Description Usage Arguments Details Value References Examples
View source: R/subspace_LRSC.R
Low-Rank Subspace Clustering (LRSC) constructs the connectivity of the data by solving
\textrm{min}_C \|C\|_*\quad\textrm{such that}\quad A=AC,~C=C^\top
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
\textrm{min}_C \|C\|_* + \frac{τ}{2} \|A-AC\|_F^2 \quad\textrm{such that}\quad C=C^\top
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.
1 |
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. |
\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.
a named list of S3 class T4cluster
containing
a length-n vector of class labels (from 1:k).
name of the algorithm.
vidal_low_2014T4cluster
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)
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