pcaL1 (version 1.5.7)

l1pcastar: L1-PCA*

Description

Performs a principal component analysis using the algorithm L1-PCA* described by Brooks, Dula, and Boone (2013)

Usage

l1pcastar(X, projDim=1, center=TRUE, projections="none")

Value

'l1pcastar' returns a list with class "l1pcastar" containing the following components:

loadings

the matrix of variable loadings. The matrix has dimension ncol(X) x ncol(X). The columns define the projected subspace.

scores

the matrix of projected points. The matrix has dimension nrow(X) x projDim.

dispExp

the proportion of L1 dispersion explained by the loadings vectors. Calculated as the L1 dispersion of the score on each component divided by the L1 dispersion in the original data.

projPoints

the matrix of projected points in terms of the original coordinates. The matrix has dimension nrow(X) x ncol(X).

Arguments

X

data, must be in matrix or table form

projDim

number of dimensions to project data into, must be an integer, default is 1

center

whether to center the data using the median, default is TRUE

projections

whether to calculate reconstructions and scores using the L1 norm ("l1") the L2 norm ("l2") or not at all ("none", default)

Details

The calculation is performed according to the algorithm described by Brooks, Dula, and Boone (2013). The algorithm finds successive directions of minimum dispersion in the data by finding the L1-norm best-fit hyperplane at each iteration. Linear programming instances are solved using Clp (http://www.coin-or.org)

References

1. Brooks J.P., Dula J.H., and Boone E.L. (2013) A Pure L1-Norm Princpal Component Analysis, Computational Statistics & Data Analysis, 61:83-98. DOI:10.1016/j.csda.2012.11.007

2. Zhou, Y.-H. and Marron, J.S. (2016) Visualization of Robust L1PCA, Stat, 5:173-184. DOI:10.1002/sta4.113

Examples

##for a 100x10 data matrix X, 
## lying (mostly) in the subspace defined by the first 2 unit vectors, 
## projects data into 1 dimension.
X <- matrix(c(runif(100*2, -10, 10), rep(0,100*8)),nrow=100) +
                 matrix(c(rep(0,100*2),rnorm(100*8,0,0.1)),ncol=10)
myl1pcastar <- l1pcastar(X)

##projects data into 2 dimensions.
myl1pcastar <- l1pcastar(X, projDim=2, center=FALSE, projections="l1")

## plot first two scores
plot(myl1pcastar$scores)