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Numerical reproduction of traditional classifications and automatic

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vegetation identification Miquel de Cáceres1, 2,*, Xavier Font1, Paloma Vicente1, Francesc Oliva2 1

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Department of Plant Biology, University of Barcelona, Avda. Diagonal 645, Barcelona, ES08028, Spain; 2 Department of Statistics, University of Barcelona, Avda. Diagonal 645, Barcelona, ES-08028, Spain; * Corresponding author; E-mail: [email protected] Abstract

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Questions: Is it possible to develop an expert system to provide reliable automatic identifications

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of plant communities at the precision level of phytosociological associations? How can unreliable

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expert-based knowledge be discarded before applying supervised classification methods?

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Material: We used 3677 relevés from Catalonia (Spain), belonging to eight orders of terrestrial

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vegetation. These relevés were classified by experts into 222 low-level units (associations or

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subassociations).

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Methods: We reproduced low-level expert-defined vegetation units as independent fuzzy clusters

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by using the Possibilistic C-means algorithm. Those relevés detected as transitional between

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vegetation types were excluded in order to maximize the number of units numerically

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reproduced. Cluster centroids were then considered static and used to perform supervised

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classifications of vegetation data. Finally, we evaluated the classifier’s ability to correctly

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identify the unit of both typical (i.e. training) and transitional relevés.

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Results: Only 166 out of 222 (75%) of the original units could be numerically reproduced.

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Almost all the unrecognized units were subassociations. Among the original relevés, 61% were

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deemed transitional or untypical. Typical relevés were correctly identified 95% of times, while

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the efficiency of the classifier on transitional data was only 64%. However, if the second

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classifier’s choice was also considered the rate of correct classification for transitional relevés

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was 80%.

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Conclusions: Our approach stresses the transitional nature of relevé data coming from vegetation

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databases. Relevé selection is justified in order to adequately represent the vegetation concepts

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associated to expert-defined units.

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Keywords: Fuzzy sets; Expert systems; Possibilistic C-means; Phytosociological data;

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Syntaxonomy.

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Introduction

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During recent years, there has been a renewed interest in vegetation classification, even in

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parts of the world with little phytosociological tradition (e.g. Rodwell et al. 1995, Jennings 2003).

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Nature managers are in need of consistent systems of vegetation classification. Indeed, assigning

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a meaningful vegetation type to the plant community observed in a sampling site is the first step

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in applied ecological studies, such as landscape mapping, vegetation conservation or restoration

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planning. Such assignment (i.e. the determination of the community type) would be a simpler

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task if the identification of possible types was done through the use of remote expert systems of

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vegetation classification (Noble 1987). Up to date, there is no expert system specially designed

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for providing web-based vegetation classification services on the basis of species

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composition/abundance. Nevertheless, several local computer programs are already available for

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this purpose (van Tongeren 1986, Hill 1996, Pot 1997, Tichý 2002, van Tongeren et al. 2008),

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and Czech vegetation scientists distribute expert system configurations to be used locally within

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the JUICE program (Chytrý 2007).

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Methodologically speaking, the act of identifying the predefined class or classes to which a

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given plant community may be assigned is usually called supervised classification. Standard

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statistical tools such as quadratic discriminant analysis (Ejrnæs et al. 2004) and specially artificial 2

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neural networks (Cerná & Chytrý 2005) have recently been advocated as efficient

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methodological approaches for the identification of plot data. Simpler but more easily

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interpretable approaches consist in calculating resemblance values between the target relevé and

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each of the predefined vegetation units. After that, the relevé is identified with the nearest unit(s).

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Relevé resemblance computation may be performed by combining information from species

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composition, abundance values, and/or the presence of diagnostic species (van Tongeren 1986,

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Hill 1989, Kocí et al. 2003, Tichý 2005, van Tongeren et al. 2008). Another approach consists in

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identifying potential units by progressing downward from higher to lower hierarchical levels (Pot

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1997). In either the case, a classifier is developed from a training data set of plot observations

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whose classification is previously known and is assumed to be valid. Such assumption can be a

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source of problems in expert domains where it does not hold, or when there is no consensus on

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the classification of the training set. Traditional expert-based vegetation classifications usually

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suffer from several inconsistencies (i.e. different researchers used variable and sometimes not

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explicitly stated classification criteria) and/or contain loosely defined units (i.e. plant

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communities defined by the occurrence, dominance, or absence of particular species). Under this

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scenario supervised classification methods may spread potentially wrong knowledge if traditional

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expert-defined classifications are not previously validated using a common classification

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criterion. Since contemporary vegetation scientists are increasingly using numerical clustering

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(i.e. unsupervised) methods to derive new vegetation units (Mucina & van der Maarel 1989,

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Mucina 1997), they should also be used to review traditional classifications. However, note that

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current conservation policies, like those of the Natura 2000 networking program, are based on

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habitat definitions (e.g. the CORINE biotopes manual, Devillers et al. 1991), which in turn rely

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on traditional phytosociological units. Therefore drastic changes in regional/national vegetation

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classifications can be problematic and should be avoided. Even if traditional vegetation units are

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considered valid, we believe the classification criterion of supervised classifications should be 3

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congruent with the one used in the original classification of the training data set. Otherwise,

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either the efficiency and/or interpretation of results may be affected. This explains why

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supervised approaches emulating traditional phytosociological concepts perform better when the

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expert classification of the training set is used instead of that resulting from numerical clustering

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analyses (e.g. van Tongeren et al. 2008).

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The aim of this paper is to propose a methodological framework for translating low-level

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expert-defined vegetation units into an automatic vegetation identifier. It consists of two main

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steps. First, we use Possibilistic C-means, a fuzzy unsupervised classification method, to

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reproduce expert-defined vegetation units. Second, clusters centroids resulting from the first step

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are used to identify new observations by means of a fuzzy classifier. We use the traditional

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phytosociological classification of the Catalan vegetation to build numerical clusters and to

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evaluate the classifier’s ability to provide satisfactory answers at the precision level of

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association.

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Material and Methods

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Data sets and data transformations

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We took the traditional phytosociological classification of terrestrial vegetation in Catalonia,

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northeast of Spain. In order to span a broad range of vegetation types, we considered eight

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syntaxonomical orders (see Table 1), which include different types of grasslands, shrublands and

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forests. For each order we compiled all relevés from those phytosociological associations

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containing at least 3 representatives. Relevés were drawn from the Biodiversity Data Bank of

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Catalonia (Font 2008). Original authors of the relevés had assigned them to associations or

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subassociations that were fitted into the syntaxonomical classification made by Bolòs & Vigo

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(1984). Only Brometalia erecti grasslands had undergone a numerical revision, based on

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correspondence analyses, of the original expert-based classification (Font 1993). We did not 4

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perform any stratified re-sampling (Knollová et al. 2005) neither an elimination of those relevés

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with unusually small or large plot sizes (Otýpková & Chytrý 2006). Relevé compilation resulted

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in eight distinct datasets, one corresponding to each order. Taken together, we considered 3677

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relevés, which belong to 222 distinct low-level (i.e. association or subassociation) vegetation

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units. These vegetation types were the expert knowledge to be validated and emulated by means

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of numerical methods.

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Species nomenclature was homogenized using a regional flora (Bolòs et al. 1990). Unsure

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plant determinations, determinations not reaching the species level and taxon names not

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appearing in the flora were eliminated. Although they are not consistently reported, we kept

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cryptogam records because they are diagnostic for some vegetation units. Braun-Blanquet cover-

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abundance values were first transformed to the nine-degree ordinal scale (van der Maarel 1979).

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We then applied the Hellinger transformation (Legendre & Gallagher 2001). The Hellinger

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distance (Rao 1995, Legendre & Legendre 1998) is equal to the chord distance (Orlóci 1967)

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computed after taking the square root of the abundance values. The multivariate space provided

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by the Hellinger distance was used to define numerical clusters reproducing expert-defined

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vegetation units.

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Cluster model

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In the opinion of many vegetation scientists, vegetation types are not crisp classes but types

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that are conceptually vague and fuzzy (e.g. Dale 1988, Moraczewski 1993, Willner 2006).

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Therefore, any numerical classification of vegetation should allow some degree of overlap and

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even allow leaving some relevés unclassified. Setting a hierarchical tree or a partition (either

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fuzzy or crisp) as classification model seemed excessively constraining to us. In addition, we

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wanted a cluster model where new clusters could be defined without changing all those clusters

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previously defined. Due to these two reasons, we turned our attention to the Possibilistic C5

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Means algorithm (PCM, Krishnapuram & Keller 1993, 1996), which implements a clustering

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model where clusters are both fuzzy and independent. PCM algorithm originated from Fuzzy C-

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means (FCM, Bezdek 1981) an unsupervised partitive clustering procedure well-known among

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vegetation scientists (Marsili-Libelli 1989, Mucina 1997). Table 2 summarizes the mathematical

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differences between PCM and FCM models. In the possibilistic approach, fuzzy membership

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values are not relative (i.e. probabilistic) as in FCM, but are interpreted absolute cluster

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typicalities. Cluster independence is obtained because the partition constrain of FCM is

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eliminated. That is, for any object the sum of its possibilistic membership values does not have to

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be one. Resulting from this fundamental difference, PCM is a mode-seeking algorithm. That is, in

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PCM each vegetation cluster corresponds to a dense region in the multivariate space of relations

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between plots. A single PCM run can be regarded as c independent runs of an algorithm looking

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for a single cluster (Davé & Krishnapuram 1997). The PCM model solves the FCM problem

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raised by Dale (1995), consisting on the possible data contamination resulting from types not

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well represented and whose centre lies outside the available data. Fig. 1 further illustrates the

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differences between the two models, by showing their corresponding results on relevé data from

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three xerophytic grassland associations.

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Reproduction of traditional units into numerical clusters

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Whenever possible, we create one possibilistic fuzzy cluster for each traditional low-level

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vegetation unit (syntaxonomical association or subassociation). One additional advantages of

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PCM over FCM is that it avoids the need of specifying the number of clusters to be sought.

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Instead, distinct clusters are permitted as long as they represent distinguishable dense regions of

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the multivariate space. In our case, we considered two clusters as distinguishable when their

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amount of overlap was less than 10% (see below). We used this criterion to detect poorly defined

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vegetation units. Moreover, relevé databases may be plagued with noisy and transitional plot 6

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data. Including indiscriminately all the available relevés would preclude the PCM algorithm from

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distinguishing many expert-defined units. Therefore some relevés were discarded during the

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reproduction process.

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The following steps were performed for each of the eight datasets: We started by taking those

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relevés belonging to the first low-level vegetation unit. The one-cluster PCM algorithm was then

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run on this initial training relevé set, using the three closest relevés as starting cluster members.

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The fuzziness exponent was set to m = 1.03, which is a rather crisp value but allowed higher

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sensitivity of the algorithm. The PCM cluster size parameter (ηi in Table 2) was then

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progressively augmented in order to make the cluster grow. This was done by using a method

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described in De Cáceres et al. (2006), which allows finding appropriate PCM cluster sizes. Once

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grown, the relevés showing very low membership values (i.e. with uij < 0.0001) were excluded

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from the training data set and stored in a set of transitional (non-typical) relevés. The final cluster

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configuration was also stored. After reproducing this first unit, the relevés belonging to the next

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vegetation unit were included in the training relevé set, and we let the previously defined PCM

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cluster(s) “react” to the newly added relevés by running the PCM algorithm from its last

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configuration, also allowing for changes in the cluster size parameter (De Cáceres et al. 2006). It

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could happen that some of the newly added relevés become members (i.e. with a possibilistic

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fuzzy membership uij > 0.1) of any of the previous cluster(s). In this case, those relevés were

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deemed transitional, and they were also excluded from the training set and stored in the

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transitional set. We then reloaded the stored cluster configuration(s) and the “reacting” process

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was rerun without the noisy transitional relevés. This was repeated until all previously-defined

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PCM cluster(s) were stable to the new relevés. Note that this process of discarding relevés could

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leave a given vegetation unit without enough relevés for being translated into a numerical cluster.

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If enough relevés were left, we used the three closest relevés as starting cluster members for a 7

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new PCM cluster, which was grown as described above. Any given PCM cluster reproducing a

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low-level expert unit was only accepted whenever it fulfilled the following three conditions: (a)

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The sum of membership values for the fuzzy cluster set (i.e. its cardinality) was equal or greater

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than 3; (b) all relevés with a membership value for the fuzzy cluster above 0.1 had been classified

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by experts into the same vegetation type (this condition ensured that the PCM cluster represented

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the proper vegetation concept); and (c) the proportion of overlap between the fuzzy cluster and

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any of the remaining PCM clusters was lower than 10%. Cluster overlap between any pair of

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clusters was calculated as the cardinality of the fuzzy intersection set divided by the cardinality of

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the fuzzy union set. Whenever a cluster failed to be accepted, a distinct set of three relevés was

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used as starting cluster configuration. The steps above-described were iteratively repeated until

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all the traditional low-level vegetation units had been considered. Subassociations were given

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priority over associations as units to be reproduced. This algorithm yielded three sets: (1) a final

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training set, made of typical relevés only (this is hereafter also referred to as the typical relevé

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set); (2) a transitional set, containing those relevés that were outliers or similar to more than one

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numerical cluster; and (3) a set of PCM fuzzy clusters corresponding to reproduced expert-

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defined vegetation units.

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Supervised classification of relevés

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We used the probabilistic approach of FCM to perform supervised classifications. In order to

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use this unsupervised method in a supervised mode, the centroid coordinates for each of the fuzzy

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clusters must be considered static (but see the leave-one-out procedure below). Supervised FCM

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classification of any relevé j was performed in two simple steps: (1) Compute eij, the distance

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between the relevé j and each fixed cluster centroid i; and (2) Compute uij, the relevé fuzzy

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membership to each cluster i, by using the FCM membership function (eq. 1 in Table 2). We set

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the fuzziness exponent to m = 1.2 in this case, as recommended by several authors (e.g. Marsili-

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Libelli 1989, Podani 1990, Escudero & Pajarón 1994).

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Evaluation of the classifier

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Our objective was to assess the performance of the classifier by measuring its rate of correct

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identification at the precision level of association. If a given association (and its possible

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subassociations) had not been reproduced, it was not represented in the set of fuzzy clusters.

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Hence, its relevés could not be used to evaluate the classifier’s performance. However, if some

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subassociations of an association or the association itself had been reproduced, then all its

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subassociations were considered to be represented because in this case the classifier was capable

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of returning a correct answer at the level of association.

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Both typical and transitional relevé sets were used for the evaluation of the classifier. Since

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relevés of the transitional set had been discarded in the definition of PCM clusters, they could be

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used as a test set. However, relevés of the typical (training) set exerted an attraction on the

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centroids, and thus their re-classification was biased. Aiming to remove this bias, we used a

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leave-one-out crossvalidation procedure. For each training relevé to be classified we temporarily

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removed it from the training set and the PCM clusters were allowed to “react” as explained

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above. After this step, identification could be done without the influence of the target relevé on

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cluster centroids.

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The classifier responses were homogenized at the level of association. For each represented

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association within each order we estimated the sensitivity and positive predictive power of the

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classifier (see Cerná & Chytrý 2005 for details). We also calculated rates of correct association

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identification for each of the eight datasets, and for all datasets taken together. In order to gain

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more detailed information on the classifier’s performance, we repeated this efficiency assessment

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also taking into account the second choice as an additional source of correct identification.

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Results

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Reproduction of traditional units

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Among the 222 original low-level units, 166 (75%) could be numerically reproduced using

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strategy described (see Table 1). Only two of the 56 non-reproduced units were associations. The

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remaining 54 non-reproduced units were subassociations, which means that in all these cases

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other subassociations of the same association could be reproduced. Approximately 39% of the

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original relevés were finally kept in the training set, but this percentage varied from 31% (for

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Fagetalia beech forests) to 57% (for Galio-Alliarietalia megaforb communities). Hence, nearly

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25% of the expert-defined vegetation units and 61% of the relevés can be considered of

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transitional nature following our cluster building criteria.

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Performance of the vegetation classifier

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The two non-reproduced associations accounted for 27 relevés. The remaining 3650 relevés

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belonged to associations represented in the classifier, so they were used to assess its performance.

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We report detailed result tables on the sensitivity and positive predictive power for each

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association in App. 1. We show in Table 3 the rates of correct identification computed for the

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eight datasets independently and altogether. The overall rate of correct association identification

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for the typical relevés was very high: 95% of relevés were classified into the correct association

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in the first choice, and 99% taking into account the first and second choices of the classifier (see

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Table 3). This high rate of success is not surprising, since the relevés of this set were those

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which, by definition, were closest to cluster centroids. In contrast, the classifier identified the

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correct association for 64% of the relevés of the transitional set. Nevertheless, if we take into

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account the transitional nature of these relevés, the percentage of correct identification using the 10

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first and second choices may be a more realistic measure of performance. Over all

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phytosociological orders, this latter percentage was 79.5%. Identification of beech forests

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(Fagetalia sylvaticae) was the least successful (66%) and that of Quercus ilex forests and related

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communities (Quercetalia ilicis) the most successful (89.3%). When considering both typical and

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transitional relevé, the estimated overall efficiency of the classifier was 76.3% of correct

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identification on first choice, and 86.9% considering also the classifier’s second choice.

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Discussion

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Reproduction of traditional classifications

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Several attempts of reproduction of traditional vegetation classifications usually forced the

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reproduction of all expert-defined units into the classifier (e.g. van Tongeren 1986, Hill 1989, van

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Tongeren et al. 2008). In the case of Kocí et al. (2003), the use of the Cocktail algorithm

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(Bruelheide 2000) allowed excluding poorly differentiated units, but their approach was still

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essentially expert-based (Chytrý 2007). Going a step further, we stressed here the necessity of

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validating traditional vegetation units through the use of an unsupervised clustering method.

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Although we tried to maximize the amount of vegetation types that could be numerically

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reproduced, 25% of the original low-level units turned out to be impossible to stand.

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Subassociations turned out to be more difficult to reproduce because many of them are

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traditionally defined as a subclass of an association that shows a tendency towards an

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ecologically neighbouring association (in other words, they are transitional).

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Moreover, in previous approaches relevé identification was usually performed using

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assignment rules that were different from the rules originally used in the classification of training

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data (e.g. Kocí et al. 2003, Tichý 2005, van Tongeren et al. 2008). We preferred to use the

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resemblance in species abundance values only, as a simple common criterion for both

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unsupervised and supervised classification. Not using Cocktail’s species groups but overall 11

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species composition has the advantage that it allows reproducing units lacking differential species

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(i.e. ‘basal’ or ‘central’ communities). However, the classifier is not expected to provide accurate

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results with such units due to their high variability and amount of transitional relevés.

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Performance of the vegetation classifier

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Whereas inconsistency in the original classification methods can be avoided by applying

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numerical clustering, it reappears when attempting to evaluate the efficiency of the classifier

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because the reference classification is expert-based. That is, the precision in the original

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assignments may be affecting the percentages of successful identification. In addition, relevés

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belonging to transitional subassociations were more difficult to classify correctly than relevés

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belonging to reproduced vegetation units (even if both were represented at the level of

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association). This occurred because the classifier lacked centroids to represent these units and

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hence its relevés were assigned to one of the neighbouring units. The high number of

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unrecognized subassociations in Fagetalia beech forests (see Table 1) may account for the low

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classifier results on this data set (Table 2). There are other possible sources of low supervised

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classification efficiency, derived from inconsistencies in the sampling methods that different

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authors use. Otýpková & Chytrý (2006) showed that smaller plots tend to produce less stable

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ordinations in data sets of low beta diversity. The lecture of their findings in terms of

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classification is that relevés from small plots may be easily misclassified because of their higher

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degree of variability both in species presence and abundance. The same reasoning may be applied

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to the inconsistent recording of cryptogams.

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Sampling and the appropriate representation of vegetation types

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We carefully selected the relevés included in the training set, which certainly is a critical point

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in our approach and must be justified. Statistically speaking, such relevé selection is still a

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subjective decision that completely biases sampling and precludes any inference on the validity 12

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of groups. Hence, one cannot expect to accurately reflect the real patterns of vegetation.

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Moreover, Cerná & Chytrý (2005) found that selecting plots with diagnostic species as training

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set resulted in lower efficiency of neural network classifiers compared to using a randomly

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selected training set. Nevertheless, nowadays vegetation scientists generally agree that vegetation

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is mainly of continuous nature. Therefore, as long as an optimal vegetation sampling theory is

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lacking, statistical inference on clustering results will remain a delicate subject (e.g. Rolecek et

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al. 2007). Meanwhile, vegetation classification should not aim at discovering true vegetation

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types, but should provide a knowledge basis for performing applied ecological studies. Having

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this in mind, we considered more important to keep the vegetation concept to be reproduced very

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clear. We set a specific point in the multivariate space (i.e. the cluster centroid) as the

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representative of the expert-defined unit. Not including transitional relevés into the centroid

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definition helped in keeping it as an ideal type. Ensuring that the nomenclatural type relevé (if

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available) shows a high membership to the unit would be a way to allow using the syntaxon name

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for the fuzzy cluster.

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Limitations of the numerical cluster model

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Note that our numerical cluster model assumes roughly spherical clusters, both when building

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PCM clusters and when executing the FCM classifier. One of Dale’s (1995) criticisms to FCM

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was its inability to cope with non-spherical cluster shapes. Although it is possible allow

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hyperellipsoidal clusters in FCM and PCM algorithms (Krishnapuram & Keller 1993), by taking

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into account the cluster variance-covariance matrix. Another limitation of our approach is that

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FCM membership function works better with clusters of similar size. PCM typicality function

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may be used instead, but at the expense of obtaining values which cannot be interpreted as

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probabilities.

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Final remarks and future work 13

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In our opinion, vegetation scientists should decide whether they would prefer: (1) a vegetation

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classifier designed as an interface to communicate expert vegetation knowledge to non-experts;

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or (2) a computer program like the former, but which could also promote the revision of the

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expert knowledge itself. In the first case the program would simply run supervised classification

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methods from a knowledge that would be assumed to be true. In contrast, in the second case the

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system would allow doubting expert knowledge, and even changing his point of view. We

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believed this second model was more flexible and promising. We implemented our proposals in a

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set of related computer programs called Araucaria (see App. 2 and

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http://biodiver.bio.ub.es/vegana/araucaria). One of them allows experts to feed the classifier with

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new plot data, and see how the current set of PCM clusters “reacts” to this new information.

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Regarding future developments, we strongly believe that a comparison of vegetation

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classification methodologies is necessary, not only in terms of efficiency but also aiming a

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unification of traditional and numerical approaches. Since vegetation classifications are

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regionally restricted, studying solutions for biogeographical issues (e.g. vicariant units) would be

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another interesting research topic. Nevertheless, large-scale vegetation expert systems (say valid

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for all Europe) will certainly be difficult to develop.

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Acknowledgements

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We would like to thank Lubomir Tichý and an anonymous reviewer for their very useful

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comments on a previous version of this manuscript. This study was supported by a Ph.D. grant

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awarded by the “Comissionat per a Universitats i Recerca” (1999SGR00059), of the

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“Departament d’Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya”

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(2001 FI 00269), and by a research project from the Spanish “Ministerio de Educación y Ciencia”

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(CGL2006-13421-C04-01/BOS).

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416

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417

18

Phytosociological order

Short description

Non-reproduced units

Training (typical) rel.

their low-level classification.

Reproduced units

418

Original relevés

Table 1. The eight phytosociological orders studied and results of the numerical reproduction of

Original units

417

Brometalia erecti

mesophytic or slightly xerophytic pastures

30

531

26

4

231

Origanetalia vulgaris

herb communities growing on forest fringes

12

133

10

2

67

Galio-Alliarietalia

megaforb sciophilous communities

13

124

12

1

71

Prunetalia spinosae

shrub communities growing on decideous forest fringes

18

353

16

2

161

Populetalia albae

riverine meso-macroforests growing on wet fluvisols with high water-table

17

199

10

7

107

Quercetalia ilicis

mediterranean woodlands, scrublands and maquis

31

753

25

6

254

Quercetalia pubescentis

submediterranean decideous oak woodlands

41

651

30

11

243

Fagetalia sylvaticae

beech forests

60

933

37

23

286

222

3677

166

56

1420

Total

419 420 421

Table 2: Main mathematical characteristics of the Fuzzy C-means (FCM) and Possibilistic C-

422

means (PCM) clustering algorithms. FCM Fuzzy membership definition

c

!

i =1

c

uij = 1 for all objects j = 1, ..., n c

Optimisation function

PCM

!

i =1

c

n

i =1 j =1

c

Membership function

n

for all objects j = 1, ..., n

c

n

i =1

j =1

J PCM = ! ! (uij ) m eij2 + ! #i ! (1 " uij ) m

J FCM = ! ! (uij ) m eij2

uij = 1 / ! (eij / elj ) 2 /( m "1)

uij > 0

i =1 j =1

(1)

uij = 1 /(1 + (eij2 / "i )1/( m!1) )

(2)

l =1

423 424

19

424

Table 3. Classification efficiency of the numerical classifier at the association level. Column

425

blocks list the efficiency on the typical and transitional relevé sets, as well as the overall

426

efficiency for the represented associations. Ass.: Number of represented associations. %:

427

Percentage of relevés correctly classified; L/U: Lower/upper 95% confidence limits following the

428

binomial distribution. Typical 1st choice Phytosociological order

429

L

Transitional 1st/2nd choice

U

%

L

U

1st choice Rel.

%

L

Represented

1st/2nd choice U

%

L

U

1st choice Rel.

%

L

1st/2nd choice

Ass.

Rel.

%

U

Brometalia erecti

20

231

97.4

94.4 99.0

99.1

96.9 99.9

285

68.8 63.5

74.6

85.6 81.1 89.6

516

81.6 78.4 85.2

91.7 89.1 94.0

%

L

U

Origanetalia vulgaris

10

67

92.5

83.4 97.5

100.0

94.6 100.0

66

39.4 27.6

52.2

78.8 67.0 87.9

133

66.2 57.5 74.1

89.5 83.0 94.1

Galio-Alliarietalia

11

71

94.4

86.2 98.4

97.2

90.2 99.7

53

56.6 42.3

70.2

73.6 59.7 84.7

124

78.2 69.9 85.1

87.1 79.9 92.4

Prunetalia spinosae

9

161

96.3

92.1 98.6

98.8

95.6 99.8

192

72.9 66.0

79.1

85.9 80.2 90.5

353

83.6 79.3 87.3

91.8 88.4 94.4

Populetalia albae

7

107

92.5

85.8 96.7

94.4

88.2 97.9

92

64.1 53.5

73.9

82.6 73.3 89.7

199

79.4 73.1 84.8

88.9 83.7 92.9

Quercetalia ilicis

13

254

99.2

97.2 99.9

99.2

97.2 99.9

487

80.9 79.4

86.7

89.3 88.2 93.8

741

87.2 86.7 91.5

92.7 92.2 95.9

Quercetalia pubescentis

10

243

90.5

86.1 93.9

98.8

96.4 99.7

408

65.7 60.9

70.3

82.1 78.0 85.7

651

75.0 71.4 78.2

88.3 85.6 90.7

Fagetalia sylvaticae

22

286

96.2

93.2 98.1

99.0

97.0 99.8

647

49.0 45.1

52.9

66.0 62.2 69.6

933

63.5 60.3 66.5

76.1 73.2 78.8

Total 102

1420

95.4

94.2 96.4

98.6

97.8 99.1

2230

64.1 62.1

66.2

79.5 77.9 81.3

3650

76.3 75.1 77.9

86.9 86.0 88.2

430 431

20

431

Fig. 1: Example of clustering results of FCM and PCM on relevés belonging to three grassland

432

associations of Brometalia erecti. (a) Classical multidimensional scaling coordinates from Bray-

433

Curtis distances, with the original vegetation units labelled using different symbols (filled circles:

434

Koelerio-Avenuletum ibericae; squares: Adonido-Brometum erecti; diamonds: Lino viscosi-

435

Brometum erecti; empty circles: intermediate artificial relevés created by averaging randomly-

436

selected relevés from the three groups). (b) FCM (m=1.2) solution with three groups. (c) PCM

437

(m=1.09) solution with three groups, after setting appropriate reference distance parameters as

438

described in De Cáceres et al. (2006). Symbol size and colour intensity are function of the

439

object’s largest membership value.

440 441 442 443 444 445 446

21