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I know that before doing PCA we need to normalize and scale the data by feature.

I am wondering what it will be happened if the normalization and the scaling operations would be calculated for each observation. How should the results be interpreted?

Thank you in advance Best

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Firstly, your columns would all need to be comparable to each other for row normalisation to somehow be meaningful. I.e. they all have to be measuring the same thing. Secondl, if you normalise across rows you lose the relative magnitudes between rows because you're scaling every row relative to itself. This is sometimes desirable in image processing for example where you might flatten a matrix into a vector and normalise it, and stack a bunch of flattened vectors together to form a matrix, but its otherwise unusual.

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