seriation (version 1.2-0)

dissimilarity: Dissimilarities and Correlations Between Seriation Orders

Description

Calculates dissimilarities/correlations between seriation orders in a list.

Usage

ser_cor(x, y = NULL, method = "spearman", reverse = FALSE, test = FALSE)
ser_dist(x, y = NULL, method = "spearman", reverse = FALSE)
ser_align(x, method = "spearman")

Arguments

x

set of seriation orders as a list with elements which can be coerced into ser_permutation_vector objects.

y

if not NULL then a single seriation order can be specified. In this case x has to be a single seriation order and not a list.

method

a character string with the name of the used measure. Available measures are: "kendall", "spearman", "manhattan", "euclidean", "hamming", and "ppc" (positional

reverse

a logical indicating if the orders should also be checked in reverse order and the best value (highest correlation, lowed distance) is reported. This only affect ranking-based measures and not precedence invariant measures (e.g., ppc).

test

a logical indicating if a correlation test should be performed.

Value

• ser_dist returns an object of class dist. ser_align returns a new list with elements of class ser_permutation.

Details

ser_cor calculates the correlation between two sequences (orders). Not that a seriation order and its reverse are identical and purely an artifact due to the method that creates the order. This is a major difference to rankings. For ranking-based correlation measures (Spearman and Kendall) the absolute value of the correlation is returned for reverse = TRUE (in effect returning the correltation for the reversed order). If test = TRUE then the appropriate test for association is performed and a matrix with p-values is returned as the attribute "p-value". Note that no correction for multiple testing is performed.

For ser_dist, the correlation coefficients (Kendall's tau and Spearman's rho) are converted into a dissimilarity by taking one minus the correlation value. Note that Manhattan distance between the ranks in a linear order is equivalent to Spearman's footrule metric (Diaconis 1988). reverse = TRUE returns the pairwise minima using also reversed orders.

The positional proximity coefficient (ppc) is a precedence invariant measure based on the squared positional distances in two permutations (see Goulermas et al 2015). We use the normalized value (i.e., the generalized correlation coefficient). The similarity measure is converted into a dissimilarity via $1-ppc$. For this precedence invariant measure reverse is ignored.

ser_align tries to normalize the direction in a list of seriations such that ranking-based methods can be used. We add for each permutation also the reversed order to the set and then use a modified version of Prim's algorithm for finding a minimum spanning tree (MST) to choose if the original seriation order or its reverse should be used. We use the orders first added to the MST. Every time an order is added, its reverse is removed from the possible remaining orders.

References

P. Diaconis (1988): Group Representations in Probability and Statistics. Institute of Mathematical Statistics, Hayward, CA.

J.Y. Goulermas, A. Kostopoulos, and T. Mu (2015): A New Measure for Analyzing and Fusing Sequences of Objects. IEEE Transactions on Pattern Analysis and Machine Intelligence. Forthcomming.

See Also

ser_permutation_vector

Examples

set.seed(1234)
## seriate dist of 50 flowers from the iris data set
data("iris")
x <- as.matrix(iris[-5])
x <- x[sample(1:nrow(x), 50),]
rownames(x) <- 1:50
d <- dist(x)

## Create a list of different seriations
methods <- c("HC_single", "HC_complete", "OLO", "GW", "R2E", "VAT", 
  "TSP", "Spectral", "SPIN", "MDS", "Identity", "Random")

os <- sapply(methods, function(m) {
  cat("Doing", m, "... ")
  tm <- system.time(o <- seriate(d, method = m))
  cat("took", tm[3],"s.
")
  o
})

## Compare the methods using distances (default is based on 
## Spearman's rank correlation coefficient)
ds <- ser_dist(os)
hmap(ds, margin=c(7,7))

## Compare using actual correlation (reversed orders have low or 
## negative correlation!)
cs <- ser_cor(os)
hmap(cs, margin=c(7,7))

## Also check reversed seriation orders. 
## Now all but random and identity are highly positive correlated
cs2 <- ser_cor(os, reverse = TRUE)
hmap(cs2, margin=c(7,7))
  
## Use Manhattan distance of the ranks (i.e., Spearman's foot rule)
ds <- ser_dist(os, method="manhattan")
plot(hclust(ds))

## Also check reversed orders
ds <- ser_dist(os, method="manhattan", reverse = TRUE)
plot(hclust(ds))