Hi Luca > x_3_dimensional = x.dot(spca.components_.T) # this is equivalent to > spca.transform(x)
This part is specific to PCA. In general, the transform part of such a decomposition is `X * components ^ -1`. In PCA, because `components` is orthogonal, `components ^ -1` is `components.T`. The relationship between SparsePCA and PCA omits the orthogonality constraints, but adds sparsity constraints instead. The connection between the is given (only) by the reconstruction objective, which for both is `min ||X - x_transf * components||`. What you get when you call `spca.transform` is essentially solving for x_transf in `min ||X - x_transf * components||` subject to the constraints. So the reconstruction is still `x_transf * components`. Hope this helps, Vlad On Fri, Oct 17, 2014 at 11:23 AM, Luca Puggini <lucapug...@gmail.com> wrote: > > 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 > > > ------------------------------------------------------------------------------ > Comprehensive Server Monitoring with Site24x7. > Monitor 10 servers for $9/Month. > Get alerted through email, SMS, voice calls or mobile push notifications. > Take corrective actions from your mobile device. > http://p.sf.net/sfu/Zoho > _______________________________________________ > Scikit-learn-general mailing list > Scikit-learn-general@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/scikit-learn-general > ------------------------------------------------------------------------------ Comprehensive Server Monitoring with Site24x7. Monitor 10 servers for $9/Month. Get alerted through email, SMS, voice calls or mobile push notifications. Take corrective actions from your mobile device. http://p.sf.net/sfu/Zoho _______________________________________________ Scikit-learn-general mailing list Scikit-learn-general@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/scikit-learn-general
