Timeline for Positioning the arrows on a PCA biplot
Current License: CC BY-SA 3.0
26 events
| when toggle format | what | by | license | comment | |
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| May 2, 2017 at 15:05 | comment | added | amoeba | @AntoniParellada I edited, and inserted a couple of links. | |
| May 2, 2017 at 15:05 | history | edited | amoeba | CC BY-SA 3.0 |
some links
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| May 2, 2017 at 13:06 | comment | added | amoeba | @AntoniParellada Please edit. I think I will have to edit this post later anyway to insert the things that we learnt (and will have learnt) during your investigation :) | |
| May 2, 2017 at 12:47 | comment | added | Antoni Parellada | Yes, that is what I mean - these plots are very useful, and making them pop up would allow easy access to details. | |
| May 2, 2017 at 12:44 | comment | added | amoeba | @Antoni You mean you want each figure to be a hyperlink to itself, e.g. first figure should be a hyperlink to i.sstatic.net/6ddZg.png ? Please feel free to edit, I can always fix whatever I don't like later :) Regarding the $n-1$, there is some confusion: how can unit SS be combined with unit variance? It's either one or another... I am not sure what you mean. | |
| May 2, 2017 at 12:38 | comment | added | Antoni Parellada | Looking again at your post, I see that the $\sqrt{n-1}$ is, as you mentioned also on my comment this morning, to attain unit variance, and corresponds to the middle subplots in the first and second rows of the first figure - does R biplot(), then, combine both the unit sum of squares AND unit variance? Also, it would be great if we could click on your figures to make them zoom out. I wouldn't dare edit your post :-) and I keep on blowing (Ctrl +) my entire browser to see the details. | |
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
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| Aug 24, 2016 at 23:08 | history | edited | amoeba | CC BY-SA 3.0 |
fixed two issues raised in the comments
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| Aug 24, 2016 at 22:58 | comment | added | VitoshKa | @amoeba, great answer. Two comments. 1) "length of the loading arrows approximates the variance of original variables" is not accurate, it's actually "standard deviation" of the original variables. 2) The ordering of list items is somewhat confusing. It would be much nicer to have both lists (U and V sides) sorted as in the columns of the plot. That is, have the two item lists match by "properness". | |
| Aug 14, 2015 at 7:46 | comment | added | Tom Wenseleers | Ha yes and in vegan normalisation is controlled with the "scaling" argument, whereas in biplot.prcomp it is controlled with the "scale" argument... | |
| Aug 14, 2015 at 7:38 | comment | added | Tom Wenseleers | These last ones are also called "contribution biplots"; the book by M. Greenacre "Biplots in practise" also gives a nice overview of all this; these ways of scaling apply to all methods based on the SVD (ie CA biplots, PCA biplots, LDA biplots etc); for an example of how it works see the source code ca:::plot.ca and the "map" argument | |
| Aug 14, 2015 at 7:34 | comment | added | Tom Wenseleers | Just noticed that ?ca::plot.ca has a nice overview of different possible normalisations: they distinguish row principal (form biplot=rows in principal coords, cols in standard coords), col principal (covariance biplot=cols in principal coords, rows in standard coords), symmetric biplot (rows and columns scaled to have variances equal to the singular values (square roots of eigenvalues)), rowgab and colgab (rows in principal coords and cols in standard coords multiplied by the mass of the corresponding point or vice versa) and rowgreen and colgreen (as rowgab and colgab but with sqrt(masses)) | |
| Aug 10, 2015 at 9:21 | comment | added | amoeba | I'm not sure, @Tom, I have never worked with DA biplots (and never worked with CA at all). I would need to look at a concrete example and think about it. | |
| Aug 10, 2015 at 0:15 | comment | added | Tom Wenseleers | Thanks for this detailed explanation - quick additional question: how do these scaling considerations apply to linear discriminant analysis biplots, as in stackoverflow.com/questions/17232251/…, or correspondence analysis biplots? Does this sqrt(n-1) scaling work the same there? | |
| Apr 12, 2015 at 22:56 | history | bounty ended | gung - Reinstate Monica | ||
| Apr 8, 2015 at 12:43 | history | edited | amoeba | CC BY-SA 3.0 |
added 123 characters in body
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| Apr 8, 2015 at 11:04 | comment | added | ttnphns | Another "further reading" might be added to this deserving answer. stats.stackexchange.com/q/119746/3277 - for a reader to understand what is "loading plot" and that it is an example of "variables in (reduced-rank) subject space". Therefore biplot is, in a sense, "variable space"+"subject space" in one representation. | |
| Apr 6, 2015 at 22:11 | history | edited | amoeba | CC BY-SA 3.0 |
added two links
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| Apr 6, 2015 at 21:07 | comment | added | amoeba | Thanks a lot, @gung! This is the first time somebody awards a bounty to my answer post hoc :) I will take another look at it to see if anything can be improved. | |
| Apr 6, 2015 at 16:09 | comment | added | gung - Reinstate Monica | +6, this deserves more than 3 upvotes. | |
| Apr 1, 2015 at 5:38 | vote | accept | ktdrv | ||
| Mar 19, 2015 at 10:12 | history | edited | amoeba | CC BY-SA 3.0 |
clarified the mysterious scaling of 0.8
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| Mar 14, 2015 at 0:05 | history | edited | amoeba | CC BY-SA 3.0 |
rearranged everything
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| Mar 13, 2015 at 11:13 | history | edited | amoeba | CC BY-SA 3.0 |
I read Gabriel's paper and clarified his point of view in my answer
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| Mar 13, 2015 at 10:20 | history | edited | amoeba | CC BY-SA 3.0 |
inserted a link, small edits
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| Mar 13, 2015 at 0:00 | history | answered | amoeba | CC BY-SA 3.0 |
