Alan P. Reynolds

Clustering Rules: A Comparison of Partitioning and Hierarchical Clustering Algorithms

Previous research has resulted in a number of different algorithms for rule discovery. Two approaches discussed here, the ‘all-rules’ algorithm and multi-objective metaheuristics, both result in the production of a large number of partial classification rules, or ‘nuggets’, for describing different subsets of the records in the class of interest. This paper describes the application of a number of different clustering algorithms to these rules, in order to identify similar rules and to better understand the data.

The application of k-medoids and PAM to the clustering of rules

Earlier research has resulted in the production of an ‘all-rules’ algorithm for data-mining that produces all conjunctive rules of above given confidence and coverage thresholds. While this is a useful tool, it may produce a large number of rules. This paper describes the application of two clustering algorithms to these rules, in order to identify sets of similar rules and to better understand the data.

Developments on a multi-objective metaheuristic (MOMH) algorithm for finding interesting sets of classification rules

In this paper, we experiment with a combination of innovative approaches to rule induction to encourage the production of interesting sets of classification rules. These include multi-objective metaheuristics to induce the rules; measures of rule dissimilarity to encourage the production of dissimilar rules; and rule clustering algorithms to evaluate the results obtained. Our previous implementation of NSGA-II for rule induction produces a set of cc-optimal rules (coverage-confidence optimal rules). Among the set of rules produced there may be rules that are very similar. We explore the concept of rule similarity and experiment with a number of modifications of the crowding distance to increasing the diversity of the partial classification rules produced by the multi-objective algorithm.

A multi-objective GRASP for partial classification

Metaheuristic algorithms have been used successfully in a number of data mining contexts and specifically in the production of classification rules. Classification rules describe a class of interest or a subset of this class, and as such may also be used as an aid in prediction. The production and selection of classification rules for a particular class of the database is often referred to as partial classification. Since partial classification rules are often evaluated according to a number of conflicting objectives, the generation of such rules is a task that is well suited to a multi-objective (MO) metaheuristic approach. In this paper we discuss how to adapt well known MO algorithms for the task of partial classification. Additionally, we introduce a new MO algorithm for this task based on a greedy randomized adaptive search procedure (GRASP). GRASP has been applied to a number of problems in combinatorial optimization, but it has very seldom been used in a MO setting, and generally only through repeated optimization of single objective problems, using either linear combinations of the objectives or additional constraints. The approach presented takes advantage of some specific characteristics of the data mining problem being solved, allowing for the very effective construction of a set of solutions that form the starting point for the local search phase of the GRASP. The resulting algorithm is guided solely by the concepts of dominance and Pareto-optimality. We present experimental results for our partial classification GRASP and other MO metaheuristics. These show that such algorithms are generally very well suited to this data mining task and furthermore, the GRASP brings additional efficiency to the search for partial classification rules.

Rule Induction Using Multi-Objective Metaheuristics: Encouraging Rule Diversity

Previous research produced a multi-objective metaheuristic for partial classification, where rule dominance is determined through the comparison of rules based on just two objectives: rule confidence and coverage. The user is presented with a set of descriptions of the class of interest from which he may select a subset. This paper presents two enhancements to this algorithm, describing how the use of modified dominance relations may increase the diversity of rules presented to the user and how clustering techniques may be used to aid in the presentation of the potentially large sets of rules generated.

Rule induction for classification using multi-objective genetic programming

Multi-objective metaheuristics have previously been applied to partial classification, where the objective is to produce simple, easy to understand rules that describe subsets of a class of interest. While this provides a useful aid in descriptive data mining, it is difficult to see how the rules produced can be combined usefully to make a predictive classifier. This paper describes how, by using a more complex representation of the rules, it is possible to produce effective classifiers for two class problems. Furthermore, through the use of multi-objective genetic programming, the user can be provided with a selection of classifiers providing different trade-offs between the misclassification costs and the overall model complexity.

Complexity in de Sitter Space

We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter boundaries. The bulk holographic duals include solutions with or without a horizon. If we compute the complexity from the spatial volume, we find results consistent with general expectations, but the conjectured bound on the growth rate is not saturated. If we compute complexity from the action of the Wheeler–de Witt patch, we find qualitative differences from the volume calculation, with states of smaller energy having larger complexity than those of larger energy, even though the latter have bulk horizons.

A multiobjective GRASP for rule selection

This paper describes the application of a multiobjective GRASP to rule selection, where previously generated simple rules are combined to give rule sets that minimize complexity and misclassfication cost. As rule selection performance depends heavily on the diversity and quality of the previously generated rules, this paper also investigates a range of multiobjective approaches for creating this initial rule set and the effect on the quality of the resulting classifier.

Butterflies with rotation and charge

We explore the butterfly effect for black holes with rotation or charge. We perturb rotating BTZ and charged black holes in 2+1 dimensions by adding a small perturbation on one asymptotic region, described by a shock wave in the spacetime, and explore the effect of this shock wave on the length of geodesics through the wormhole and hence on correlation functions. We find the effect of the perturbation grows exponentially at a rate controlled by the temperature; dependence on the angular momentum or charge does not appear explicitly. We comment on issues affecting the extension to higher-dimensional charged black holes.

Scheduling a manufacturing plant using simulated annealing and simulation

A technique for scheduling a class of manufacturing plants is described. The technique uses a simulated annealing module to create partial schedules, which are then completed and evaluated by a simulation module. The simulation module is equipped with a number of rules which it uses to complete schedules. A mathematical specification is given defining the type of scheduling problem with which we have been concerned. The derivation of a mixed integer linear programming model from this specification is discussed. The complexity of such a model for practical instances justifies the use of heuristic approaches. Results from using our approach on a case study derived from a real-world problem are presented.