I think the documentation is correct. U, a.k.a. "the code" or "the activations" has shape (n_samples, n_components) and V a.k.a. "the dictionary" or "the components" has shape (n_components, n_features) in both case.
We could use n_components uniformly instead of n_atoms for consistency's sake (and just make sure that the "components" is a synonym for "dictionary atoms" in the literature). I think V_k is fine because the dimension with size n_components is the first dimension of V. If you spot issues or other things that are unclear or incomplete in the doc, please feel free to open an issue on github. You can also directly submit a pull request if you are familiar with git. The website is built from the docs that live in the "doc/" subfolder of the repo. -- Olivier
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