Remembering Thoughts

# PCA

Principal Components Analysis (PCA) allows us to study and explore a set of quantitative variables measured on a set of objects

###### Core Idea

With PCA we seek to reduce the dimensionality (reduce the number of variables) of a data set while retaining as much as possible of the variation present in the data

Before performing a PCA(or any other multivariate method) we should start with some preliminary explorations

• Descriptive statistics
• Basic graphical displays
• Distribution of variables
• Pair-wise correlations among variables
• Perhaps transforming some variables
• ETC

The minimal output from any PCA should contain 3 things:

Eigenvalues provide information about the amount of variability captured by each principal component

Scores or PCs (principal components) that provide coordinates to graphically represent objects in a lower dimensional space

Loadings provide information to determine what variables characterize each principal component

###### Some questions to keep in mind
• How many PCs should be retained?
• How good (or bad) is the data approximation with the retained PCs?
• What variables characterize each PC?
• Which variables are influential, and how are they correlated?
• Which variables are responsible for the patterns among objects?
• Are there any outlier objects?

http://genomicsclass.github.io/book/pages/pca_svd.html

http://www.r-bloggers.com/using-r-two-plots-of-principal-component-analysis/

http://www.sthda.com/english/wiki/principal-component-analysis-in-r-prcomp-vs-princomp-r-software-and-data-mining