[Numpy-discussion] performance matrix multiplication vs. matlab
Matthieu Brucher
matthieu.brucher@gmail....
Mon Jun 8 06:09:02 CDT 2009
2009/6/8 David Warde-Farley <dwf@cs.toronto.edu>:
>
> On 8-Jun-09, at 1:17 AM, David Cournapeau wrote:
>
>> I would not be surprised if David had this paper in mind :)
>>
>> http://www.cs.toronto.edu/~roweis/papers/empca.pdf
>
> Right you are :)
>
> There is a slight trick to it, though, in that it won't produce an
> orthogonal basis on its own, just something that spans that principal
> subspace. So you typically have to at least extract the first PC
> independently to uniquely orient your basis. You can then either
> subtract off the projection of the data on the 1st PC and find the
> next one, one at at time, or extract a spanning set all at once and
> orthogonalize with respect to the first PC.
>
> David
Also Ch. Bishop has an article on using EM for PCA, Probabilistic
Principal Components Analysis where I think he proves the equivalence
as well.
Matthieu
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