Does principle component analysis reduce the dimensionality of the predictors or simply reduce the shape (m x n)

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Both, though it doesn't reduce m.

Strictly speaking, all PCA does is identify new principal components (variables/dimensions/axes) and rank them in order of how much variance is captured by each. You don't actually need to use the new variables - or you could use all of them and not reduce dimensionality at all.

Typically, you pick the first X principal components that capture some % of the total variance in your data. This reduces dimensionality, which is the same as reducing the n dimension of your data since n = number of variables.

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Yes, or a table of explained variance (eigenvalue ratios). Selecting the number of principal components can be done subjectively (making a judgment call) or possibly through a cross validation.

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Dimensionality = shape

likeuplifting

Ahhh that clears up so much confusion lol I seen the two terms but thought they were different

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