LSR: Least Squares Regression

In T4cluster: Tools for Cluster Analysis

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 + λ \|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 λ 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

\insertRef

hutchison_robust_2012T4cluster

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)

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