A new clustering algorithm with multiple runs of iterative procedures

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A hybrid methodology for data clustering

This thesis introduces and evaluates a new hybrid method for the searching for groups in data - a process referred to as cluster analysis. The Agglomerative - Partitional Clustering methodology (APC) proposed in this work is a novel solution to the clustering problem intended for use with large, noisy data sets and capable of recovering clusters of arbitrary shape. Large sample size, noise and nonhyperellipsoidal cluster shapes can create difficulties for many clustering algorithms. Many commonly used clustering techniques are too inefficient to handle large data sets found in many data analysis problems or are limited by the fact that they implicitly or explicitly define clusters as being hyperellipsoidal (i.e. “globular” in shape) and can therefore fail to recover other types of cluster structure. Moreover, the presence of noise can also make detection of cluster structures problematic, particularly for clustering techniques that are explicitly designed to handle nonhyperellipsoidal cluster structures. APC is able to circumvent these difficulties by hybridising a number of diverse approaches to clustering. Large data sets are dealt with by hybridising fast pattern partitioning techniques with hierarchical and density search methods. Arbitrary cluster shapes are handled by a unique linked line segment representation of cluster shape. In short, rather than representing clusters with their centroids, the clusters are represented via a piecewise linear approximation of the cluster structure. This enables APC to represent any cluster shape that is piecewise linearly approximatable. The purpose of this thesis, therefore, is to introduce APC and to evaluate the ability of APC to recover cluster structure under the conditions described above. First, it is argued that there is a dearth of clustering techniques that can process large, noisy data sets where there exists arbitrarily shaped clusters. Next, the APC approach to clustering is described in detail. Here it is discussed how APC is able to handle voluminous and noisy data without being constrained to any particular cluster shapes. Moreover, as APC represents a hybridisation of clustering strategies and techniques, different ways of implementing APC are also evaluated. The remainder of this thesis is concerned with the evaluation of APC. First, APC is empirically compared to other clustering methods via Monte Carlo simulation on a number of complex data sets. A wide variety of experimental conditions examining cluster shape, dispersion, noise and dimensionality are covered. The use of APC as a data reduction method is also examined. This final experiment also highlights the utility of the linked line segment representation of cluster shape proposed in this thesis. Finally, the concluding chapter summarises the results and limitations of this thesis and discusses some future directions this research could take