ALSCPC: minimize the objective function Phi(D) by using of the...

In ALSCPC: Accelerated line search algorithm for simultaneous orthogonal transformation of several positive definite symmetric matrices to nearly diagonal form.

Description

The ALS.CPC function implement ALS algorithm based on the update formula

\bold{D_{k+1}} = R_{\bold{D_k}} (-β^{m_k} \ α \ grad(Φ (\bold{D}_k)))

until convergence (i.e. |Φ(\bold{D}_k)-Φ (\bold{D}_{k+1})| ≤ ε) and return the orthogonal matrix \bold{D}_r, r is the smallest nonnegative integer k such that |Φ(\bold{D}_k)-Φ (\bold{D}_{k+1})| ≤ ε.

Usage

ALS.CPC(alpha,beta,sigma,epsilon,G,nval,D,S)

Arguments

alpha	positive real number.
beta	real number belong to (0,1).
sigma	real number belong to (0,1).
epsilon	small positive constant controlling error term.
G	number of groups in common principal components analysis.
nval	a numeric vector containing the positive integers of sample sizes minus one in each group.
D	an initial square orthogonal matrix of order p, where p is group dimensionality.
S	a list of length G of positive definite symmetric matrices of order p.

Value

An orthogonal matrix such that minimize Φ(\bold{D}).

Author(s)

Dariush Najarzadeh

References

Absil, P. A., Mahony, R., & Sepulchre, R. (2009). Optimization algorithms on matrix manifolds. Princeton University Press.

Examples

nval<-numeric(3) 
nval[[1]]<-49
nval[[2]]<-49
nval[[3]]<-49
S<-vector("list",length=3)
setosa<-iris[1:50,1:4]; names(setosa)<-NULL
versicolor<-iris[51:100,1:4]; names(versicolor)<-NULL
virginica<-iris[101:150,1:4]; names(virginica)<-NULL
S[[1]]<-as.matrix(var(versicolor))
S[[2]]<-as.matrix(var(virginica))
S[[3]]<-as.matrix(var(setosa))
D<-diag(4)
ALS.CPC(10,0.5,0.4,1e-5,G=3,nval,D,S)

ALSCPC documentation built on May 2, 2019, 2:11 a.m.