l1pca: L1-PCA

In pcaL1: L1-Norm PCA Methods

L1-PCA

Description

Performs a principal component analysis using the algorithm L1-PCA given by Ke and Kanade (2005).

Usage

   l1pca(X, projDim=1, center=TRUE, projections="l1", 
	 initialize="l2pca", tolerance=0.0001, iterations=10)

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 ("l1", default) or L2 ("l2") norm.
initialize	initial guess for loadings matrix. Options are: "l2pca" - use traditional PCA/SVD, "random" - use a randomly-generated matrix. The user can also provide a matrix as an initial guess.
tolerance	sets the convergence tolerance for the algorithm, default is 0.0001.
iterations	sets the number of iterations to run before returning the result, default is 10.

Details

The calculation is performed according to the linear programming-based algorithm described by Ke and Kanade (2005). The method is a locally-convergent algorithm for finding the L1-norm best-fit subspace by alternatively optimizing the scores and the loadings matrix at each iteration. Linear programming instances are solved using Clp (http://www.coin-or.org)

Value

'l1pca' returns a list with class "l1pca" containing the following components:

loadings	the matrix of variable loadings. The matrix has dimension ncol(X) x projDim. The columns defined 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 (reconstructions). The matrix has dimension nrow(X) x ncol(X).

References

Ke Q. and Kanade T. (2005) Robust L1 norm factorization in the presence of outliers and missing data by alternative convex programming, IEEE Conference on Computer Vision and Pattern Recognition. DOI:10.1109/CVPR.2005.309

Examples

##for 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)
myl1pca <- l1pca(X)

##projects data into 2 dimensions.
myl1pca <- l1pca(X, projDim=2, center=FALSE, 
                 tolerance=0.00001, iterations=20)

## plot first two scores
plot(myl1pca$scores)

pcaL1 documentation built on Jan. 22, 2023, 1:55 a.m.