Robust techniques and applications in fuzzy clustering
Authors: Rajesh N. Dave
Venue:  (2005)

This dissertation addresses issues central to fuzzy classification. The issue of sensitivity to noise and outliers of least squares minimization based clustering techniques, such as Fuzzy c-Means (FCM) and its variants is addressed. In this work, two novel and robust clustering schemes are presented and analyzed in detail. They approach the problem of robustness from different perspectives. The first scheme scales down the FCM memberships of data points based on the distance of the points from the cluster centers. Scaling done on outliers reduces their membership in true clusters. This scheme, known as the Mega-clustering, defines a conceptual mega-cluster which is a collective cluster of all data points but views outliers and good points differently (as opposed to the concept of Dav&eacute;'s Noise cluster). The scheme is presented and validated with experiments and similarities with Noise Clustering (NC) are also presented. The other scheme is based on the feasible solution algorithm that implements the Least Trimmed Squares (LTS) estimator. The LTS estimator is known to be resistant to noise and has a high breakdown point. The feasible solution approach also guarantees convergence of the solution set to a global optima. Experiments show the practicability of the proposed schemes in terms of computational requirements and in the attractiveness of their simplistic frameworks. The issue of validation of clustering results has often received less attention than clustering itself. Fuzzy and non-fuzzy cluster validation schemes are reviewed and a novel methodology for cluster validity using a test for random position hypothesis is developed. The random position hypothesis is tested against an alternative clustered hypothesis on every cluster produced by the partitioning algorithm. The Hopkins statistic is used as a basis to accept or reject the random position hypothesis, which is also the null hypothesis in this case. The Hopkins statistic is known to be a fair estimator of randomness in a data set. The concept is borrowed from the clustering tendency domain and its applicability to validating clusters is shown here. A unique feature selection procedure for use with large molecular conformational datasets with high dimensionality is also developed. The intelligent feature extraction scheme not only helps in reducing dimensionality of the feature space but also helps in eliminating contentious issues such as the ones associated with labeling of symmetric atoms in the molecule. The feature vector is converted to a proximity matrix, and is used as an input to the relational fuzzy clustering (FRC) algorithm with very promising results. Results are also validated using several cluster validity measures from literature. Another application of fuzzy clustering considered here is image segmentation. Image analysis on extremely noisy images is carried out as a precursor to the development of an automated real time condition state monitoring system for underground pipelines. A two-stage FCM with intelligent feature selection is implemented as the segmentation procedure and results on a test image are presented. A conceptual framework for automated condition state assessment is also developed.