Forwarding your question to the mailing-list. On Thu, Jul 14, 2016 at 10:33 PM, Christos Lataniotis < [email protected]> wrote:
> Dear Mathieu Blondel, > > I am a PhD student working on some machine-learning aspects related to > dimensionality reduction. One of the methods that is of interest to me is > kernel PCA so I tested the implementation that is offered by scikit-learn > which I think is the most complete from the ones I could find on the web. > > I would like to ask for some clarification regarding the way you > implemented the inverse transform, i.e. solving the pre-image problem. > > Although the paper from Bakir et. al, 2004 is cited, I think there is some > difference in your implementation and the methodology that is discussed on > that paper. Bakir suggests ‘learning' the pre-image map by solving a kernel > ridge regression problem with some kernel function, say l, that is > different than the kernel function, say k, that is used in kernel PCA, > However by going through the source code of your implementation I think > that kernel functions l and k coincide. It that correct? If yes, is there > some justification (e.g. empirical) for making such assumption? I am asking > this because as far as I have read in the literature selecting the kernel > function l is kind of an open question still so I would expect it to be a > parameter that can be selected by the user on top of selecting the kernel > function for kernel PCA. > > Thank you for your time in advance. > > Best Regards, > Christos > > > -- > Christos Lataniotis > Institute of Structural Engineering > Chair of Risk, Safety and Uncertainty Quantification ETH Zürich - HIL E > 35.1 > Wolfgang-Pauli-Str. 15 > CH-8093 Zürich, Switzerland > Tel: +41 44 633 06 70 > E-Mail: [email protected] > >
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