these dimensions is completely irrelevant - given a dimension that captures some amount of variability, the negation of that dimension also captures the exact same amount of variability. Because of this, the positive/negative direction of a PCA dimension may be arbitrarily chosen. Different software packages may produce different results depending on how they are coded, and slight variations in the input data could also result in a near-identical but flipped PCA plot.

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