Introduction
This document compares the seriation methods available in the package
seriation using a sample of 30 flowers from the popular
Iris dataset and randomizes the order of the objects.
Distance seriation
We first register more seriation methods. Some of these methods require installing additional packages.
The following methods will be used (a few slow methods are skipped).
methods <- sort(list_seriation_methods("dist"))
methods <- setdiff(methods, c("BBURCG", "BBWRCG", "Enumerate", "GSA", "SGD", "SGLS"))
methods ## [1] "ARSA" "DendSer" "DendSer_ARc" "DendSer_BAR"
## [5] "DendSer_LPL" "DendSer_PL" "GW" "GW_average"
## [9] "GW_complete" "GW_single" "GW_ward" "HC"
## [13] "HC_average" "HC_complete" "HC_single" "HC_ward"
## [17] "Identity" "isoMDS" "MDS" "MDS_angle"
## [21] "MDS_smacof" "OLO" "OLO_average" "OLO_complete"
## [25] "OLO_single" "OLO_ward" "optics" "QAP_2SUM"
## [29] "QAP_BAR" "QAP_Inertia" "QAP_LS" "R2E"
## [33] "Random" "Reverse" "Sammon_mapping" "Spectral"
## [37] "Spectral_norm" "SPIN_NH" "SPIN_STS" "TSP"
## [41] "VAT"Details about the method can be found in the manual
page for seriate().
We use a loop to run the function seriate() with each
method and calculate criterion measures which indicate how good the
order is.
orders <- list()
criterion <- list()
for (m in methods) {
cat(m)
tm <- system.time(orders[[m]] <- seriate(d, method = m))
criterion[[m]] <- data.frame(time = tm[1]+tm[2], rbind(criterion(d, orders[[m]])))
cat(" took", tm[1]+tm[2], "sec.\n")
}## ARSA took 0.2 sec.
## DendSer took 0.329 sec.
## DendSer_ARc took 0.401 sec.
## DendSer_BAR took 0.33 sec.
## DendSer_LPL took 0.392 sec.
## DendSer_PL took 0.402 sec.
## GW took 0.194 sec.
## GW_average took 0.191 sec.
## GW_complete took 0.199 sec.
## GW_single took 0.188 sec.
## GW_ward took 0.192 sec.
## HC took 0.192 sec.
## HC_average took 0.19 sec.
## HC_complete took 0.191 sec.
## HC_single took 0.192 sec.
## HC_ward took 0.186 sec.
## Identity took 0.192 sec.
## isoMDS took 0.199 sec.
## MDS took 0.195 sec.
## MDS_angle took 0.197 sec.
## MDS_smacof took 0.195 sec.
## OLO took 0.187 sec.
## OLO_average took 0.189 sec.
## OLO_complete took 0.189 sec.
## OLO_single took 0.194 sec.
## OLO_ward took 0.191 sec.
## optics took 0.187 sec.
## QAP_2SUM took 0.191 sec.
## QAP_BAR took 0.191 sec.
## QAP_Inertia took 0.192 sec.
## QAP_LS took 0.19 sec.
## R2E took 0.191 sec.
## Random took 0.182 sec.
## Reverse took 0.182 sec.
## Sammon_mapping took 0.188 sec.
## Spectral took 0.189 sec.
## Spectral_norm took 0.184 sec.
## SPIN_NH took 0.212 sec.
## SPIN_STS took 0.194 sec.
## TSP took 0.185 sec.
## VAT took 0.186 sec.
criterion <- do.call(rbind, criterion)We align the seriation orders. The reason is that an order 1, 2, 3
and 3, 2, 1 are equivalent and just an artifact of the algorithm.
Aligning will reverse some orders so they are better aligned. Then we
sort the orders from best to worst according to a popular seriation
criterion measure called Gradient_weighted.
orders <- ser_align(orders)
best_to_worse <- order(criterion[["Gradient_weighted"]], decreasing = TRUE)
orders <- orders[best_to_worse]
criterion <- criterion[best_to_worse, ]Comparison between methods
We can compare the seriation methods by how similar the orders are that they produce (measured using Spearman). The following code calculates distances between orders and then performs hierarchical clustering.
The reordered dendrogram clearly shows a group of methods based on hierarchical clustering focused on path length and another group that tries to optimize the other seriation measures.
Here is a table to compare the seriation methods on different
criterion measures. Use the interactive table to sort the methods given
different measures. Note that some are maximized and some should be
minimized. Details about the measures can be found in the manual
page for criterion().
Matrix seriation
Matrix seriation reorders rows and columns of a data matrix. We perform the same steps as for distances in the previous section.
methods <- sort(list_seriation_methods("matrix"))
# AOE if for correlation matrices only
methods <- setdiff(methods, c("AOE"))
methods ## [1] "BEA" "BEA_TSP" "BK_unconstrained" "CA"
## [5] "Heatmap" "Identity" "LLE" "Mean"
## [9] "PCA" "PCA_angle" "Random" "Reverse"Performing seriation.
orders <- list()
criterion <- list()
for (m in methods) {
cat(m)
tm <- system.time(orders[[m]] <- seriate(x, method = m))
criterion[[m]] <- data.frame(time = tm[1]+tm[2], rbind(criterion(x, orders[[m]])))
cat(" took", tm[1]+tm[2], "sec.\n")
}## BEA took 0.584 sec.
## BEA_TSP took 0.583 sec.
## BK_unconstrained took 0.197 sec.
## CA took 0.192 sec.
## Heatmap took 0.576 sec.
## Identity took 0.194 sec.
## LLE took 0.202 sec.
## Mean took 0.193 sec.
## PCA took 0.188 sec.
## PCA_angle took 0.192 sec.
## Random took 0.202 sec.
## Reverse took 0.191 sec.
criterion <- do.call(rbind, criterion)Visualize the results
best_to_worse <- order(criterion[["Moore_stress"]], decreasing = FALSE)
orders <- orders[best_to_worse]
criterion <- criterion[best_to_worse, ]
