The same dataset

OPTIMCLASS: Simultaneous identification of optimal clustering method and optimal

number of clusters in vegetation classification studies

Tichy Lubomír1, Chytry Milan1, Botta-Dukát Zoltán2, Hájek Michal1; Talbot Stephen S.3

1Masaryk University, Brno, Czech Republic2Hungarian Academy of Sciences, Vácrátot, Hungary

3U.S. Fish and Wildlife Service, Anchorage, USA

Why do we need a method for identification of optimal clustering algorithm and optimal number of clusters?

The same dataset

-A huge variety of clustering methods produce “reasonable” results.

-Subjective selection of the clustering method and no. of clusters is usually based on empirical experience

Why do we need a method for identification of optimal clustering algorithm and optimal number of clusters?

Methods published:

Most algorithms identify the optimal partition mathematically, without considering ecological interpretation

The Method

A posteriori description of phytosociological tables is based on

diagnostic species

Diagnostic species describes a cluster. Therefore, the number of diagnostic species determines whether the classified table can be sufficiently interpreted.

Species 1 98788 12112 3.211Species 2 51123 1223. 11132Species 3 23132 ..... .....Species 4 ..2.4 112.. 1..5.Species 5 ..... .1.1. 1.213

The Method The samedataset:

The Method

Measure of the classification quality: the total sum of diagnostic species

Fisher’s Exact Test

calculates the probability of observed occurrence of species across clusters for a right-tailed test hypothesis

– The measure reduces the importance of very small clusters.

– Easy interpretation: the more diagnostic species in the dataset, the better description of the clusters.

The Method Test on three different datasets

Southern Siberia, Sayan Mountains (310 plots; forest, steppe and tundra vegetation)

Central Europe, Carpathians (241 plots; mire vegetation)

Alaska, Kenai Peninsula(171 plots; wetlands)

The Method Classifications tested

Flexible beta clustering WARD‘s clustering

UPGMA(PC-ORD)

Cover transformations (percentages, log percentages,

Braun-Blanquet, presence/absence)

Distance measures(Bray-Curtis, Manhattan,

Euclidean)

Ordinal cluster analysis(SYN-TAX)

Modified TWINSPAN classification

(JUICE) The sequence of splits in divisive

classification is determined by internal heterogeneity of clusters.

Therefore, any number of clusters is possible

(three modifications of pseudospecies cut levels)

Distance measures (Kruskal-Wallis, Kendall,

Gower-Podani coefficient)

Results Sayan Mountains, Siberia(310 plots, 1036 species)

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Probability = 10-9

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Untransformed cover data

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Euclidean distance measure

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Manhattan distance measure

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Bray-Curtis distance measure

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UPGMA

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Ward‘s method

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Flexible beta -0.25

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Ordinal cluster analyses (SYN-TAX)

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Modified TWINSPAN

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The Method Test on three different datasets

Southern Siberia, Sayan Mountains (310 plots; forest, steppe and tundra vegetation)

Central Europe, Carpathians (241 plots; mire vegetation)

Alaska, Kenai Peninsula(171 plots; wetlands)

Similar results:

Conclusions

Classifications based on transformed cover values give better results than percentage covers.

Euclidean distance - slightly poorer results than Manhattan or Bray-Curtis distances.

UPGMA clustering method - poorer results than Ward’s and Flexible beta methods.

No significant difference between ordinal cluster analysis proposed by Podani (SYN-TAX 2000) and other clustering methods.

Modified TWINSPAN – performs well with small numbers of clusters.

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Modified TWINSPAN classification

The same dataset

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