seriation - Infrastructure for Ordering Objects Using Seriation - R package

This package provides the infrastructure for ordering objects with an implementation of several seriation/sequencing/ordination techniques to reorder matrices, dissimilarity matrices, and dendrograms (see below for a full list). Also provides (optimally) reordered heatmaps, color images and clustering visualizations like dissimilarity plots, and visual assessment of cluster tendency plots (VAT and iVAT).

Installation

Stable CRAN version: install from within R with

install.packages("seriation")

Current development version: Download package from AppVeyor or install from GitHub (needs devtools).

library("devtools")
install_github("mhahsler/seriation")

Usage

Load library, read data and calculate distances. Then use default seriation.

library(seriation)
data("iris")
x <- as.matrix(iris[-5])
x <- x[sample(1:nrow(x)),]

d <- dist(x)
order <- seriate(d)
order

object of class ‘ser_permutation’, ‘list’
contains permutation vectors for 1-mode data

  vector length seriation method
1           150             ARSA

Compare quality.

rbind(
 random = criterion(d),
 reordered = criterion(d, order)
)

          AR_events AR_deviations       RGAR Gradient_raw Gradient_weighted Path_length
random       550620    948833.712 0.49938328          741         -1759.954   392.77766
reordered     54846      9426.094 0.04974243       992214       1772123.418    83.95758
            Inertia Least_squares       ME Moore_stress Neumann_stress     2SUM      LS
random    214602194      78852819 291618.0    927570.00     461133.357 29954845 5669489
reordered 356945979      76487641 402332.1     13593.32       5274.093 17810802 4486900

Available Seriation Method

The following methods are available for dissimilarity data:

• ARSA - Simulated annealing (linear seriation)
• Branch-and-bound to minimize the unweighted/weighted column gradient
• DendSer - Dendrogram seriation heuristic to optimize various criteria
• GA - Genetic algorithm with warm start to optimize various criteria
• GW - Hierarchical clustering reordered by Gruvaeus and Wainer heuristic
• HC - Hierarchical clustering (single link, avg. link, complete link)
• Identity permutation
• MDS - Multidimensional scaling (metric, non-metric, angle)
• OLO - Hierarchical clustering with optimal leaf ordering
• OPTICS - Ordering points to identify the clustering structure.
• QAP - Quadratic assignment problem heuristic (2-SUM, linear seriation, inertia, banded anti-Robinson form)
• R2E - Rank-two ellipse seriation
• Random permutation
• Spectral seriation (unnormalized, normalized)
• SPIN - Sorting points into neighborhoods (neighborhood algorithm, side-to-site algorithm)
• TSP - Traveling sales person solver to minimize the Hamiltonian path length
• TSNE - Order of the 1D t-distributed stochastic neighbor embedding (t-SNE)
• UMAP - Order of the 1D embedding produced by uniform manifold approximation and projection
• VAT - Order of the visual assessment of clustering tendency ordering

A detailed comparison of the methods is available in the paper An experimental comparison of seriation methods for one-mode two-way data. (read the preprint).

The following methods are available for matrices:

• BEA - Bond Energy Algorithm to maximize the measure of effectiveness (ME)
• Identity permutation
• PCA - First principal component or angle on the projection on the first two principal components
• Random permutation
• TSP - Traveling sales person solver to maximize ME

References

• Reference manual for package seriation
• Michael Hahsler, Kurt Hornik and Christian Buchta, Getting Things in Order: An Introduction to the R Package seriation, Journal of Statistical Software, 25(3), 2008.
• Michael Hahsler. An experimental comparison of seriation methods for one-mode two-way data. European Journal of Operational Research, 257:133-143, 2017. (read the preprint)
• Seriation package vignette with complete examples.