Dimension Reduction

These are notes and material from a course on Dimension Reduction given as part of the Australian Mathematical Sciences Institute (AMSI) Winter School.

Lectures

This short course covers:

Motivation
Principal Components Analysis (PCA)
Multidimensional Scaling (MDS)
Kernel PCA
Autoencoders
Manifolds
Isomap
Local Linear Embedding
Laplacian Eigenmaps
Evaluation of Dimension Reduction techniques

All slides were made using Yihui Xie's Xaringan package. They are available on my personal website. They can be printed as pdf files using a browser with Google Chrome generally working best. Note that many of the plots are interactive and will not render well when printed as pdf.

If you want to build the slides yourself, simply clone the repository. Note that you will have to run the command xaringan::summon_remark() once before knitting the r markdown document.

Textbook

The notes are my own but much of the course is inspired by the excellent text

Izenman, A. J. (2008). "Modern multivariate statistical techniques. Regression, classification and manifold learning.", Springer.

In particular Chapter 7 (especially section 7.2), Chapter 13 and Chapter 16 provide a good supplement to this course.

Software

All coding is done using R and the packages of the tidyverse. Of tremendous use is the package dimRed by Guido Kraemer available on CRAN and Github. The packages broom, png and kpca should also be installed if you want to work through the tutorials.

Tutorials

Tutorials are available on the course website. A single R markdown file generates a pdf both with and without solutions. Simply change line 17 to Tutorial 1 Solutions or Tutorial 2 Solutions if you need to generate the files with solutions, and anything else if you do not want solutions.

Data

Data can be found in the data folder. They are also available on the course website. The datasets are: