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I have performed PCA in my dataset. The first 3 components explain 90% variance of the data points. Can I add these principle components to get a score?

SCORE = PC1+PC2+PC3

For example, all my features are related to the liquidity of bank customers. In theory, the principle components will try to find the variance between the data points. And the variance will be based on the features I used (i.e Liquidity). Let's say the highest and lowest scores I obtained by adding PCs are 5 and 10. Will the customer having score of 5 and the customer having a score of 10 mean they are the most liquid and the least liquid customers (or vice versa)? Does this score mean anything?

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  • $\begingroup$ PCA scores are sign invariant, so adding them up does not make sense. $\endgroup$ Commented Jul 30, 2020 at 1:32

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Since applying PCA simply transforms the feature space, adding PCA values doesn't make any more sense than normalizing and then adding the original feature values.

I don't have the domain knowledge to say whether it makes sense to use the sum of your liquidity measurements as an overall liquidity measurement, but applying PCA wouldn't affect that.

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