Dear Nelle,
Thanks for your reply.
I do understand that the majority of kernels are psd.
Yet I am currently dealing with non psd kernel such as sigmoid kernel in
[1] and optimal assignment kernel in [2, 3].
In [1], Lin suggest an implementation of SVM for non psd kernels.
So my question is does scikit learn handle this case.
Best Regards,
Benjamin
[1] Lin, H. T., & Lin, C. J. (2003). A study on sigmoid kernels for SVM and
the training of non-PSD kernels by SMO-type methods. *submitted to Neural
Computation*, 1-32.
[2] Fröhlich, H., Wegner, J. K., Sieker, F., & Zell, A. (2005, August).
Optimal assignment kernels for attributed molecular graphs. In *Proceedings
of the 22nd international conference on Machine learning* (pp. 225-232).
ACM.
[3] Vert, J. P. (2008). The optimal assignment kernel is not positive
definite. *arXiv preprint arXiv:0801.4061*.
On Sat, May 31, 2014 at 5:28 AM, Nelle Varoquaux <[email protected]>
wrote:
> Hello,
> Indeed, SVM methods only work with positive definite kernels (as all
> kernel methods in Machine Learning). This is because you can view pd kernel
> as inner product, which you can't if the kernel isn't pd. Kernel methods
> (including SVM) "only" replace inner products with kernels, thus mapping
> the space of the features to a usually larger, more complex feature space
> as defined by the kernel function.
> Hope that clarifies,
> N
>
>
> On 29 May 2014 07:56, Benjamin Li <[email protected]> wrote:
>
>> Dear all,
>>
>> I am new to scikit learn and I want to ask a question about the SVM
>> module.
>> Does the SVM module support non-psd kernel matrix?
>>
>> Ive found that in the web page ("
>> http://scikit-learn.org/stable/modules/svm.html";) there are lines about
>> the kernel matrix:
>>
>> >1.2.7.1. SVC
>> >....
>> > Q is an n by n positive semidefinite matrix, Q_{ij} \equiv K(x_i, x_j)
>> and \phi (x_i)^T \phi (x) is the kernel.
>>
>> Does this imply that the SVC module only support psd kernel matrix?
>>
>> Thank you.
>>
>> Best Regards,
>> Benjamin Li
>>
>>
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>
>
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