R package seriation - Infrastructure for Ordering Objects Using Seriation

CRAN version stream r-universe status CRAN RStudio mirror downloads


Seriation arranges a set of objects into a linear order given available data with the goal of revealing structural information. This package provides the infrastructure for ordering objects with an implementation of many seriation/ordination techniques to reorder data matrices, dissimilarity matrices, correlation matrices, and dendrograms (see below for a complete list). The package provides several visualizations (grid and ggplot2) to reveal structural information, including permuted image plots, reordered heatmaps, Bertin plots, clustering visualizations like dissimilarity plots, and visual assessment of cluster tendency plots (VAT and iVAT).

Here are some quick guides and references

The following R packages use seriation: adepro, arulesViz, baizer, ChemoSpec, ClusteredMutations, corrgram, corrplot, corrr, dendextend, DendSer, dendsort, disclapmix, elaborator, flexclust, ggraph, heatmaply, MEDseq, ockc, pergola, protti, RMaCzek, SFS, tidygraph, treeheatr, vcdExtra

To cite package ‘seriation’ in publications use:

Hahsler M, Hornik K, Buchta C (2008). “Getting things in order: An introduction to the R package seriation.” Journal of Statistical Software, 25(3), 1-34. ISSN 1548-7660, doi:10.18637/jss.v025.i03 https://doi.org/10.18637/jss.v025.i03.

  title = {Getting things in order:  An introduction to the R package seriation},
  author = {Michael Hahsler and Kurt Hornik and Christian Buchta},
  year = {2008},
  journal = {Journal of Statistical Software},
  volume = {25},
  number = {3},
  pages = {1--34},
  doi = {10.18637/jss.v025.i03},
  month = {March},
  issn = {1548-7660},


Stable CRAN version: Install from within R with


Current development version: Install from r-universe.

    repos = c("https://mhahsler.r-universe.dev". "https://cloud.r-project.org/"))


The used example dataset contains the joint probability of disagreement between Supreme Court Judges from 1995 to 2002. The goal is to reveal structural information in this data. We load the library, read the data, convert the data to a distance matrix, and then use the default seriation method to reorder the objects.


d <- as.dist(SupremeCourt)
##           Breyer Ginsburg Kennedy OConnor Rehnquist Scalia Souter Stevens
## Ginsburg   0.120                                                         
## Kennedy    0.250    0.267                                                
## OConnor    0.209    0.252   0.156                                        
## Rehnquist  0.299    0.308   0.122   0.162                                
## Scalia     0.353    0.370   0.188   0.207     0.143                      
## Souter     0.118    0.096   0.248   0.220     0.293  0.338               
## Stevens    0.162    0.145   0.327   0.329     0.402  0.438  0.169        
## Thomas     0.359    0.368   0.177   0.205     0.137  0.066  0.331   0.436
order <- seriate(d)
## object of class 'ser_permutation', 'list'
## contains permutation vectors for 1-mode data
##   vector length seriation method
## 1             9         Spectral

Here is the resulting permutation vector.

##    Scalia    Thomas Rehnquist   Kennedy   OConnor    Souter    Breyer  Ginsburg 
##         6         9         5         3         4         7         1         2 
##   Stevens 
##         8

Next, we visualize the original and permuted distance matrix.

pimage(d, main = "Judges (original alphabetical order)")
pimage(d, order, main = "Judges (reordered by seriation)")

Darker squares around the main diagonal indicate groups of similar objects. After seriation, two groups are visible.

We can compare the available seriation criteria. Seriation improves all measures. Note that some measures are merit measures while others represent cost. See the manual page for details.

rbind(alphabetical = criterion(d), seriated = criterion(d, order))
##              2SUM AR_deviations AR_events BAR Gradient_raw Gradient_weighted
## alphabetical  872        10.304        80 1.8            8              0.54
## seriated      811         0.064         5 1.1          158             19.76
##              Inertia Lazy_path_length Least_squares LS MDS_stress  ME
## alphabetical     267              6.9           967 99       0.62  99
## seriated         364              4.6           942 86       0.17 101
##              Moore_stress Neumann_stress Path_length RGAR   Rho
## alphabetical          7.0            3.9         1.8 0.48 0.028
## seriated              2.5            1.3         1.1 0.03 0.913

Some seriation methods also return a linear configuration where more similar objects are located closer to each other.

##    Breyer  Ginsburg   Kennedy   OConnor Rehnquist    Scalia    Souter   Stevens 
##      0.24      0.28     -0.15     -0.11     -0.27     -0.42      0.21      0.61 
##    Thomas 
##     -0.41

We can see a clear divide between the two groups in the configuration.

Available seriation methods to reorder dissimilarity data

Seriation methods for dissimilarity data reorder the set of objects in the data. The methods fall into several groups based on the criteria they try to optimize, constraints (like dendrograms), and the algorithmic approach.

Dendrogram leaf order

These methods create a dendrogram using hierarchical clustering and then derive the seriation order from the leaf order in the dendrogram. Leaf reordering may be applied.

Dimensionality reduction

Find a seriation order by reducing the dimensionality to 1 dimension. This is typically done by minimizing a stress measure or the reconstruction error.


These methods try to optimize a seriation criterion directly, typically using a heuristic approach.

Other Methods

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

Available seriation methods to reorder data matrices, count tables, and data.frames

For matrices, rows and columns are reordered.

Seriating rows and columns simultaneously

Row and column order influence each other.

Seriating rows and columns separately using dissimilarities

Seriate rows in a data matrix

These methods need access to the data matrix instead of dissimilarities to reorder objects (rows). The same approach can be applied to columns.

Other methods