LRR: Low-Rank Representation

In T4cluster: Tools for Cluster Analysis

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

\insertRef

liu_robust_2010T4cluster

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)

T4cluster documentation built on Nov. 5, 2025, 5:55 p.m.