Module III, Class 2

4 Maio 2021, 14:30 • Jorge Filipe Campinos Landerset Cadima

Online class, Monday May 17, 14h30-17h00
[Slides 45-85] Eigenvalues/vectors in R. More properties of PCs. PCA on standardized data (correlation matrix PCA): its purpose and properties. The correlation matrix PCA of the crayfish data. The effects of centering and scaling in the representation of the data in both spaces (R^p and R^n). Interpreting PCs: tools and warnings. An alternative property optimized by correlation matrix PCs. The generalized eigenvalue problem. The Singular Value Decomposition of a generic matrix. PCA as an SVD of the centred data matrix (divided by the square root of n-1). SVDs in R. Yet another view of PCA: approximating an nxp data matrix by an nxp matrix of lower rank; the Eckart-Young theorem.