Hi Vlad thanks for the answer.
I was thinking about that and I am not 100 % sure that this is right.
If we consider SPCA to work as PCA than we do:
x_3_dimensional = x.dot(spca.components_.T) # this is equivalent to
spca.transform(x)
and so the reconstruction of x is x_reconstruction =
x_3_dimensional.dot(spca.components_)
This works on PCA because the components are orthogonal
components_.dot(components_.T) = Id
In SPCA this does not hold any more.
So I am not sure that the reconstruction can be obtained in this way.
What do you think about that?
Thanks,
Luca
Hi Luca,
The other part of the decomposition that you're missing is available
in `spca.components_` and has shape `(n_components, n_features)`. The
approximation of X is therefore `np.dot(x_3_dimensional,
spca.components_)`.
Best,
Vlad
On Thu, Oct 16, 2014 at 6:07 PM, Luca Puggini <lucapuggio@...> wrote:
> Hi,
> is there any way to reconstruct the data after SparsePCA?
>
> If I do
>
> spca = SparsePCA(alpha=1, n_components=3).fit(x)
> x_3_dimensional = SparsePCA.transform(x)
>
> How can I get the best lower rank approximation of x after SparsePCA
> decomposition?
>
> Thanks,
> Luca
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