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It is not the icj but the pca that made the “ruling”.The pca is not part of the UN, unlike the icj. It, however, rents the same venue as the icj for its cases.Both the icj and UN have repeatedly clarified the relationship with the pca.The pca is an ARBITRATION platform. It is only legally binding if all parties submit to Arbitration.Please find a dictionary for the definition of Arbitration.The pca is not a court, and China was never a party to the case. The Philippines essentially paid for a single party Arbitration, which is an absurd legal proposition.Apparently, President duterte made reference to 30 million dollars owed to the Philippines that was promised by the United States if it pursued the case, with an eager and compliant pca ready to help.Now, he is stuck with a useless “ruling” and a huge legal bill.

PCA doesn’t have any disadvantages. If used correctly, it should filter out the noise, and you should be left with a stronger signal.However, a related question is, what are the limitations of PCA, that is, when can you apply PCA on a dataset for dimensionality reduction. For this, we need to know about the assumptions that are used in PCA:Linearity : PCA assumes that the principle components are a linear combination of the original features. If this is not true, PCA will not give you sensible results.Large variance implies more structure : PCA uses variance as the measure of how important a particular dimension is. So, high variance axes are treated as principle components, while low variance axes are treated as noise.Orthogonality : PCA assumes that the principle components are orthogonal.Here are some example datasets where PCA fails because the above assumptions do not hold:[The red arrows denote the principle axes, which do not capture the complete signal.]Since PCA is a fairly old technique, there has been considerable work on improving it when the above assumptions do not hold. Depending on your use case, you may want to use one of these more advanced techniques.Here’s a well-written tutorial on PCA — A Tutorial on Principle Components Analysis. The above points, including the figure, are from this paper.

Both LDA and PCA are linear transformation techniques: LDA is a supervised whereas PCA is unsupervised (ignores class labels).You can picture PCA as a technique that finds the directions of maximal variance:And LDA as a technique that also cares about class separability (note that here, LD 2 would be a very bad linear discriminant)Remember that LDA makes assumptions about normally distributed classes and equal class covariances (at least the multiclass version; the generalized version by Rao).If you are interested in an empirical comparison: A. M. Martinez and A. C. Kak. PCA versus LDA. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 23(2):228–233, 2001).Spoiler: PCA tends to result in better classification results in an image recognition task if the number of samples for a given class was relatively small