l1pcahp {pcaL1}

L1-PCAhp

Description

Performs a principal component analysis using the algorithm L1-PCAhp described by Visentin, Prestwich and Armagan (2016)

Usage

   l1pcahp(X, projDim=1, center=TRUE, projections="none", 
           initialize="l2pca", threshold=0.0001)

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).

initialize

method for initial guess for loadings matrix. Options are: "l2pca" - use traditional PCA/SVD, "random" - use a randomly-generated matrix.

threshold

sets the convergence threshold for the algorithm, default is 0.001.

Details

The calculation is performed according to the algorithm described by Visentin, Prestwich and Armagan (2016). The algorithm computes components iteratively in reverse, using a new heuristic based on Linear Programming. Linear programming instances are solved using Clp (http://www.coin-or.org).

Value

'l1pcahp' returns a list with class "l1pcahp" 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).

References

Visentin A., Prestwich S., and Armagan S. T. (2016) Robust Principal Component Analysis by Reverse Iterative Linear Programming, Joint European Conference on Machine Learning and Knowledge Discovery in Databases, 593-605. DOI:10.1007/978-3-319-46227-1_37

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)
myl1pcahp <- l1pcahp(X)

##projects data into 2 dimensions.
myl1pcahp <- l1pcahp(X, projDim=2, center=FALSE, projections="l1")

## plot first two scores
plot(myl1pcahp$scores)