This thesis describes the results of a collaborative research programme between the Department of Electronics & Electrical Engineering, University of Glasgow, and the Centre for Respiratory Investigation, Glasgow Royal Infirmary. The research was initially aimed at studying lung sound using signal processing and pattern recognition techniques. The use of pattern recogntion techniques was largely confined to exploratory data analysis which led to an interest in the methods themselves. A study was carried out to apply recent research in computational geometry to clustering Two geometric structures, the Gabriel graph and the relative neighbourhood graph, are both defined by a region of influence. A generalization of these graphs is used to find the conditions under which graphs defined by a region of influence are connected and planar. The Gabriel graph may be considered to be just planar and the relative neighbourhood graph to be just connected. From this two variable regions of influence were defined that were aimed at producing disconnected graphs and hence a partitioning of the data set, A hierarchic clustering based on relative distance may be generated by varying the size of the region of influence. The value of the clustering method is examined in terms of admissibility criteria and by a case study. An interactive display to complement the graph theoretical clustering was also developed. This display allows a partition in the clustering to be examined. The relationship between clusters in the partition may be studied by using the partition to define a contracted graph which is then displayed. Subgraphs of the original graph may be used to provide displays of individual clusterso This display should provide additional information about a partition and hence allow the user to understand the data better. The remainder of the work in this thesis concerns the application of pattern recogntition techniques to the analysis of lung sound signals. Breath sound was analysed using frequency domain methods since it is basically a continuous signal. Initially, a rather ad hoc method was used for feature extraction which was based on a piecewise constant approximation to the amplitude spectrum. While this method provided a useful set of features, it is clear that more systematic methods are required. These methods were used to study lung sound in four groups of patients: (1) normal patients, (2) patients with asbestosis, (3) patients with cryptogenic fibrosing alveolitis (CFA) and (4) patients with interstitial pulmonary oedema. The data sets were analysed using principal components analysis and the new graph theroretical clustering method (this data was used as a case study for the clustering method). Three groups of patients could be identified from the data;- (a) normal subjects, (b) patients with fibrosis of the lungs (asbestosis & CFA) and (c) patients with pulmonary oedema. These results suggest that lung sound may be able to make a useful contribution to non-invasive diagnosis. However more extensive studies are required before the real value of lung sound in diagnosis is established
