isopam: Isopam (Clustering)

In isopam: Clustering of Sites with Species Data

Isopam (Clustering)

Description

Isopam classification is performed either as a hierarchical, divisive method or as non-hierarchical partitioning. Isopam is designed for matrices representing species abundances in plots and with a diagnostic species approach in mind. It optimises clusters and cluster numbers for concentration of indicative species in groups. Predefined indicative species and cluster medoids can optionally be added for a semi-supervised classification.

Usage

     isopam(dat, c.fix = FALSE, c.max = 6, l.max = FALSE, stopat = c(1,7),
            sieve = TRUE, Gs = 3.5, ind = NULL, centers = NULL, 
            distance = 'bray', k.max = 100, d.max = 7, juice = FALSE, 
            polishing = c('strict', 'relaxed'), ...)

     ## S3 method for class 'isopam'
identify(x, ...)
     ## S3 method for class 'isopam'
plot(x, ...)
     ## S3 method for class 'isopam'
summary(object, ...)
     ## S3 method for class 'isopam'
print(x, ...)
     

Arguments

dat	data matrix: each row corresponds to an object (typically a plot), each column corresponds to a descriptor (typically a species). All variables must be numeric. Missing values (NAs) are not allowed. At least 3 rows (plots) are required.
c.fix	number of clusters (defaults to FALSE). If a number is given, non-hierarchical partitioning is performed, c.max is ignored and l.max is set to one.
c.max	maximum number of clusters per partition. Applies to all splits.
l.max	maximum number of hierarchy levels. Defaults to FALSE (no maximum number). Note that divisions may stop well before this number is reached (see stopat). Use l.max = 1 for non-hierarchical partitioning (or use c.fix).
stopat	vector with stopping rules for hierarchical clustering. Two values define if a partition should be retained in hierarchical clustering: the first determines how many indicator species must be present per cluster, the second defines the standardized G-value that must be reached by these indicators. stopat is not effective at the first hierarchy level or in non-hierarchical partitioning.
sieve	logical. If TRUE (the deafult), only species exceeding a threshold defined by Gs are used in the search for a good clustering solution. Their number is multiplied with their mean standardized G-value. The product is used as optimality criterion. If FALSE all species are used for optimization.
Gs	threshold (standardized G value) for species to be considered in the search for a good clustering solution. Effective with sieve = TRUE.
ind	optional vector of column names from dat defining species used as indicators. This turns Isopam in an expert system. Replaces the automated selection of indicators with sieve = TRUE (ind overrules sieve).
centers	optional vector with indices (numeric) or names (character) of observations used as cluster cores (supervised classification).
distance	name of a dissimilarity index for the distance matrix used as a starting point for Isomap. Any distance measure implemented in packages vegan (predefined or using a designdist equation) or proxy can be used (see details).
k.max	maximum Isomap k.
d.max	maximum number of Isomap dimensions.
juice	logical. If TRUE input files for Juice are generated.
polishing	treatment of rare or invariant species and plots with few species. In the case of polishing = "strict" (default), species with only one occurrence or no variance and plots with only one species are omitted during clustering. If "relaxed" is used, only missing and invariant species and empty plots are removed.
...	other arguments used by juice or passed to S3 functions plot and identify (see dendrogram and hclust).
x	isopam result object in methods plot, print and identify.
object	isopam result object in method summary.

Details

Isopam is described in Schmidtlein et al. (2010). It consists of dimensionality reduction (Isomap: Tenenbaum et al. 2000; isomap in vegan) and partitioning of the resulting ordination space (PAM: Kaufman & Rousseeuw 1990; pam in cluster). The classification is performed either as a hierarchical, divisive method, or as non-hierarchical partitioning. It has the following features: partitions are optimized for the occurrence of species with high fidelity to groups; it optionally selects the number of clusters per division; the shapes of groups in feature space are not restricted to spherical or other regular geometric shapes (thanks to the underlying Isomap algorithm); the distance measure used for the initial distance matrix can be freely defined.

In semi-supervised mode, clusters are build around the provided medoids. Pre-defined indicator species are not as constraining, even if preference is given to cluster solutions in which their fidelity is maximized. It depends on the data how much they affect the result.

Using polishing = "strict" reduces noise introduced by rare species and random outcomes due to species-poor plots, which consequently are not allocated. If you have the feeling that species with only one occurrence and plots with only one species should also contribute to the clustering, work with polishing = "relaxed", where only empty plots and missing species are excluded. This comes at the risk of noise and unstable results caused by coincidental species occurrences.

The preset distance measure is Bray-Curtis (Odum 1950). Distance measures are passed to vegdist or to designdist in vegan. If this does not work it is passed to dist in proxy. Measures available in vegan are listed in vegdist. Isopam does not accept distance matrices as a replacement for the original data matrix because it operates on individual descriptors (species).

Isopam is slow with large data sets. It switches to a slow mode when an internally used lookup array does not fit into RAM. It is used for the results of the search for an optimal parameterisation (selection of Isomap dimensions and -k, optionally selection of cluster numbers) does not fit into RAM.

plot creates (and silently returns) an object of class dendrogram and calls the S3 plot method for that class. identify works just like identify.hclust.

Value

call	generating call
distance	distance measure used by Isomap
flat	observations (plots) with group affiliation. Running group numbers for each level of the hierarchy.
hier	observations (plots) with group affiliation. Group identifiers reflect the cluster hierarchy. Not present with only one level of partitioning.
medoids	observations (plots) representing the medoids of the resulting groups.
analytics	table summarizing parameter settings for the partitioning steps. Name: name of the respective parent cluster (0 in case of the first partition); Subgroups: number of subgroups; Isomap.dim: Isomap dimensions used; Isomap.k.min: minimum possible Isomap k; Isomap.k: Isomap k used; Isomap.k.max: maximum possible Isomap k; Ind.N: number of indicators reaching or exceeding Gs; Ind.Gs: the average standardized G value of these indicators; and Global.Gs: the average standardized G value of all descriptors (species).
centers_usr	Cluster centers suggested by user.
ind_usr	Indicators suggested by user.
indicators	Indicators used.
dendro	an object of class hclust representing the clustering (as used by plot). Not present with only one level of partitioning.
dat	data used

Note

With very small datasets, the indicator based optimization may fail. In such cases consider using sieve = FALSE instead of the default method.

Author(s)

Sebastian Schmidtlein with contributions from Jason Collison and Lubomir Tichý

References

Odum, E.P. (1950): Bird populations in the Highlands (North Carolina) plateau in relation to plant succession and avian invasion. Ecology 31: 587–605.

Kaufman, L., Rousseeuw, P.J. (1990): Finding groups in data. Wiley.

Schmidtlein, S., Tichý, L., Feilhauer, H., Faude, U. (2010): A brute force approach to vegetation classification. Journal of Vegetation Science 21: 1162–1171.

Tenenbaum, J.B., de Silva, V., Langford, J.C. (2000): A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323.

See Also

isotab for a table of descriptor (species) frequencies in clusters and fidelity measures. There is a plot method associated to isotab objects that visualizes species fidelities to clusters.

Examples

     ## load data to the current environment
     data(andechs)
     
     ## call isopam with the standard options
     ip <- isopam(andechs)

     ## print function
     ip
     
     ## examine cluster hierarchy
     plot(ip)

     ## retrieve cluster vectors
     clusters <- ip$flat
     clusters
     
     ## same but hierarchical style (available with cluster trees)
     hierarchy <- ip$hier 
     hierarchy

     ## frequency table
     it <- isotab(ip)
     it

     ## plot with species fidelities (equalized phi)
     plot(it)

     ## non-hierarchical partitioning with three clusters
     ip <- isopam(andechs, c.fix = 3)
     ip

     ## limiting the set of species used in cluster search
     ip <- isopam(andechs, ind = c("Car_pan", "Sch_fer"), c.fix = 2)
     ip

     ## supervised mode with fixed cluster medoids
     ip <- isopam(andechs, centers = c("p20", "p22"))
     ip

     

isopam documentation built on April 3, 2025, 9:24 p.m.