I constructed a PCA plot from a very high-dimensional dataset that contains features relating to fraud. After creating the PCA plot, I created a biplot with the features to see how they interact. The biplot is shown below:

enter image description here

I'm slightly confused with interpreting the 4 separate quadrants.

In the bottom left quadrant, a small number of features have negative scores for both PCA 1 and PCA 2 and I have therefore assumed they explain little variance for both PCs although these features are assumingly correlate given they are clustered?

In the bottom right quadrant, we see again that a number of features are clustered but this time posses positive scores for PCA 1 - should this be interpreted as these features having a lot of influence on the variation captured by PCA 1? and vice-versa for the top left quadrant.

The top right quadrant has the most features and these features score positively for both PCA 1 and PCA 2 which I've interpreted as these features being the most important in my dataset as influence a lot of variation in both PCs.

I've also concluded that PCA 1 accounts for the most variants and the features it has in its positive quadrants should be focused on.

Is this a fair assessment and interpretation of the Biplot that I have created? I'm not sure that I'm looking at the core tenets of a PCA biplot or that perhaps I'm missed something. Thank you very much in advance!

  • $\begingroup$ We're seeing PCA 2 loadings vs. PCA 1 loadings, true? Negative doesn't mean little explanation, it's close to zero that indicates little explanatory power. So anything close to zero means "not much", whereas the longer vectors have more explanatory power. If the angles of two vectors are close, then then you're looking at tighter positive correlation. If orthogonal, then no correlation. If closer to 180 degrees then negative correlation. $\endgroup$
    – C8H10N4O2
    Jul 19, 2021 at 15:15
  • $\begingroup$ Hi @C8H10N4O2 - thanks for the reply. Yes - you're seeing PCA 2 loadings vs. PCA 1 loadings. With respect to the point you're making to longer vectors, are you saying from the plot above, the vectors in the top right and bottom right have the most explanatory powers given they all score positively? $\endgroup$
    – softmax55
    Jul 19, 2021 at 15:25
  • $\begingroup$ I think you will find the information you need in the linked thread. Please read it, & the links contained in it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. $\endgroup$ Jul 19, 2021 at 15:31


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