Here is code from Bryan Shader that illustrates how R does PCA: SVAPCA2.R
… and an announcement … for the time-being we’re going to suspend our meetings due to the anticipated spread of COVID19. So there will be no meeting on 13 March 2020, nor during spring break (20 March). We will see from there and maybe we’ll get together via Zoom or something else thereafter.
Let’s follow up on this thread on Twitter, posted by a population genomicist at Ancestry.com
Cholesky decomposition in context of non-centered parameterizations of multivariate hierarchical Bayesian models
The follow-on course to the introduction linear algebra class. Matrix methods expands on the fundamental concepts discussed and introduces some additional ideas that are also very useful, such as positive-definite matrices, singular value decomposition, etc.
Free (or paid, if you want a certificate), self-paced linear algebra courses from a number of institutions.
Singular Value Decomposition (SVD)
SVD is a fundamental factorization technique that is used a in wide variety of situations and fields that vary from statistics (e.g., principal component analysis) to fluid flow (e.g., dynamical systems).
I (Jason) have been really enjoying this playlist. Great explanations of SVD with coding examples (Matlab and Python) and applications (e.g., image compression, fast approximations of fluid flow, PCA).
What may be of particular interest to some in this group is discussion of Robust Principal Component Analysis (RPCA), which is a means of dealing with matrices that are missing lots of data.
Principal Component Analysis (PCA)
A specific application of SVD focused on finding the rotation of a matrix that maximizes the most variation along a set of axes (columns) that have been standardized.