PenOpt: Solve the internal minimization problem

In l1spectral: An L1-Version of the Spectral Clustering

Description

This internal function of the l1-spectral clustering algorithm solves the l1-minimization problem and recover the community indicators of the clusters.

Usage

PenOpt(U, n, elements, iteration, pen, k)

Arguments

U	The eigenvector matrix.
n	The number of nodes of the connected component to cluster.
elements	The representative elements of the connected component to cluster.
iteration	The cluster we aim at recovering.
pen	The penalty (to be chosen among "lasso" and "thresholdedLS").
k	The number of clusters.

Value

v The community indicator of cluster iteration.

Author(s)

Camille Champion, Magali Champion

See Also

l1_spectralclustering, l1_spectral, l1spectral.

Examples

 ###################################
 # Solving the minimization problem
 ###################################

 # 1st: create data
 Data <- CreateDataSet(k=3, n=20, p=list(p_inside=0.1,p_outside=0.1))

 # 2nd: find the structure, the opt number of clusters and the representative elements
 Structure <- FindStructure(Data$A_hat)
 Clusters <- FindNbrClusters(A = Data$A_hat, structure = Structure)
 Elements <- FindElement(A = Data$A_hat, structure = Structure, clusters = Clusters)

 Structure_tmp <- Structure$groups[[1]] # the first component
 A_tmp <- Data$A_hat[Structure$groups[[1]],Structure$groups[[1]]]
 n <- ncol(A_tmp)
 k <- Clusters$nbr_clusters$Component1 # number of clusters to create
 Elements_tmp <- Elements$indices$Component1 # the elements of the first component

 # 3rd: perform svd
 svd <- eigen(A_tmp)
 eigenvalues <- sort(svd$values,index.return=TRUE)
 eigenvectors <- svd$vectors[,eigenvalues$ix]

 # 4th: solve the minimization problem
 i <- 1 # the cluster we aim at recovering
 U <- t(eigenvectors[,1:(n-k+i-1)])
 v <- PenOpt(U, n, elements = Elements_tmp, iteration = i, pen = "lasso", k) # for lasso

 # the same with the least-squared threshold
 v <- PenOpt(U, n, elements = Elements_tmp, iteration = i, pen = "thresholdedLS", k)

l1spectral documentation built on Jan. 27, 2022, 1:07 a.m.