Robust techniques and applications in fuzzy clustering

This dissertation addresses issues central to frizzy 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 Dave\u27s 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

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory

A hybrid interval type-2 semi-supervised possibilistic fuzzy c-means clustering and particle swarm optimization for satellite image analysis

Although satellite images can provide more information about the earth’s surface in a relatively short time and over a large scale, they are affected by observation conditions and the accuracy of the image acquisition equipment. The objects on the images are often not clear and uncertain, especially at their borders. The type-1 fuzzy set based fuzzy clustering technique allows each data pattern to belong to many different clusters through membership function (MF) values, which can handle data patterns with unclear and uncertain boundaries well. However, this technique is quite sensitive to noise, outliers, and limitations in handling uncertainties. To overcome these disadvantages, we propose a hybrid method encompassing interval type-2 semi-supervised possibilistic fuzzy c-means clustering (IT2SPFCM) and Particle Swarm Optimization (PSO) to form the proposed IT2SPFCM-PSO. We experimented on some satellite images to prove the effectiveness of the proposed method. Experimental results show that the IT2SPFCM-PSO algorithm gives accuracy from 98.8% to 99.39% and is higher than that of other matching algorithms including SFCM, SMKFCM, SIIT2FCM, PFCM, SPFCM-W, SPFCM-SS, and IT2SPFCM. Analysis of the results by indicators PC-I, CE-I, D-I, XB-I, t -I, and MSE also showed that the proposed method gives better results in most experiments

Fuzzy clustering with entropy regularization for interval-valued data with an application to scientific journal citations

In recent years, the research of statistical methods to analyze complex structures of data has increased. In particular, a lot of attention has been focused on the interval-valued data. In a classical cluster analysis framework, an interesting line of research has focused on the clustering of interval-valued data based on fuzzy approaches. Following the partitioning around medoids fuzzy approach research line, a new fuzzy clustering model for interval-valued data is suggested. In particular, we propose a new model based on the use of the entropy as a regularization function in the fuzzy clustering criterion. The model uses a robust weighted dissimilarity measure to smooth noisy data and weigh the center and radius components of the interval-valued data, respectively. To show the good performances of the proposed clustering model, we provide a simulation study and an application to the clustering of scientific journals in research evaluation

Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic, volume 2

Papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by the National Aeronautics and Space Administration and cosponsored by the University of Houston, Clear Lake, held 1-3 Jun. 1992 at the Lyndon B. Johnson Space Center in Houston, Texas are included. During the three days approximately 50 papers were presented. Technical topics addressed included adaptive systems; learning algorithms; network architectures; vision; robotics; neurobiological connections; speech recognition and synthesis; fuzzy set theory and application, control and dynamics processing; space applications; fuzzy logic and neural network computers; approximate reasoning; and multiobject decision making