isopam: Isopam (Clustering)

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

Isopam classification is performed either as a hierarchical, divisive method, or as non-hierarchical partitioning. Optimizes clusters and optionally cluster numbers for maximum performance of group indicators. Developed for matrices representing species abundances in plots.

Usage

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     isopam (dat, c.fix = FALSE, c.opt = TRUE, 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) 
     
     ## S3 method for class 'isopam'
identify(x, ...)
     ## S3 method for class 'isopam'
plot(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.opt and c.max are ignored and l.max is set to one.

c.opt

if TRUE (the default) cluster numbers are optimized in the range between 2 and c.max (slow and thorough). If FALSE groups are divided into two subgroups (quick and dirty).

c.max

maximum number of clusters per partition. Applies to all partitioning steps if c.opt = TRUE.

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 indicators 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 descriptors (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 descriptors are used for optimization.

Gs

threshold (standardized G value) for descriptors (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 descriptors (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 observations used as cluster cores (supervised classification).

distance

distance measure for the distance matrix used as a starting point for Isomap. Any distance measure implemented in packages vegan or proxy can be used (see details).

k.max

maximum Isomap k.

d.max

maximum number of Isomap dimensions.

...

other arguments to S3 functions plot and identify corresponding to hclust.

juice

logical. If TRUE input files for Juice are generated.

x

an isopam result object.

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. Compared to other clustering methods, it has the following features: (a) it optimizes partitions for the performance of group indicators (typically species) or for maximum average 'fidelity' of descriptors to groups; (b) it optionally selects the number of clusters per division; (c) the shapes of groups in feature space are not limited to spherical or other regular geometric shapes (thanks to the underlying Isomap algorithm) and (d) the distance measure used for the initial distance matrix can be freely defined.

Currently, the plot and identify methods for class isopam simply link to the hclust object $dendro resulting from isopam in case of hierarchical partitioning. The methods work just like plot.hclust and identify.hclust.

The preset distance measure is Bray-Curtis (Odum 1950). Distance measures are passed to vegdist in vegan. If vegan does not know the given measure it is passed to dist in proxy. Measures available in vegan are listed in vegdist. Measures registered in proxy can be listed with summary(pr_DB) once proxy is loaded. New measures can be defined and registered as described in ?pr_DB. Isopam can't deal with distance matrices as a replacement for the original data matrix because it operates on individual descriptors (species).

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 final 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.

dendro

an object of class hclust representing the clustering. Not present with only one level of partitioning.

dat

data used

Note

For large datasets, Isopam may need too much memory or too much computation time. The optimization procedure (selection of Isomap dimensions and -k, optionally selection of cluster numbers) is based on a brute force approach that takes its time with large data sets. Low speed is inherent to the method, so don't complain. If used with data not representing species in plots make sure that the indicator approach is appropriate.

With very small datasets, the indicator based optimization may fail. In such cases consider using filtered = 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) frequency in clusters.

Examples

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     ## load data to the current environment
     data(andechs)
     
     ## call isopam with the standard options
     ip<-isopam(andechs)
     
     ## examine cluster hierarchy
     plot(ip)
     
     ## examine grouping
     ip$flat 

     ## examine frequency table (second hierarchy level)
     isotab(ip, 2)
     
     ## non-hierarchical partitioning
     ip<-isopam(andechs,c.fix=3)
     ip$flat
     
     

isopam documentation built on May 1, 2019, 8:02 p.m.

Related to isopam in isopam...