PCA dimentional reduction

Question

I try to plot three values of a VCF file (QUAL, DP, and rate of phasing) for all the SNPs in the file.

I thought that a PCA plot would be a good way to reduce dimensions of the plot, and to compare values although they were not on the same scale.

I have tried to build the PCA with different R packages as ggbiplot and pca3d, but its seems that the distribution of the dots cloud is always skewed as a dimension is missing. Find below the code used for generating the ggbiplot.

Would anyone have some advises to reduce three values with different scales to two-dimensional PCA?

library(devtools) 
library(ggbiplot) 

# Create the dataframe
df <- df[c("quality", "phasing", "depth")]  

# Create the PCA dataset
pop.pca   <- prcomp(df, center = TRUE,scale. = TRUE)

# Create the plot
ggbiplot(pop.pca) +     
scale_y_continuous(trans='log10') +
scale_x_continuous(trans='log10')

Answer 1

There isn't a dimension missing because PC1 and PC2 are "summaries" of all your variable. Infact, PC1 is a linear combination of your feature, calculate like: PC1 = v1*feature1 + v2*feature2 + v3*feature3 + ... where v1,v2 and v3 are scalar number calculated directly by PCA model.

PCA calculed n PC, where n is equal to your number of feature and are selected the first and the second PC because are those that explain the greatest variability in the system.

For a complete example in R follow this link