Class 2 (Module III)

18 Maio 2022, 15:00 • Jorge Filipe Campinos Landerset Cadima

[Slides PCA+LDA 51-65 + 69-117] Interpreting PCA in the space of variables. Some additional remarks about PCA. The Singular Value Decomposition of a generic matrix. PCA as the SVD of the centred data matrix. SVDs in R. Biplots: concept, construction and interpretation. Mahalanobis distances. Biplots in R. An example of biplots: the crayfish data (both Covariance and Correlation Matrix PCA). Linear Discriminant Analysis: introduction, the classification matrix, Fisher's formulation of the problem, the generalized eigenvalue problem and the solution to the problem. Properties of discriminant axes. Discriminant axes as the linear combinations of the original variables which maximize the F-test statistic in a one-way ANOVA over the grouping factor. Alternative formulations of LDA, all equivalent to minimizing the angle between the column-space of the centred data and the column-space of the classification matrix. Classification of new individuals using the discriminant axes. LDA in R: the lda command in the MASS package; its usage and characteristics.

Nota: Esta aula foi leccionada na sexta-feira, dia 27.5.22, das 14h30 às 17h10, na Sala S1, simultaneamente presencial e por zoom.