1 Welcome to DMML Lab 1

In week 1, we have studied how to use principal component analysis (PCA) to perform dimension reduction.

Before implementing PCA, we should always check that the variables are continuous and perform some exploratory analysis. Some useful codes include:

str, skim, summary, cor #for numerical summaries
plot, pairs #for graphical summaries

Next, we perform PCA by using the command princomp. If the variables have been recorded on different scales or they have very different variances, then it is advisable to base the analysis on the sample correlation matrix; in this case, we set the second argument cor to TRUE. Otherwise, covariance matrix is preferred (no need to include the second argument).

my.pca <- princomp(my.data, cor=TRUE) #correlation-based PCA
my.pca <- princomp(my.data) #covariance-based PCA

To determine the number of principal components to be retained, we could use Proportion of Variation, Kaiser's method and Cattell's method. The former two methods require the standard deviation of each principal component, which can be found by using summary(my.pca) or my.pca$sdev. The last method requires a scree plot, which can be produced by using plot(my.pca).

Finally, once PCA is performed, we can interpret the principal components by looking at the loadings (my.pca$loadings). Observations in the new PC coordinate system, i.e. scores, are stored in my.pca$scores. A new observation can be projected into the PC space by using predict(my.pca, new.data).