How to interpret a PCA score plot? I get a following score plot for the breast cancer dataset. The score plot has been clustered into two categories. I want to know what inferences could I draw from it?


The content of the interpretation will depend on the interpretation of the two components. Do the groups of variables that load strongly in each component have a coherent meaning? Assuming the two components that emerged are coherent (and this coherence is going to be convincing to readers of your research), you can say a couple of things, but you could also test these hypotheses in statistical tests with OLS or a t-test or similar (for my first point) and OLS or correlation (for my second point).
First, you can say that category membership has a strong relationship with component 1, but category membership has an unclear or weak(er) relationship with component 2. So you would expect (and can test that) the mean value of the first component for the blue group to be greater than the mean for the yellow group. For component 2, this relationship is not clear, but you could test it to show whether the means are significantly different.
There also appears to be a correlation between C1 and C2 for the yellow group but less so for the blue group. You could subset your dataset into yellow and blue data sets and perform a correlation test on each. It seems clear that the correlation coefficients would be different for the two groups. The meaning behind this difference in correlations depends on the coherence and "meaning" of the components, as interpretable by which variables are loading strongly in each component.
