I have just completed the changes that I could perform for the unconstrained ordination portion.
I attempted to improve the quality and clarity of the presentation to the best of my ability. Further effort should be allocated to this workshop so the PCoA and NMDS explanation can be improved and be more comparable to the PCA explanation.
Below I list all changes that have been performed in this pull-request:
Extended the explanation of variance, covariance, eigenvalues, eigenvectors.
Improved explanation and added algebra for linear transformations;
Improved explanation (with algebra) for eigendecomposition;
Added visualization containing shear transformation to clarify the explanation of eigenvectors;
Added explanation about orthogonality (including direct and simple algebra);
Added explanation about maximization (including algebra);
Added clarification about unconstrained ordination, including a summary of the methods that will be learned;
Added explanation and clarification on the basis of PCA;
Modified the explanation of PCA to include calculation and coding from scratch, which progressively represents each step in plots, so participants can understand how eigenvalues and eigenvectors can be projected onto the Cartesian space, what are loadings, how to obtain and represent the score matrix and rotate the data;
Added comparisons from the from-scratch calculations to the main R functions, so participants can assimilate how to obtain the corresponding information;
Added explanation on the use of the Kaiser-Guttman criterium to select eigenvectors;
Added explanation on the use of the broken-stick model to select eigenvectors;
Replaced several figures that were loaded from the directory by R code-mediated direct-plotting;
Moved correspondence analysis to the bottom of the workshop (i.e. so it is not instructed) to provide more time for PCA, PCoA and nMDS;
Removed unnecessary repetitive slides that included other ways of visualizing biplots (including some that would not work with xaringan);
Added PlaneGeometry to the packages;
Corrected issues with style, slide position and rearrangement, and grammar.
Hi!
I have just completed the changes that I could perform for the unconstrained ordination portion.
I attempted to improve the quality and clarity of the presentation to the best of my ability. Further effort should be allocated to this workshop so the PCoA and NMDS explanation can be improved and be more comparable to the PCA explanation.
Below I list all changes that have been performed in this pull-request: