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.

SSQP(data, k = 2, lambda = 1e-05, ...)

## Arguments

data an $$(n\times p)$$ matrix of row-stacked observations. the number of clusters (default: 2). regularization parameter (default: 1e-5). extra parameters for the gradient descent algorithm including maxitermaximum number of iterations (default: 100). abstoltolerance level to stop (default: 1e-7).

## 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

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

# \donttest{
## 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