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PCA (Principal Component Analysis) is often used to represent 2d or 3d plot of the data, where y=PC2 and x=PC1 (eventually z=PC3). Given that there is an 'order' between components, it makes sense to use the first two (three) to represent data (since the first one is the direction which maximizes the data variance, the second one is the second best-uncorrelated direction and so on).

LDA (Linear Discriminant Analysis) is also sometimes used to plot data. In cases in which more than 3 classes are involved (so that k>2 LDs are produced), should one assume that the first two (or three) linear discriminant are the ones which better represent data (as one does with PCA) or not? Why?

ImAUser
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  • Some of relevant threads: https://stats.stackexchange.com/q/12861/3277, https://stats.stackexchange.com/q/22884/3277, https://stats.stackexchange.com/q/169436/3277, https://stats.stackexchange.com/a/190821/3277. – ttnphns Aug 25 '18 at 18:40
  • https://stats.stackexchange.com/a/315488/164061 in this question I showed a graph that provides some intuition about the difference between lda and pca. The point of discriminant analysis is to show the *difference* between groups, so the first components, with the largest difference make more sense (in pca on the other hand this difference between groups might still be in higher components). This comment could be seen as a short answer, I am not sure. It is difficult to say because your issue seems relatively trivial to me, but maybe you could explain a bit more your troubles with lda. – Sextus Empiricus Aug 25 '18 at 18:41
  • Thank you both. Yes, the question was trivial: basically, I was not sure if the LDs were 'ordered' - the first explaining more 'separateness'. I found [this](https://arxiv.org/pdf/1404.1100.pdf) tutorial on PCA super-intuitive (even in its mathematical derivation, even for someone who should definitely refresh his linear algebra background). Do you know if something similar exists for LDA? – ImAUser Aug 25 '18 at 22:33

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