SSC {T4cluster}

Sparse Subspace Clustering

Description

Sparse Subspace Clustering (SSC) assumes that the data points lie in a union of low-dimensional subspaces. The algorithm constructs local connectivity and uses the information for spectral clustering. SSC is an implementation based on basis pursuit for sparse reconstruction for the model without systematic noise, which solves

\textrm{min}_C \|C\|_1\quad\textrm{such that}\quad diag(C)=0,~D=DC

for column-stacked data matrix D. If you are interested in full implementation of the algorithm with sparse outliers and noise, please contact the maintainer.

Usage

SSC(data, k = 2)

Arguments

data

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

k

the number of clusters (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

Elhamifar E, Vidal R (2009). “Sparse Subspace Clustering.” In 2009 IEEE Conference on Computer Vision and Pattern Recognition, 2790–2797. ISBN 978-1-4244-3992-8.

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 SSC algorithm with k=2, 3, and 4
output2 = SSC(data, k=2)
output3 = SSC(data, k=3)
output4 = SSC(data, k=4)

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

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(3,4))
plot(dat2[,1],dat2[,2],pch=19,cex=0.3,col=lab2,main="K=2:PCA")
plot(data[,1],data[,2],pch=19,cex=0.3,col=lab2,main="K=2:Axis(1,2)")
plot(data[,1],data[,3],pch=19,cex=0.3,col=lab2,main="K=2:Axis(1,3)")
plot(data[,2],data[,3],pch=19,cex=0.3,col=lab2,main="K=2:Axis(2,3)")

plot(dat2[,1],dat2[,2],pch=19,cex=0.3,col=lab3,main="K=3:PCA")
plot(data[,1],data[,2],pch=19,cex=0.3,col=lab3,main="K=3:Axis(1,2)")
plot(data[,1],data[,3],pch=19,cex=0.3,col=lab3,main="K=3:Axis(1,3)")
plot(data[,2],data[,3],pch=19,cex=0.3,col=lab3,main="K=3:Axis(2,3)")

plot(dat2[,1],dat2[,2],pch=19,cex=0.3,col=lab4,main="K=4:PCA")
plot(data[,1],data[,2],pch=19,cex=0.3,col=lab4,main="K=4:Axis(1,2)")
plot(data[,1],data[,3],pch=19,cex=0.3,col=lab4,main="K=4:Axis(1,3)")
plot(data[,2],data[,3],pch=19,cex=0.3,col=lab4,main="K=4:Axis(2,3)")
par(opar)