Minimum message length clustering, environmental heterogeneity and the variable Poisson model

Dale, M. B.

doi:10.1556/comec.2.2001.2.4

Cited by 7 publications

(3 citation statements)

References 29 publications

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“…A similar reduction could occur by changing the acceptable distribution of variation within clusters, with a choice between Poisson, Gaussian, t-distribution and gamma distribution being provided within the present program. Dale (2001) has examined the effects of choosing Poisson or Gaussian distributions. A non-hierarchical clustering was obtained using 120 random starts of the SNOB program (Wallace and Dowe 2000).…”

Section: Methodsmentioning

confidence: 99%

Hierarchical clusters of vegetation types

Wallace¹,

Dale²

2005

Community Ecology

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IntroductionAlthough other methods of organising data have been used , unsupervised clustering has been widely employed in analysing vegetation data. Most such analyses have used hierarchical clustering methods; for example, the widespread Braun-Blanquet method (Westhoff and van der Maarel 1978) is formidably hierarchical in its approach. Whatever the a priori likelihood that vegetation falls neatly into the nested clusters demanded by such a model, it is surely more appropriate to test if a hierarchy does provide a better model of the data than alternatives, such as Galois lattices (Rodin et al. 1998) or Gaussian response curves (ter Braak and Prentice 1988). This, of course, requires that we have some means of measuring the quality of a model. The Minimum Message Length (MML) principle (Wallace and Dowe 2000) provides just such a measure; the shorter the message length, the higher the prior probability of the model. (2000) SNOB. This provides a general regionalisation using a nonhierarchical clustering. A variant of the program incorporates possible spatial correlations (Wallace 1998) and thereby encourages spatial contiguity of cluster members but this was not used. The program does not provide a segmentation (cf. Oliver et al. 1998) with crisp boundaries for clusters. Instead it employs a fuzzy assignment of things to clusters; such fuzziness is necessary to obtain consistent estimates of cluster parameters.Boulton and Wallace (1973a,b) presented a method (HSNOB) using MML estimation for hierarchical clustering. This means that we can actually make a comparison of non-hierarchic and hierarchic analyses based on the message lengths. In this paper we propose to first examine the concept of hierarchy, and then consider possible reasons why vegetation might have such structure. We shall then examine the application of HSNOB and compare the hierarchical and non-hierarchical solutions to determine Hierarchical clusters of vegetation types Abstract:In this paper, we examine possible sources of hierarchical (nested) structure in vegetation data. We then use the Minimum Message length principle to provide a rational means of comparing hierarchical and non-hierarchical clustering. The results indicate that, with the data used, a hierarchical solution was not as efficient as a nonhierarchical one. However, the hierarchical solution seems to provide a more comprehensible solution, separating first isolated types, probably caused from unusual contingent events, then subdividing the more diverse areas before finally subdividing the less diverse. By presenting this in 3 stages, the complexity of the non-hierarchical result is avoided. The result also suggests that a hierarchical analysis may be useful in determining 'homogeneous' areas.Abbreviatons: MML -Minimum Message Length; MUAP -Modifiable unit area problem.

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Section: Methodsmentioning

confidence: 99%

Hierarchical clusters of vegetation types

Wallace¹,

Dale²

2005

Community Ecology

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“…The possibility of using the estimates of the Poisson parameters to provide a variable Poisson model (Stevens 1937) for the species is interesting and will be examined further elsewhere (Dale 2001). The result, treated at face value, does suggest that spatially vegetation can be regarded as a series of relatively small patches.…”

Section: Substantivementioning

confidence: 99%

Minimum message length clustering: an explication and some applications to vegetation data

Dale

Salmina

Mucina³

2001

Community Ecology

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In this paper, we examine the application of a particular approach to induction, the minimum message length principle and illustrate some of the problems that can be addressed through its use. The MML principle seeks to identify an optimal model within some specified parameterised class of models and for this paper we have chosen to concentrate on a single model class, that of mixture separation or fuzzy clustering. The first section presents, in outline, an MML methodology for fuzzy clustering. We then present some applications, including the nature of the within-cluster model, examination of the univocality of results for different groups of species and the effectiveness of presence data compared to purely quantitative data. Finally, we examine some possibilities of extending MML methodology to include within-class correlation of species, the existence of dependence between observed samples and the comparison of different classes of models.

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“…Kolmogorov complexity is different than 'Solomonoff complexity' (Solomonoff, 1964) and different from the 'Minimum Message Length' (MML) which was defined by Wallace and others (Wallace, 2005;Wallace & Dowe, 1999). The Minimum Message Length has already been used in ecology (Dale, 2001) and is based on Shannon's theory of information and on Bayes's rule. Solomonoff complexity is based on the theory of Turing machines and gives a probabilistic distribution of the set of binary strings as a model for the probability corresponding to the data of a string.…”

Section: Introductionmentioning

confidence: 99%

The Algorithmic Complexity of Landscapes

Papadimitriou

2012

Landscape Research

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A method to evaluate the algorithmic complexity of landscapes is developed here, based on the notion of Kolmogorov complexity (or K-complexity). The K-complexity of a landscape is calculated from a string x of symbols representing the landscape's features (e.g. land use), whereby each symbol belongs to an alphabet L, and can be defined as the size of the shortest string y that fully describes x. K-complexity presents several useful aspects as a measure of landscape complexity: a) it is a direct measure of complexity and not a surrogate measure, well supported by the literature of Informatics; b) it is easy to apply to landscapes of 'small' size' c) it can be used to compare the complexity of two or more landscapes; d) it allows calculations of a landscape's changes in complexity with time; e) it can be a descriptor not only of the landscape's structural complexity, but also of its functional complexity; and f) it makes possible to distinguish two landscapes with the same diversity but with different complexity.

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Minimum message length clustering, environmental heterogeneity and the variable Poisson model

Cited by 7 publications

References 29 publications

Hierarchical clusters of vegetation types

Hierarchical clusters of vegetation types

Minimum message length clustering: an explication and some applications to vegetation data

The Algorithmic Complexity of Landscapes

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