SSQP {T4cluster} | R Documentation |
Subspace Segmentation via Quadratic Programming
Description
Subspace Segmentation via Quadratic Programming (SSQP) solves the following problem
\textrm{min}_Z \|X-XZ\|_F^2 + \lambda \|Z^\top Z\|_1 \textrm{ such that }diag(Z)=0,~Z\leq 0
where X\in\mathbf{R}^{p\times n}
is a column-stacked data matrix. The computed Z^*
is
used as an affinity matrix for spectral clustering.
Usage
SSQP(data, k = 2, lambda = 1e-05, ...)
Arguments
data |
an |
k |
the number of clusters (default: 2). |
lambda |
regularization parameter (default: 1e-5). |
... |
extra parameters for the gradient descent algorithm including
|
Value
a named list of S3 class T4cluster
containing
- cluster
a length-
n
vector of class labels (from1:k
).- algorithm
name of the algorithm.
References
Wang S, Yuan X, Yao T, Yan S, Shen J (2011). “Efficient Subspace Segmentation via Quadratic Programming.” In Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, AAAI'11, 519–524.
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))$vectors[,1:2]
dat2 = data%*%proj
## run SSQP for k=3 with different lambda values
out1 = SSQP(data, k=3, lambda=1e-2)
out2 = SSQP(data, k=3, lambda=1)
out3 = SSQP(data, k=3, lambda=1e+2)
## extract label information
lab1 = out1$cluster
lab2 = out2$cluster
lab3 = out3$cluster
## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(dat2, pch=19, cex=0.9, col=lab1, main="SSQP:lambda=1e-2")
plot(dat2, pch=19, cex=0.9, col=lab2, main="SSQP:lambda=1")
plot(dat2, pch=19, cex=0.9, col=lab3, main="SSQP:lambda=1e+2")
par(opar)