# LRSC: Low-Rank Subspace Clustering In T4cluster: Tools for Cluster Analysis

## Description

Low-Rank Subspace Clustering (LRSC) constructs the connectivity of the data by solving

for the uncorrupted data scenario where A is a column-stacked data matrix. In the current implementation, the first equality constraint for reconstructiveness of the data can be relaxed by solving

controlled by the regularization parameter τ. If you are interested in enabling a more general class of the problem suggested by authors, please contact maintainer of the package.

## Usage

 1 LRSC(data, k = 2, type = c("relaxed", "exact"), tau = 1) 

## Arguments

 data an (n\times p) matrix of row-stacked observations. k the number of clusters (default: 2). type type of the problem to be solved. tau regularization parameter for relaxed-constraint problem.

## Details

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.

## 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

vidal_low_2014T4cluster

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 ## 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))$vectors[,1:2] dat2 = data%*%proj ## run LRSC algorithm with k=2,3,4 with relaxed/exact solvers out2rel = LRSC(data, k=2, type="relaxed") out3rel = LRSC(data, k=3, type="relaxed") out4rel = LRSC(data, k=4, type="relaxed") out2exc = LRSC(data, k=2, type="exact") out3exc = LRSC(data, k=3, type="exact") out4exc = LRSC(data, k=4, type="exact") ## extract label information lab2rel = out2rel$cluster lab3rel = out3rel$cluster lab4rel = out4rel$cluster lab2exc = out2exc$cluster lab3exc = out3exc$cluster lab4exc = out4exc\$cluster ## visualize opar <- par(no.readonly=TRUE) par(mfrow=c(2,3)) plot(dat2, pch=19, cex=0.9, col=lab2rel, main="LRSC Relaxed:K=2") plot(dat2, pch=19, cex=0.9, col=lab3rel, main="LRSC Relaxed:K=3") plot(dat2, pch=19, cex=0.9, col=lab4rel, main="LRSC Relaxed:K=4") plot(dat2, pch=19, cex=0.9, col=lab2exc, main="LRSC Exact:K=2") plot(dat2, pch=19, cex=0.9, col=lab3exc, main="LRSC Exact:K=3") plot(dat2, pch=19, cex=0.9, col=lab4exc, main="LRSC Exact:K=4") par(opar) 

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