Your cache administrator is webmaster. Will the formula be valid then? In the context of your question (comparing two sets of kPCA axes for one given $\mathbf x$) the first term is a constant and so the only relevant term is the Edit After helpful comments, I have the following revised question.

Your cache administrator is webmaster. A good method for estimating which is better is to transform the new sample to each of the PCA spaces, truncate the coefficients, transform back and check the reconstruction error. Actually, it makes your question more interesting (+1) and I will try to provide a answer later today or tomorrow. –amoeba Oct 13 '14 at 18:20 | show 1 more comment How to explain the concept of test automation to a team that only knows manual testing?

I think I might have to get more dimensions for the PCA, though. –yoki Oct 13 '14 at 17:00 Any idea on how to do this on Kernel PCA? The system returned: (22) Invalid argument The remote host or network may be down. asked 2 years ago viewed 404 times active 2 years ago Blog Stack Overflow Podcast #92 - The Guerilla Guide to Interviewing Get the weekly newsletter! when to use IIS UrlRewrite Rules Why would breathing pure oxygen be a bad idea?

Oracle: Does enabling a PK rebuild its index? Instead, we apply kernel trick and compute principal components directly, by eigen-decomposition of the kernel matrix $\mathbf K$: if its eigenvectors are $\mathbf V$ and eigenvalues are on the diagonal of current community blog chat Cross Validated Cross Validated Meta your communities Sign up or log in to customize your list. Please try the request again.

In it, you'll get: The week's top questions and answers Important community announcements Questions that need answers see an example newsletter By subscribing, you agree to the privacy policy and terms What do you do when you have an entire class of underachievers? Now consider the reconstruction error in the target space: \begin{align} \|\phi(\mathbf x) - \mathbf U_p^\vphantom{\top} \mathbf U_p^\top \phi(\mathbf x)\|^2 &= \|\phi(\mathbf x)\|^2 - \|\mathbf U_p^\top \phi(\mathbf x)\|^2 \\ &= k(\mathbf x, The system returned: (22) Invalid argument The remote host or network may be down.

Please try the request again. Generated Wed, 26 Oct 2016 06:55:53 GMT by s_wx1157 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.3/ Connection more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed Sorry for all the scrutiny, but I would really like my toy example (at least) to work properly.

Your cache administrator is webmaster. It obviously cannot be simply inverted, and using pseudo-inverse for $V$ yields an ill-conditioned problem. Your cache administrator is webmaster. As far as I see, when (numerically) very small negative or positive eigenvalues are obtained, the reconstruction will have errors. –yoki Oct 15 '14 at 17:51 1 Okay, to answer

up vote 1 down vote favorite 1 I have two PCA bases obtained by decomposition of two groups of training data. Generated Wed, 26 Oct 2016 06:55:53 GMT by s_wx1157 (squid/3.5.20) Your cache administrator is webmaster. Which means that you take your test sample, project on the first $p$ components, and look at the variance.

The system returned: (22) Invalid argument The remote host or network may be down. How can I decide which PCA basis fits better each test sample? Generated Wed, 26 Oct 2016 06:55:53 GMT by s_wx1157 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection Are there any historically significant examples?

more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation Science Please try the request again. Not the answer you're looking for? share|improve this answer edited Oct 15 '14 at 16:30 answered Oct 14 '14 at 15:48 amoeba 29.3k8103167 1 @ido: yes, kernel scalar product of the test vector to itself (so

Actually, it means that in the context of your question (comparing two sets of PCA axes for one $\mathbf x$) the only relevant term is the second, which is simply the The system returned: (22) Invalid argument The remote host or network may be down. now I can't use an "inverse" transform. –yoki Oct 13 '14 at 17:58 1 @ido: Yes, it would also work for kernel PCA. Browse other questions tagged classification pca kernel-trick or ask your own question.

Can this be done? Please try the request again. When to use "ĉu" instead of "se"? I updated the answer. –amoeba Oct 15 '14 at 16:27 1 It is probable to get zero eigenvalues, or otherwise very close.

Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the What reasons are there preventing me from using an old edition text? Please try the request again. Your way is probably fine too. –amoeba Oct 15 '14 at 20:52 | show 4 more comments Your Answer draft saved draft discarded Sign up or log in Sign up

Now it should work out. For any given $\mathbf x$ it is a constant. Generated Wed, 26 Oct 2016 06:55:53 GMT by s_wx1157 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.4/ Connection This should already lead to near-zero error.

Setting up some notation, if $\mathbf x$ is your test sample and $\mathbf U_p$ a matrix with $p$ leading principal axes in columns, then the reconstruction error is given by $$L This you know. Your cache administrator is webmaster. Problems from using Office 64bit Print some JSON what does one mean by numerical integration is too expensive?

The higher the variance -- the better the fit. That sounds reasonable. So you can take your test sample, project it on the first $p$ components, and look at the variance. Would it be ok to eat rice using spoon in front of Westerners?