LRR {T4cluster}

Low-Rank Representation

Description

Low-Rank Representation (LRR) constructs the connectivity of the data by solving

\textrm{min}_C \|C\|_*\quad\textrm{such that}\quad D=DC

for column-stacked data matrix D and \|\cdot \|_* is the nuclear norm which is relaxation of the rank condition. If you are interested in full implementation of the algorithm with sparse outliers and noise, please contact the maintainer.

Usage

LRR(data, k = 2, rank = 2)

Arguments

data

an (n\times p) matrix of row-stacked observations.

k

the number of clusters (default: 2).

rank

sum of dimensions for all k subspaces (default: 2).

Value

a named list of S3 class T4cluster containing

cluster

a length-n vector of class labels (from 1:k).

algorithm

name of the algorithm.

References

Liu G, Lin Z, Yu Y (2010). “Robust Subspace Segmentation by Low-Rank Representation.” In Proceedings of the 27th International Conference on International Conference on Machine Learning, ICML'10, 663–670. ISBN 978-1-60558-907-7.

Examples

## generate a toy example
set.seed(10)
tester = genLP(n=100, nl=2, np=1, iso.var=0.1)
data   = tester$data
label  = tester$class

## do PCA for data reduction
proj = base::eigen(stats::cov(data))$vectors[,1:2]
dat2 = data%*%proj

## run LRR algorithm with k=2, 3, and 4 with rank=4
output2 = LRR(data, k=2, rank=4)
output3 = LRR(data, k=3, rank=4)
output4 = LRR(data, k=4, rank=4)

## extract label information
lab2 = output2$cluster
lab3 = output3$cluster
lab4 = output4$cluster

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(dat2, pch=19, cex=0.9, col=lab2, main="LRR:K=2")
plot(dat2, pch=19, cex=0.9, col=lab3, main="LRR:K=3")
plot(dat2, pch=19, cex=0.9, col=lab4, main="LRR:K=4")
par(opar)