## R–Data Exploration

# 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?

###### Links

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

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

https://www.dropbox.com/s/mjdtdpgji74cut1/PCA_with_R.pdf?dl=0

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