An information measure for hierarchic classification

Boulton, D. M.; Wallace, Chris S.

doi:10.1093/comjnl/16.3.254

Cited by 35 publications

(22 citation statements)

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“…Solomonoff (1964) proposed MML encoding as a basis for inductive inference. Wallace and Boulton (1968) applied it in producing a practical classification algorithm and later an algorithm for hierarchical classification (Boulton and Wallace 1973). Georgeff and Wallace (1984) give a good introduction to MML methods, and Wallace and Freeman (1987) describe the statistical foundations.…”

Section: P(handd) = P(d [ H) P(h) = P(h [ D)p(d)mentioning

confidence: 99%

Finite-state models in the alignment of macromolecules

1992

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Minimum message length encoding is a technique of inductive inference with theoretical and practical advantages. It allows the posterior odds-ratio of two theories or hypotheses to be calculated. Here it is applied to problems of aligning or relating two strings, in particular two biological macromolecules. We compare the r-theory, that the strings are related, with the null-theory, that they are not related. If they are related, the probabilities of the various alignments can be calculated. This is done for one-, three-, and five-state models of relation or mutation. These correspond to linear and piecewise linear cost functions on runs of insertions and deletions. We describe how to estimate parameters of a model. The validity of a model is itself an hypothesis and can be objectively tested. This is done on real DNA strings and on artificial data. The tests on artificial data indicate limits on what can be inferred in various situations. The tests on real DNA support either the three- or five-state models over the one-state model. Finally, a fast, approximate minimum message length string comparison algorithm is described.

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Section: P(handd) = P(d [ H) P(h) = P(h [ D)p(d)mentioning

confidence: 99%

Finite-state models in the alignment of macromolecules

1992

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“…The hierarchical clustering was obtained using a program, HSNOB, developed by Wallace from earlier proposals of Boulton and Wallace (1973a). Details are presented in Appendix 1.…”

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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“…1] that, even though MML had been in print many times over since 1968 [Wallace and Boulton, 1968, p. 185, sec. 2;Boulton and Wallace, 1969;1970, p. 64, col. 1;Boulton and Wallace, 1973b, sec. 1, col. 1;1973c;1975, sec.…”

Section: Strict MML (Smml)mentioning

confidence: 99%

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

Dowe¹

2011

Philosophy of Statistics

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An information measure for hierarchic classification

Cited by 35 publications

References 0 publications

Finite-state models in the alignment of macromolecules

Finite-state models in the alignment of macromolecules

Hierarchical clusters of vegetation types

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

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