pcal1 {pcaL1} | R Documentation |
PCA-L1
Description
Performs a principal component analysis using the algorithm PCA-L1 given by Kwak (2008).
Usage
pcal1(X, projDim=1, center=TRUE, projections="none", initialize="l2pca")
Arguments
X |
data, must be in |
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 |
initial guess for first component. Options are: "l2pca" - use traditional PCA/SVD, "maxx" - use the point with the largest norm, "random" - use a random vector. The user can also provide a vector as the initial guess. |
Details
The calculation is performed according to the algorithm described by Kwak (2008). The method is a locally-convergent algorithm for finding successive directions of maximum L1 dispersion.
Value
'pcal1' returns a list with class "pcal1" containing the following components:
loadings |
the matrix of variable loadings. The matrix has dimension ncol(X) x projDim. 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 (reconstructions). The matrix has dimension nrow(X) x ncol(X). |
References
Kwak N. (2008) Principal component analysis based on L1-norm maximization, IEEE Transactions on Pattern Analysis and Machine Intelligence, 30: 1672-1680. DOI:10.1109/TPAMI.2008.114
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)
mypcal1 <- pcal1(X)
##projects data into 2 dimensions.
mypcal1 <- pcal1(X, projDim=2, center=FALSE, projections="l1")
## plot first two scores
plot(mypcal1$scores)