SSC: Sparse Subspace Clustering

In T4cluster: Tools for Cluster Analysis

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

\insertRef

elhamifar_sparse_2009T4cluster

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)

T4cluster documentation built on Aug. 16, 2021, 9:07 a.m.