Victor J. Rayward-Smith

Fuzzy cluster analysis : methods for classification, data analysis and image recognition

Introduction. Basic Concepts. Classical Fuzzy Clustering Algorithms. Linear and Ellipsoidal Prototypes Shell Prototypes. Polygonal Object Boundaries. Cluster Estimation Models. Cluster Validity. Rule Generation with Clustering. Appendix. Bibliography.

The next release problem

Companies developing and maintaining complex software systems need to determine the features that should be added to their system as part of the next release. They will wish to select these features to ensure the demands of their client base are satisfied as much as possible while at the same time ensuring that they themselves have the resources to undertake the necessary development. This situation is modelled in this paper and the problem of selecting an optimal next release is shown to be NP-hard. The use of various modern heuristics to find a high quality but possibly suboptimal solution is described. Comparative studies of these heuristics are given for various test cases.

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 computation of nearly minimal Steiner trees in graphs

The computation of a minimal Steiner tree for a general weighted graph is known to be NP‐hard. Except for very simple cases, it is thus computationally impracticable to use an algorithm which produces an exact solution. This paper describes a heuristic algorithm which runs in polynomial time and produces a near minimal solution. Experimental results show that the algorithm performs satisfactorily in the rectilinear case. The paper provides an interesting case study of NP‐hard problems and of the important technique of heuristic evaluation.

On finding Steiner vertices

Given a graph G = (V, E), finding the Steiner tree in G for some set of special vertices V′ ⊂ V″, is equivalent to finding the minimum spanning tree in the subgraph of G induced by V′ ∪ V″, where V″ is the set of Steiner vertices. In this paper, we consider ways of deciding which vertices of V are in V″ and compare the performance of various heuristic algorithms.

UET scheduling with unit interprocessor communication delays

Abstract We consider the problem of scheduling a partially ordered set of unit execution time (UET) tasks on m > 1 processors where there is a communication delay of unit time between any pair of distinct processors. We show that the problem of finding an optimal schedule is NP-hard. A greedy schedule is one where no processor remains idle if there is some task available which it could process. We establish that the length of an arbitrary greedy schedule, ω c g satisfies w c g 3− 2 m w c opt − 1− 1 m where ω c opt is the length of the optimal schedule. We define a generalized list schedule (a type of greedy schedule) and discuss anomalous behavour of such schedules with respect to speed-up. The relevance of these results to the implementation of parallel languages is discussed.

Fitness Distance Correlation and Ridge Functions

Fitness Distance Correlation has been proposed as a measure of function optimization difficulty. This paper describes a class of functions, named the Ridge Functions which, according to the measure, should be highly misleading. However, all functions tested were optimized easily by both a GA and a simple hill climbing algorithm. Scatter graph analysis of Ridge functions gave little guidance due to the large number of functions with an identical scatter graph, the majority of which are not in the class of Ridge functions and are not simple to optimize.

Feature Subset Selection within a Simulated Annealing DataMining Algorithm

An overview of the principle feature subset selection methods isgiven. We investigate a number of measures of feature subset quality, usinglarge commercial databases. We develop an entropic measure, based upon theinformation gain approach used within ID3 and C4.5 to build trees, which isshown to give the best performance over our databases. This measure is usedwithin a simple feature subset selection algorithm and the technique is usedto generate subsets of high quality features from the databases. A simulatedannealing based data mining technique is presented and applied to thedatabases. The performance using all features is compared to that achievedusing the subset selected by our algorithm. We show that a substantialreduction in the number of features may be achieved together with animprovement in the performance of our data mining system. We also present amodification of the data mining algorithm, which allows it to simultaneouslysearch for promising feature subsets and high quality rules. The effect ofvarying the generality level of the desired pattern is alsoinvestigated.

Data mining rules using multi-objective evolutionary algorithms

In data mining, nugget discovery is the discovery of interesting classification rules that apply to a target class. In previous research, heuristic methods (genetic algorithms, simulated annealing and tabu search) have been used to optimise a single measure of interest. This paper proposes the use of multi-objective optimisation evolutionary algorithms to allow the user to interactively select a number of interest measures and deliver the best nuggets (an approximation to the Pareto-optimal set) according to those measures. Initial experiments are conducted on a number of databases, using an implementation of the fast elitist non-dominated sorting genetic algorithm (NSGA), and two well known measures of interest. Comparisons with the results obtained using modern heuristic methods are presented. Results indicate the potential of multi-objective evolutionary algorithms for the task of nugget discovery.

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.