Hierarchical clustering based on dissimilarity or beta-diversity

This function generates a hierarchical tree from a dissimilarity (beta-diversity) data.frame, calculates the cophenetic correlation coefficient, and can get clusters from the tree if requested by the user. The function implements randomization of the dissimilarity matrix to generate the tree, with a selection method based on the optimal cophenetic correlation coefficient. Typically, the dissimilarity data.frame is a bioregion.pairwise.metric object obtained by running similarity or similarity and then similarity_to_dissimilarity.

Usage

hclu_hierarclust(
  dissimilarity,
  index = names(dissimilarity)[3],
  method = "average",
  randomize = TRUE,
  n_runs = 30,
  keep_trials = FALSE,
  optimal_tree_method = "best",
  n_clust = NULL,
  cut_height = NULL,
  find_h = TRUE,
  h_max = 1,
  h_min = 0
)

Arguments

dissimilarity: the output object from dissimilarity() or similarity_to_dissimilarity(), or a dist object. If a data.frame is used, the first two columns represent pairs of sites (or any pair of nodes), and the next column(s) are the dissimilarity indices.
index: name or number of the dissimilarity column to use. By default, the third column name of dissimilarity is used.
method: name of the hierarchical classification method, as in hclust. Should be one of "ward.D", "ward.D2", "single", "complete", "average" (= UPGMA), "mcquitty" (= WPGMA), "median" (= WPGMC) or "centroid" (= UPGMC).
randomize: a boolean indicating if the dissimilarity matrix should be randomized, to account for the order of sites in the dissimilarity matrix.
n_runs: number of trials to randomize the dissimilarity matrix.
keep_trials: a boolean indicating if all random trial results. should be stored in the output object (set to FALSE to save space if your dissimilarity object is large).
optimal_tree_method: a character indicating how the final tree should be obtained from all trials. The only option currently is "best", which means the tree with the best cophenetic correlation coefficient will be chosen.
n_clust: an integer or an integer vector indicating the number of clusters to be obtained from the hierarchical tree, or the output from partition_metrics. Should not be used at the same time as cut_height.
cut_height: a numeric vector indicating the height(s) at which the tree should be cut. Should not be used at the same time as n_clust.
find_h: a boolean indicating if the height of cut should be found for the requested n_clust.
h_max: a numeric indicating the maximum possible tree height for the chosen index.
h_min: a numeric indicating the minimum possible height in the tree for the chosen index.

Value

A list of class bioregion.clusters with five slots:

name: character containing the name of the algorithm
args: list of input arguments as provided by the user
inputs: list of characteristics of the clustering process
algorithm: list of all objects associated with the clustering procedure, such as original cluster objects
clusters: data.frame containing the clustering results

In the algorithm slot, users can find the following elements:

trials: a list containing all randomization trials. Each trial contains the dissimilarity matrix, with site order randomized, the associated tree and the cophenetic correlation coefficient (Spearman) for that tree
final.tree: a hclust object containing the final hierarchical tree to be used
final.tree.coph.cor: the cophenetic correlation coefficient between the initial dissimilarity matrix and final.tree

Details

The function is based on hclust. The default method for the hierarchical tree is average, i.e. UPGMA as it has been recommended as the best method to generate a tree from beta diversity dissimilarity (Kreft and Jetz 2010) .

Clusters can be obtained by two methods:

Specifying a desired number of clusters in n_clust
Specifying one or several heights of cut in cut_height

To find an optimal number of clusters, see partition_metrics()

References

Kreft H, Jetz W (2010). “A framework for delineating biogeographical regions based on species distributions.” Journal of Biogeography, 37, 2029–2053.

Author

Boris Leroy (leroy.boris@gmail.com), Pierre Denelle (pierre.denelle@gmail.com) and Maxime Lenormand (maxime.lenormand@inrae.fr)

Examples

comat <- matrix(sample(0:1000, size = 500, replace = TRUE, prob = 1/1:1001),
20, 25)
rownames(comat) <- paste0("Site",1:20)
colnames(comat) <- paste0("Species",1:25)

dissim <- dissimilarity(comat, metric = "all")

# User-defined number of clusters
tree1 <- hclu_hierarclust(dissim, n_clust = 5)
#> Randomizing the dissimilarity matrix with 30 trials
#>  -- range of cophenetic correlation coefficients among
#>                      trials: 0.78 - 0.78
#> Optimal tree has a 0.78 cophenetic correlation coefficient with the initial dissimilarity
#>       matrix
#> Determining the cut height to reach 5 groups...
#> --> 0.2421875
tree1
#> Clustering results for algorithm : hclu_hierarclust 
#> 	(hierarchical clustering based on a dissimilarity matrix)
#>  - Number of sites:  20 
#>  - Name of dissimilarity metric:  Jaccard 
#>  - Tree construction method:  average 
#>  - Randomization of the dissimilarity matrix:  yes, number of trials 30 
#>  - Cophenetic correlation coefficient:  0.777 
#>  - Number of clusters requested by the user:  5 
#> Clustering results:
#>  - Number of partitions:  1 
#>  - Number of clusters:  5 
#>  - Height of cut of the hierarchical tree: 0.242 
plot(tree1)

str(tree1)
#> List of 6
#>  $ name        : chr "hclu_hierarclust"
#>  $ args        :List of 12
#>   ..$ index              : chr "Jaccard"
#>   ..$ method             : chr "average"
#>   ..$ randomize          : logi TRUE
#>   ..$ n_runs             : num 30
#>   ..$ optimal_tree_method: chr "best"
#>   ..$ keep_trials        : logi FALSE
#>   ..$ n_clust            : num 5
#>   ..$ cut_height         : NULL
#>   ..$ find_h             : logi TRUE
#>   ..$ h_max              : num 1
#>   ..$ h_min              : num 0
#>   ..$ dynamic_tree_cut   : logi FALSE
#>  $ inputs      :List of 7
#>   ..$ bipartite      : logi FALSE
#>   ..$ weight         : logi TRUE
#>   ..$ pairwise       : logi TRUE
#>   ..$ pairwise_metric: chr "Jaccard"
#>   ..$ dissimilarity  : logi TRUE
#>   ..$ nb_sites       : int 20
#>   ..$ hierarchical   : logi FALSE
#>  $ algorithm   :List of 5
#>   ..$ trials             : chr "Trials not stored in output"
#>   ..$ final.tree         :List of 7
#>   .. ..- attr(*, "class")= chr "hclust"
#>   ..$ final.tree.coph.cor: num 0.777
#>   ..$ output_n_clust     : int 5
#>   ..$ output_cut_height  : Named num 0.242
#>   .. ..- attr(*, "names")= chr "k_5"
#>  $ clusters    :'data.frame':	20 obs. of  2 variables:
#>   ..$ ID : chr [1:20] "Site5" "Site15" "Site10" "Site17" ...
#>   ..$ K_5: chr [1:20] "1" "1" "1" "1" ...
#>  $ cluster_info:'data.frame':	1 obs. of  4 variables:
#>   ..$ partition_name   : chr "K_5"
#>   ..$ n_clust          : int 5
#>   ..$ requested_n_clust: num 5
#>   ..$ output_cut_height: num 0.242
#>  - attr(*, "class")= chr [1:2] "bioregion.clusters" "list"
tree1$clusters
#>            ID K_5
#> Site5   Site5   1
#> Site15 Site15   1
#> Site10 Site10   1
#> Site17 Site17   1
#> Site8   Site8   1
#> Site1   Site1   1
#> Site12 Site12   1
#> Site3   Site3   1
#> Site9   Site9   1
#> Site18 Site18   1
#> Site4   Site4   2
#> Site6   Site6   3
#> Site20 Site20   1
#> Site11 Site11   4
#> Site16 Site16   1
#> Site14 Site14   1
#> Site7   Site7   3
#> Site13 Site13   1
#> Site19 Site19   1
#> Site2   Site2   5

# User-defined height cut
# Only one height
tree2 <- hclu_hierarclust(dissim, cut_height = .05)
#> Randomizing the dissimilarity matrix with 30 trials
#>  -- range of cophenetic correlation coefficients among
#>                      trials: 0.78 - 0.78
#> Optimal tree has a 0.78 cophenetic correlation coefficient with the initial dissimilarity
#>       matrix
tree2
#> Clustering results for algorithm : hclu_hierarclust 
#> 	(hierarchical clustering based on a dissimilarity matrix)
#>  - Number of sites:  20 
#>  - Name of dissimilarity metric:  Jaccard 
#>  - Tree construction method:  average 
#>  - Randomization of the dissimilarity matrix:  yes, number of trials 30 
#>  - Cophenetic correlation coefficient:  0.777 
#>  - Heights of cut requested by the user:  0.05 
#> Clustering results:
#>  - Number of partitions:  1 
#>  - Number of clusters:  18 
#>  - Height of cut of the hierarchical tree: 0.05 
tree2$clusters
#>        ID K_18
#> 1   Site9    1
#> 2   Site4    2
#> 3   Site3    3
#> 4  Site12    4
#> 5  Site18    5
#> 6  Site10    6
#> 7   Site7    7
#> 8  Site16    8
#> 9   Site1    9
#> 10 Site14   10
#> 11 Site13   11
#> 12  Site6   12
#> 13 Site20   13
#> 14 Site17   10
#> 15  Site5   14
#> 16 Site15   15
#> 17 Site19   15
#> 18  Site2   16
#> 19 Site11   17
#> 20  Site8   18

# Multiple heights
tree3 <- hclu_hierarclust(dissim, cut_height = c(.05, .15, .25))
#> Randomizing the dissimilarity matrix with 30 trials
#>  -- range of cophenetic correlation coefficients among
#>                      trials: 0.78 - 0.78
#> Optimal tree has a 0.78 cophenetic correlation coefficient with the initial dissimilarity
#>       matrix

tree3$clusters # Mind the order of height cuts: from deep to shallow cuts
#>            ID K_4 K_13 K_18
#> Site2   Site2   1    1    1
#> Site18 Site18   2    2    2
#> Site10 Site10   2    3    3
#> Site9   Site9   2    4    4
#> Site1   Site1   2    5    5
#> Site7   Site7   2    6    6
#> Site4   Site4   3    7    7
#> Site11 Site11   4    8    8
#> Site19 Site19   2    9    9
#> Site14 Site14   2    9   10
#> Site15 Site15   2    9   11
#> Site6   Site6   2   10   12
#> Site8   Site8   2    4   13
#> Site17 Site17   2    9    9
#> Site16 Site16   2   11   14
#> Site20 Site20   2    9   15
#> Site5   Site5   2    9   10
#> Site3   Site3   2   12   16
#> Site13 Site13   2    9   17
#> Site12 Site12   2   13   18
# Info on each partition can be found in table cluster_info
tree3$cluster_info
#>        partition_name n_clust requested_cut_height
#> h_0.25            K_4       4                 0.25
#> h_0.15           K_13      13                 0.15
#> h_0.05           K_18      18                 0.05
plot(tree3)


# Recut the tree afterwards
tree3.1 <- cut_tree(tree3, n = 5)
#> Determining the cut height to reach 5 groups...
#> --> 0.2421875

tree4 <- hclu_hierarclust(dissim, n_clust = 1:19)
#> Randomizing the dissimilarity matrix with 30 trials
#>  -- range of cophenetic correlation coefficients among
#>                      trials: 0.78 - 0.78
#> Optimal tree has a 0.78 cophenetic correlation coefficient with the initial dissimilarity
#>       matrix