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Good point, a look at the contents of the wikipedia page for dimensionality reduction makes it clear - https://en.wikipedia.org/wiki/Dimensionality_reduction

    Dimensionality reduction:

    1. Feature selection.

    2. Feature projection.

      2.1 PCA
So you could say that feature selection is dimensionality reduction but you can't say that PCA is feature selection.


> but you can't say that PCA is feature selection.

One of the steps in PCA is to select the top N eigenvectors sorted by eigenvalues. So while it is not feature selection, it can be argued that it involves a feature selection step.




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