LSR {T4cluster}

Least Squares Regression

Description

For the subspace clustering, traditional method of least squares regression is used to build coefficient matrix that reconstructs the data point by solving

\textrm{min}_Z \|X-XZ\|_F^2 + \lambda \|Z\|_F \textrm{ such that }diag(Z)=0

where X\in\mathbf{R}^{p\times n} is a column-stacked data matrix. As seen from the equation, we use a denoising version controlled by \lambda and provide an option to abide by the constraint diag(Z)=0 by zerodiag parameter.

Usage

LSR(data, k = 2, lambda = 1e-05, zerodiag = TRUE)

Arguments

data

an (n\times p) matrix of row-stacked observations.

k

the number of clusters (default: 2).

lambda

regularization parameter (default: 1e-5).

zerodiag

a logical; TRUE (default) to use the problem formulation with zero diagonal entries or FALSE otherwise.

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

Lu C, Min H, Zhao Z, Zhu L, Huang D, Yan S (2012). “Robust and Efficient Subspace Segmentation via Least Squares Regression.” In Hutchison D, Kanade T, Kittler J, Kleinberg JM, Mattern F, Mitchell JC, Naor M, Nierstrasz O, Pandu Rangan C, Steffen B, Sudan M, Terzopoulos D, Tygar D, Vardi MY, Weikum G, Fitzgibbon A, Lazebnik S, Perona P, Sato Y, Schmid C (eds.), Computer Vision -ECCV 2012, volume 7578, 347–360. Springer Berlin Heidelberg, Berlin, Heidelberg. ISBN 978-3-642-33785-7 978-3-642-33786-4.

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 LSR for k=3 with different lambda values
out1 = LSR(data, k=3, lambda=1e-2)
out2 = LSR(data, k=3, lambda=1)
out3 = LSR(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="LSR:lambda=1e-2")
plot(dat2, pch=19, cex=0.9, col=lab2, main="LSR:lambda=1")
plot(dat2, pch=19, cex=0.9, col=lab3, main="LSR:lambda=1e+2")
par(opar)