Introduction

FastPCA is a simple implementation of principal component analysis designed to run extremley fast on matrices of varying sizes. Additionally, FastPCA provides users the ability to only calculate a couple PCs at time. This allows users who are only interested in the first couple PCs to save large amounts of computing time when compared with base R implementation of PCA. The workhorse function of the algorithm is the PRIMME eigensolver (https://cran.r-project.org/web/packages/PRIMME/index.html) which allows for both partial eigendecompositon and a great increase in speed.

Installation

devtools::install_github("cresswellkg/FastPCA")
library(FastPCA)

Comparing run speeds

Below we compare run speeds with princomp from the stat package and corpcor's (https://cran.r-project.org/web/packages/corpcor/index.html) fast.svd function

#Simulating a square matrix
square_mat = matrix(runif(3000^2, 0, 200), 3000, 3000)
#Running on the matrix while only calculating first 2 PCs
time = proc.time()
FastPCA(square_mat, PCs = 2)
proc.time()-time

user  system elapsed 
18.37    0.09   18.44 

#Repeating with first 10 PCs
time = proc.time()
FastPCA(square_mat, PCs = 10)
proc.time()-time

user  system elapsed 
19.82    0.12   20.33 

#Now with base R
time = proc.time()
princomp(square_mat)
proc.time()-time

user  system elapsed 
71.35    0.25   71.97 

Runtimes on wide matrices

It is a known problem that PCA can be exceptionally slow on large p, small n matrices. These matrices are common in genomics with large-scale GWAS studies. Here, the PCA step is limited by the speed of the correlation/covariance calculation which we optimize using the coop package.

#Simulating a 50x5000 wide matrix
wide_mat = matrix(runif(50*50000, 0, 200), 50, 5000)
#Running on the matrix while only calculating first 2 PCs
time = proc.time()
FastPCA(wide_mat, PCs = 10)
proc.time()-time

user  system elapsed 
2.84    0.05    2.92 

#Using princomp
time = proc.time()
princomp(wide_mat)
proc.time()-time

user  system elapsed 
69.89    0.17   70.30 

Runtime on long matrices

Like all PCA methods, FastPCA is most efficient on long matrices. Thus, we demonstrate this with an exceptionally large matrix (5000000 x 50).

#Simulating a 5000000x50 long matrix
long_mat = matrix(runif(5e+06*50, 0, 200), 5000000, 50)
#Running on the matrix while only calculating first 2 PCs
time = proc.time()
pcs = FastPCA(long_mat, PCs = 10)
proc.time()-time

user  system elapsed 
14.80    2.73   16.25 

time = proc.time()
pc_princomp = princomp(long_mat)
proc.time()-time

user  system elapsed 
37.14    1.84   39.31 

#Redoing PCs
pcs = FastPCA(long_mat, PCs = 10)
#Plotting 1st and 3rd PC
plotPCs(pcs, PC1 = 1, PC = 3)