seriation (version 1.1-0)

dissimilarity: Dissimilarity Between Seriation Orders

Description

Calculates dissimilarities/correlations between seriation orders in a list.

Usage

seriation_dist(x, method = "spearman")
seriation_cor(x, method = "spearman")
seriation_align(x, method = "spearman")

Arguments

x

seriation orders as a list with elements of class ser_permutation.

method

a character string with the name of the used measure ("kendall", "spearman", "manhattan", "euclidean").

Value

• seriation_dist returns an object of class dist. seriation_align returns a new list with elements of class ser_permutation.

Details

For seriation_dist, the correlation coefficients (Kendall's tau and Spearman's rho) are converted into a dissimilarity by taking one minus the absolute value. The absolute value is used since a negative correlation just means that reversing the order results in a positive correlation of the same magnitude.

For the ranking-based distance measures (Manhattan and Euclidean), the direction of the distance between all seriations in forward and reverse order and use the minimum. Note that Manhattan distance between the ranks in a linear order is equivalent to Spearman's footrule metric (Diaconis 1988).

seriation_align normalizes in a list of seriations the direction such that ranking-based methods can be used. For the correlation coefficients "spearman" and "kendall" we first find the order which has the largest sum of positive correlations with all other orders. We use this order as the seed and reverse all orders that are negatively correlated. For "manhattan" and "euclidean" we add all reversed orders 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 orders.

References

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

See Also

ser_permutation_vector

Examples

## seriate dist of 20 flowers from the iris data set
data("iris")
x <- as.matrix(iris[-5])
x <- x[sample(1:nrow(x), 25),]
rownames(x) <- 1:25
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 distance ignores reversed orders)
ds <- seriation_dist(os)
hmap(ds, margin=c(7,7))

## comapte using actual correlation (reversed orders are neg. correlated!)
cs <- seriation_cor(os)
hmap(cs, margin=c(7,7))
  
## normalize direction of the seriation orders
os2 <- seriation_align(os)
cs2 <- seriation_cor(os2)
hmap(cs2, margin=c(7,7))
 
## plot the actual seriations  
for(i in os2) pimage(d, i, main = get_method(i))