Could create a new vignette with some additional PCA plots

• Plot 1 loading against another; include a circle with radius = 1 indicating that the maximum value of a load is +/- 1 since it is the cosine of an angle (and link back to "Understanding Scores and Loadings" vignette).
• Illustration/discussion of the biplot.

I've collected the following web links which may be useful as this project evolves. If we use one of these in a substantial way, we need to cite it. Check the box when the item has been reviewed and either included or rejected for inclusion (so we don't come back to it).

18 Oct 2021: Bryan put these in categories

General

• https://stats.stackexchange.com/questions/229092/how-to-reverse-pca-and-reconstruct-original-variables-from-several-principal-com
• https://stats.stackexchange.com/questions/88118/what-exactly-is-called-principal-component-in-pca/88137
• https://stats.stackexchange.com/questions/324752/why-are-pca-eigenvectors-orthogonal-but-correlated
• https://firsttimeprogrammer.blogspot.com/2018/08/pca-revisited.html
• https://towardsdatascience.com/an-intuitive-guide-to-pca-1174055fc800 good terminology
• https://stats.stackexchange.com/questions/189822/how-does-centering-make-a-difference-in-pca-for-svd-and-eigen-decomposition
• https://stats.stackexchange.com/questions/22501/is-there-an-intuitive-interpretation-of-ata-for-a-data-matrix-a/22520
• https://stats.stackexchange.com/questions/177102/what-is-the-intuition-behind-svd
• https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues/140579#140579

Use of SVD vs Eigen decomposition

• https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca
• https://stats.stackexchange.com/a/452454/26909

PCA on the correlation matrix (princomp vs prcomp vs eigen)

• https://stackoverflow.com/questions/7707507/pca-in-r-with-princomp-and-using-svd/7707720

Is there information in the later PCs?

• https://stats.stackexchange.com/questions/80446/the-first-principal-component-does-not-separate-classes-but-other-pcs-do-how-i
• https://stats.stackexchange.com/questions/101485/examples-of-pca-where-pcs-with-low-variance-are-useful

Sparse PCA

• https://stats.stackexchange.com/questions/35185/dimensionality-reduction-svd-or-pca-on-a-large-sparse-matrix
• https://stats.stackexchange.com/questions/79168/how-exactly-is-sparse-pca-better-than-pca
• https://stats.stackexchange.com/questions/305477/criteria-for-choosing-between-pca-and-sparse-pca

Image Reconstruction

• https://kieranhealy.org/blog/archives/2019/10/27/reconstructing-images-using-pca/
• https://stats.stackexchange.com/questions/177102/what-is-the-intuition-behind-svd

• Discuss how regression and PCA differ in terms of what value is being minimized/maximized. Show it graphically by overlaying a regression line with residuals and the first PC with projections on the same (small) data set.

• Add version info to all vignettes (code already in some). Perhaps in conjunction with the next item
• Add a "box" to the top of each vignette listing and cross-referencing all the vignettes. Bryan knows how to do this, he just has to go see how he did it before. This info box could include the version info. Info for the box will be in one file for easy maintenance (Completed: see "top-matter.md" for the magic).
• Use the same seed in all vignettes? Note: probably not necessary or desirable.
• Check for the TODOs in each vignette Note: as of 26 Nov all these are marked TODO:
• Use the same header sizes in each vignette. Note: Visually, I like the way the first and third header defaults look, but this messes with the TOC. Possibly use a css file to customize (Half-completed: fixed all to be 1st and 2nd level headers, fine tune later via css if still desired).
• Cross reference vigs to each other where appropriate (note: more will likely be needed)
• Use consistent language for "abstract space". I am finding that the more mathematically inclined resources use "basis". Right now I am liking the notion of a "reference frame" like they use in physics. This could be explained pretty clearly I think. Note: Bryan cleaned this up as much as possible on 26 Nov.
• Be consistent about use of variation vs signal vs variation (signal).

In the section The SVD Decomposition from the article The Math Behind PCA. It says that "The columns of U
are vectors giving the principal axes". Could it be V?

The plots in Visualizing_PCA_3D.Rmd are not showing up. Exploring work-arounds.

As of right now, all vignettes are on the devel branch and the automatic builds work. I am working my way through the vignettes, trying to pseudo-finalize them. DTH if you could please review these vignettes and make any changes you desire -- no need to have a discussion unless you think it desirable.

• Start_Here.Rmd
• Conceptual_Intro_PCA.Rmd
• Step_By_Step_PCA.Rmd
• Understanding Scores & Loadings
• Visualizing PCA in 3D
• The Math Behind PCA
• PCA Functions

I'll update this list as I complete my reviews.

We received the following e-mail from Prof. Ripley:

And it turns out the problem is not us, but with the kableExtra package we use. It looks like there has been little activity from the authors since 16 Dec 2021. I filed an issue here.

We can get by w/o this package, it just adds some nice styling. If we don't hear from them by the end of March, we'll drop the use of kableExtra. We are not the only ones in this boat.