# 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

 1 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

  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))$vectors[,1:2] dat2 = data%*%proj ## run LSR for k=3 with different lambda values out1 = LSR(data, k=3, lambda=1e-2) out2 = LSR(data, k=3, lambda=1) out3 = LSR(data, k=3, lambda=1e+2) ## extract label information lab1 = out1$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.