# grassmann.optmacg: Estimation of Distribution Algorithm with MACG Distribution In Riemann: Learning with Data on Riemannian Manifolds

 grassmann.optmacg R Documentation

## Estimation of Distribution Algorithm with MACG Distribution

### Description

For a function f : Gr(k,p) \rightarrow \mathbf{R}, find the minimizer and the attained minimum value with estimation of distribution algorithm using MACG distribution.

### Usage

grassmann.optmacg(func, p, k, ...)


### Arguments

 func a function to be minimized. p dimension parameter as in Gr(k,p). k dimension parameter as in Gr(k,p). ... extra parameters including n.startnumber of runs; algorithm is executed n.start times (default: 10). maxitermaximum number of iterations for each run (default: 100). popsizethe number of samples generated at each step for stochastic search (default: 100). ratioratio in (0,1) where top ratio*popsize samples are chosen for parameter update (default: 0.25). print.progressa logical; if TRUE, it prints each iteration (default: FALSE).

### Value

a named list containing:

cost

minimized function value.

solution

a (p\times k) matrix that attains the cost.

### Examples

#-------------------------------------------------------------------
#               Optimization for Eigen-Decomposition
#
# Given (5x5) covariance matrix S, eigendecomposition is can be
# considered as an optimization on Grassmann manifold. Here,
# we are trying to find top 3 eigenvalues and compare.
#-------------------------------------------------------------------

## PREPARE
A = cov(matrix(rnorm(100*5), ncol=5)) # define covariance
myfunc <- function(p){                # cost function to minimize
return(sum(-diag(t(p)%*%A%*%p)))
}

## SOLVE THE OPTIMIZATION PROBLEM
Aout = grassmann.optmacg(myfunc, p=5, k=3, popsize=100, n.start=30)

## COMPUTE EIGENVALUES
#  1. USE SOLUTIONS TO THE ABOVE OPTIMIZATION
abase   = Aout$solution eig3sol = sort(diag(t(abase)%*%A%*%abase), decreasing=TRUE) # 2. USE BASIC 'EIGEN' FUNCTION eig3dec = sort(eigen(A)$values, decreasing=TRUE)[1:3]

## VISUALIZE
yran = c(min(min(eig3sol),min(eig3dec))*0.95,
max(max(eig3sol),max(eig3dec))*1.05)
plot(1:3, eig3sol, type="b", col="red",  pch=19, ylim=yran,
xlab="index", ylab="eigenvalue", main="compare top 3 eigenvalues")
lines(1:3, eig3dec, type="b", col="blue", pch=19)
legend(1.55, max(yran), legend=c("optimization","decomposition"), col=c("red","blue"),
lty=rep(1,2), pch=19)
par(opar)



Riemann documentation built on March 18, 2022, 7:55 p.m.