greedy: Greedy algorithm for maximum entropy sampling

In edesign: Maximum Entropy Sampling

Description

Starting point is a network A[F] with nf points. Now one has to select ns points of a set of candidate sites to augment the existing network. The aim of maximum entropy sampling is to select a feasible D-optimal design that maximizes the logarithm of the determinant of all principal submatrices of A arising by this expansion.

It is not possible to construct a completely new network, that means nf>0. Use the dual greedy heuristic for this purpose.

This greedy algorithm starts with the submatrix A[F] and selects the best candidate of each of the stages (1..ns) to expand this matrix.

Usage

greedy(A, nf, ns, etol=0, mattest=TRUE)

Arguments

A	Spatial covariance matrix A.
nf	Number of stations are forced into every feasible solution.
ns	Number of stations have to be added to the existing network.
etol	Tolerance for checking positve definiteness (default 0)
mattest	Toggles testing matrix A for symmetry and positive definiteness (default T)

Details

A[F] denotes the principal submatrix of A having rows and columns indexed by 1..nf.

Value

A object of class monet containing the following elements:

S	Vector containing the indices of the added sites in the solution or 0 for the other sites.
det	Determinant of the principal submatrix indexed by the solution.

Author(s)

C. Gebhardt

References

Ko, Lee, Queyranne, An exact algorithm for maximum entropy sampling, Operations Research 43 (1995), 684-691.

Gebhardt, C.: Bayessche Methoden in der geostatistischen Versuchsplanung. PhD Thesis, Univ. Klagenfurt, Austria, 2003

O.P. Baume, A. Gebhardt, C. Gebhardt, G.B.M. Heuvelink and J. Pilz: Network optimization algorithms and scenarios in the context of automatic mapping. Computers & Geosciences 37 (2011) 3, 289-294

See Also

greedy, dualgreedy, maxentropy

Examples

x <- c(0.97900601,0.82658702,0.53105628,0.91420190,0.35304969,
       0.14768239,0.58000004,0.60690101,0.36289026,0.82022147,
       0.95290664,0.07928365,0.04833764,0.55631735,0.06427738,
       0.31216689,0.43851418,0.34433556,0.77699357,0.84097327)
y <- c(0.36545512,0.72144122,0.95688671,0.25422154,0.48199229,
       0.43874199,0.90166634,0.60898628,0.82634713,0.29670695,
       0.86879093,0.45277452,0.09386800,0.04788365,0.20557817,
       0.61149264,0.94643855,0.78219937,0.53946353,0.70946842)
A <- outer(x, x, "-")^2 + outer(y, y, "-")^2
A <- (2 - A)/10
diag(A) <- 0
diag(A) <- 1/20 + apply(A, 2, sum)

greedy(A,5,5)

Example output

  Entropy based monitoring network

method:  greedy 

determinant of selected cov. matrix:  134444.815798555 
total number of given locations:     20 
total number of fixed locations:     5 
total number of locations to select: 5 
total number of eligible locations:  15 
fixed locations:     1  ...  5 
eligible locations:  6  ...  20 
indices of additionally selected locations:
[1]  8  9 16 18 19

edesign documentation built on May 2, 2019, 8:24 a.m.