As I see it, the display showing the first p << n PCs adding up to 100% of the variance is plainly wrong.
I suspect it comes about via a mental short-circuit: If we try to control p using a tolerance, then that amounts to saying that the remaining PCs are effectively zero-variance, but that is (usually) not the intention at all. The common case is that the remainder terms have a roughly _constant_, small-ish variance and are interpreted as noise. Of course the magnitude of the noise is important information. -pd > On 25 Mar 2016, at 00:02 , Steve Bronder <sbron...@stevebronder.com> wrote: > > I agree with Kasper, this is a 'big' issue. Does your method of taking only > n PCs reduce the load on memory? > > The new addition to the summary looks like a good idea, but Proportion of > Variance as you describe it may be confusing to new users. Am I correct in > saying Proportion of variance describes the amount of variance with respect > to the number of components the user chooses to show? So if I only choose > one I will explain 100% of the variance? I think showing 'Total Proportion > of Variance' is important if that is the case. > > > Regards, > > Steve Bronder > Website: stevebronder.com > Phone: 412-719-1282 > Email: sbron...@stevebronder.com > > > On Thu, Mar 24, 2016 at 2:58 PM, Kasper Daniel Hansen < > kasperdanielhan...@gmail.com> wrote: > >> Martin, I fully agree. This becomes an issue when you have big matrices. >> >> (Note that there are awesome methods for actually only computing a small >> number of PCs (unlike your code which uses svn which gets all of them); >> these are available in various CRAN packages). >> >> Best, >> Kasper >> >> On Thu, Mar 24, 2016 at 1:09 PM, Martin Maechler < >> maech...@stat.math.ethz.ch >>> wrote: >> >>> Following from the R-help thread of March 22 on "Memory usage in prcomp", >>> >>> I've started looking into adding an optional 'rank.' argument >>> to prcomp allowing to more efficiently get only a few PCs >>> instead of the full p PCs, say when p = 1000 and you know you >>> only want 5 PCs. >>> >>> (https://stat.ethz.ch/pipermail/r-help/2016-March/437228.html >>> >>> As it was mentioned, we already have an optional 'tol' argument >>> which allows *not* to choose all PCs. >>> >>> When I do that, >>> say >>> >>> C <- chol(S <- toeplitz(.9 ^ (0:31))) # Cov.matrix and its root >>> all.equal(S, crossprod(C)) >>> set.seed(17) >>> X <- matrix(rnorm(32000), 1000, 32) >>> Z <- X %*% C ## ==> cov(Z) ~= C'C = S >>> all.equal(cov(Z), S, tol = 0.08) >>> pZ <- prcomp(Z, tol = 0.1) >>> summary(pZ) # only ~14 PCs (out of 32) >>> >>> I get for the last line, the summary.prcomp(.) call : >>> >>>> summary(pZ) # only ~14 PCs (out of 32) >>> Importance of components: >>> PC1 PC2 PC3 PC4 PC5 PC6 >>> PC7 PC8 >>> Standard deviation 3.6415 2.7178 1.8447 1.3943 1.10207 0.90922 >> 0.76951 >>> 0.67490 >>> Proportion of Variance 0.4352 0.2424 0.1117 0.0638 0.03986 0.02713 >> 0.01943 >>> 0.01495 >>> Cumulative Proportion 0.4352 0.6775 0.7892 0.8530 0.89288 0.92001 >> 0.93944 >>> 0.95439 >>> PC9 PC10 PC11 PC12 PC13 PC14 >>> Standard deviation 0.60833 0.51638 0.49048 0.44452 0.40326 0.3904 >>> Proportion of Variance 0.01214 0.00875 0.00789 0.00648 0.00534 0.0050 >>> Cumulative Proportion 0.96653 0.97528 0.98318 0.98966 0.99500 1.0000 >>>> >>> >>> which computes the *proportions* as if there were only 14 PCs in >>> total (but there were 32 originally). >>> >>> I would think that the summary should or could in addition show >>> the usual "proportion of variance explained" like result which >>> does involve all 32 variances or std.dev.s ... which are >>> returned from the svd() anyway, even in the case when I use my >>> new 'rank.' argument which only returns a "few" PCs instead of >>> all. >>> >>> Would you think the current summary() output is good enough or >>> rather misleading? >>> >>> I think I would want to see (possibly in addition) proportions >>> with respect to the full variance and not just to the variance >>> of those few components selected. >>> >>> Opinions? >>> >>> Martin Maechler >>> ETH Zurich >>> >>> ______________________________________________ >>> R-devel@r-project.org mailing list >>> https://stat.ethz.ch/mailman/listinfo/r-devel >>> >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-devel@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-devel >> > > [[alternative HTML version deleted]] > > ______________________________________________ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel