seriation (version 1.2-0)

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.

...

additional parameters passed on to the criterion method.

Value

• A named vector of real values.

Details

For a symmetric dissimilarity matrix $D$ with elements $d(i,j)$ where $i, j = 1 \ldots n$, 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],[object Object],[object Object],[object Object],[object Object],[object Object]

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

[object Object],[object Object]

References

S. T. Barnard, A. Pothen, and H. D. Simon (1993): A Spectral Algorithm for Envelope Reduction of Sparse Matrices. In Proceedings of the 1993 ACM/IEEE Conference on Supercomputing, 493--502. Supercomputing '93. New York, NY, USA: ACM.

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.

D. Earle and C.B. Hurley (2015): Advances in Dendrogram Seriation for Application to Visualization. Journal of Computational and Graphical Statistics, 24(1), 1--25.

L. Hubert and J. Schultz (1976): Quadratic Assignment as a General Data Analysis Strategy. British Journal of Mathematical and Statistical Psychology 29(2). Blackwell Publishing Ltd. 190--241.

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.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.

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

Yin-Jing Tien, Yun-Shien Lee, Han-Ming Wu and Chun-Houh Chen (2008): Methods for simultaneously identifying coherent local clusters with smooth global patterns in gene expression profiles, BMC Bioinformatics, 9(155), 1--16.

See Also

list_criterion_methods to query the criterion registry.

Examples

## create random data and calculate distances
m <- matrix(runif(20),ncol=2)
d <- dist(m)

## get an order for rows (optimal for the least squares criterion)
o <- seriate(d, method = "MDS")
o

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

## compare RGAR by window size (from local to global)
w <- 2:(nrow(m)-1)
RGAR <- sapply(w, FUN = function (w)
  criterion(d, o, method="RGAR", w = w))
plot(w, RGAR, type = "b", ylim = c(0,1),
  xlab = "Windows size (w)", main = "RGAR by window size")