this paper is to describe some of the relationships among the different streams and to try to clarify some of the important differences in their assumptions and development. Other studies mentioning the relationships appear in [1, Section IV, pp. 1038--1039], [2, sections 5.2, 5.5] and [3, p. 465]

. While many constructive induction algorithms focus on generating new binary attributes, this paper explores novel methods of constructing nominal and numeric attributes. We propose a new constructive operator, X-of-N. An X-of-N representation is a set containing one or more attribute-value pairs. For a given instance, the value of an X-of-N representation corresponds to the number of its attribute-value pairs that are true of the instance. A single X-of-N representation can directly and simply represent any concept that can be represented by a single conjunctive, a single disjunctive, or a single M-of-N representation commonly used for constructive induction, and the reverse is not true. In this paper, we describe a constructive decision tree learning algorithm, called XofN. When building decision trees, this algorithm creates one X-of-N representation, either as a nominal attribute or as a numeric attribute, at each decision node. The construction of X-of-N representations is carrie...

Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)), and how it has both an information-theoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace and Boulton (1968), Wallace (1986), Wallace and Dowe(1994)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components. The message length is (to within a constant) the logarithm of the posterior probability of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated, and permits multi-variate data from Gaussian, discrete multi-state, Poisson and von Mises circular dist...

Abstract: We provide a brief overview ofMinimum Message Length (MML) inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)). We then outline how MML is used for statistical parameter estimation, and how the MML intrinsic classification program, Snob (Wallace and Boulton (1968), Wallace (1986), Wallace (1990)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with model selection in intrinsic classification. We mention here the most recent extensions to Snob, permitting Poisson and von Mises circular distributions. We also survey some applications of Snob (albeit briefly), and further provide some documentation on how the user can guide Snob’s search through various models of the given data to try to obtain that model whose message length is a minimum.

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.