SSQP: Subspace Segmentation via Quadratic Programming In T4cluster: Tools for Cluster Analysis

Description

Subspace Segmentation via Quadratic Programming (SSQP) solves the following problem

\textrm{min}_Z \|X-XZ\|_F^2 + λ \|Z^\top Z\|_1 \textrm{ such that }diag(Z)=0,~Z≤q 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

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

Arguments

 data an (n\times p) matrix of row-stacked observations. k the number of clusters (default: 2). lambda 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

\insertRef

wang_efficient_2011T4cluster

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 ## 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) 

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