seriation (version 1.0-12)

criterion: Criterion for a loss/merit function for data given a permutation

Description

Compute the value for different loss functions $L$ and merit function $M$ for data given a permutation.

Usage

criterion(x, order = NULL, method = NULL)

Arguments

x

an object of class dist or a matrix (currently no functions are implemented for array).

order

an object of class ser_permutation suitable for x. If NULL, the identity permutation is used.

method

a character vector with the names of the criteria to be employed, or NULL (default) in which case all available criteria are used.

Value

• A named vector of real values.

Details

For a symmetric dissimilarity matrix $D$ with elements $d(i,j)$ where $i, j = 1 \ldots p$, the aim is generally to place low distance values close to the diagonal. The following criteria to judge the quality of a certain permutation of the objects in a dissimilarity matrix are currently implemented: [object Object],[object Object],[object Object],[object Object],[object Object]

For a general matrix $X = x_{ij}$, $i = 1 \ldots m$ and $j = 1 \ldots n$, currently the following loss/merit functions are implemented:

[object Object],[object Object]

References

G. Caraux and S. Pinloche (2005): Permutmatrix: A Graphical Environment to Arrange Gene Expression Profiles in Optimal Linear Order, Bioinformatics, 21(7), 1280--1281.

C.-H. Chen (2002): Generalized association plots: Information visualization via iteratively generated correlation matrices, Statistica Sinica, 12(1), 7--29.

L. Hubert, P. Arabie, and J. Meulman (2001): Combinatorial Data Analysis: Optimization by Dynamic Programming. Society for Industrial Mathematics.

S. Niermann (2005): Optimizing the Ordering of Tables With Evolutionary Computation, The American Statistician, 59(1), 41--46.

W.S. Robinson (1951): A method for chronologically ordering archaeological deposits, American Antiquity, 16, 293--301.

W.T. McCormick, P.J. Schweitzer and T.W. White (1972): Problem decomposition and data reorganization by a clustering technique, Operations Research, 20(5), 993-1009.

Examples

## create random data and calculate distances
m <- matrix(runif(10),ncol=2)
d <- dist(m)

## get an order for rows (optimal for the least squares criterion)
o <- seriate(m, method = "PCA", margin = 1)
o

## compare the values for all available criteria
rbind(
    unordered = criterion(d),
    ordered = criterion(d, o)
)