Hierarchical clusters of vegetation types

Abstract

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.

The management of vegetation classifications with fuzzy clustering

“…First, it is difficult to update hierarchies without rebuilding the classification from scratch. Second, acknowledging reticular relationships between low‐level vegetation types is more realistic than imposing a hierarchical structure (Wallace & Dale 2005). Third, concentrating on the definition of low‐level types does not preclude imposing further structure a posteriori .…”

“…For example, one could use Task 1 to determine the fuzzy membership of low‐level centroids to high‐level clusters. This strategy, which we believe deserves to be investigated, would allow relating levels of vegetation structure in a reticulate fuzzy way instead of imposing a hierarchical structure (Wallace & Dale 2005).…”

MML, Hybrid Bayesian Network Graphical Models, Statistical Consistency, Invariance and Uniqueness

“…0.2.3, p. 531, col. 1 and sec. 0.2.4, p. 537, col. 2] (and elsewhere), with an application of hierarchical MML mixture modelling in [Wallace and Dale, 2005], to image recognition in [Torsello and Dowe, 2008b;, with other work on MML mixture modelling in sec. 7.6, and MML applied to James-Stein estimation in [Schmidt and Makalic, 2009b].…”

Foreword re C. S. Wallace

“…However, it is a shortcoming in the current author that this immediate past sentence fails to mention Chris's work on data processing in the early cosmic ray experiments in Sydney [45,40], one of his papers that can cause some mirth [167], his analysis of nasal support [59], his direct contributions to computer science course structure, syllabi and education 27 , and vastly many other works. I have tried to cite them below -from 28 29 his first works [182,181] helping a fellow (1954) Honours student (Brian O'Brien 30 ) to get his project to work, to his last work published while he was alive [217] to his posthumously published book on MML [287] and the only other two works of his to date that have appeared posthumously [151,293] -and 31 I have also endeavoured to list them at www.csse.monash.edu.au/~dld/CSWallacePublications.…”

“…I do not exaggerate when I say that if we were to pit Chris on his own against a team including every other employee of Monash University's Faculty of I.T. (past or present, going back to the very early 1990s) and augment this team by every co-author (apart from Chris) that I have had so far 80 81 , then I have little doubt that Chris would have completed the task both more thoroughly and earlier than the assembled team 82 84 85 , MML hierarchical clustering [37] (applied in [293]), MML as a form of invariant Bayesian point estimation [291,305] 68 see also end of footnote 79 and text leading to footnote 70 69 cf. footnote 32.…”