Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved

Volume and shape in feature space on adaptive FCM in MRI segmentation.

Intensity non-uniformity (bias field) correction, contextual constraints over spatial intensity distribution and non-spherical cluster\u27s shape in the feature space are incorporated into the fuzzy c-means (FCM) for segmentation of three-dimensional multi-spectral MR images. The bias field is modeled by a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of either intensity or membership are added into the FCM cost functions. Since the feature space is not isotropic, distance measures, other than the Euclidean distance, are used to account for the shape and volumetric effects of clusters in the feature space. The performance of segmentation is improved by combining the adaptive FCM scheme with the criteria used in Gustafson-Kessel (G-K) and Gath-Geva (G-G) algorithms through the inclusion of the cluster scatter measure. The performance of this integrated approach is quantitatively evaluated on normal MR brain images using the similarity measures. The improvement in the quality of segmentation obtained with our method is also demonstrated by comparing our results with those produced by FSL (FMRIB Software Library), a software package that is commonly used for tissue classification

Learning fuzzy systems: an ojective function-approach

One of the most important aspects of fuzzy systems is that they are easily understandable and interpretable. This property, however, does not come for free but poses some essential constraints on the parameters of a fuzzy system (like the linguistic terms), which are sometimes overlooked when learning fuzzy system automatically from data. In this paper, an objective function-based approach to learn fuzzy systems is developed, taking these constraints explicitly into account. Starting from fuzzy c-means clustering, several modifications of the basic algorithm are proposed, affecting the shape of the membership functions, the partition of individual variables and the coupling of input space partitioning and local function approximation

The modified k-means algorithm and its application to type-1 diabetes glucose data clustering

A thesis submitted to the University of Bedfordshire, in fulfilment of the requirements for the degree of Master of Science by researchMost of previous studies of were concentrated on data mining algorithms for type 2 diabetes patients. This study aims to design and implement a data mining algorithm to assist doctors to diagnose and analyze type 1 diabetes patients' condition. In order to achieve the aim of this study, data of glucose of the diabetes patients have been collected first. Mainstream data mining algorithms have been then studied and compared through literatures review. A K-means algorithm has been initially selected to be applied to deal with diabetes patients' data. However, there are three disadvantages of the K-means algorithm: a) The performance of the K-means algorithm tightly relies on the order of input data. b) Outliers can determine the performance of the algorithm. c) The data samples which fall into the overlap are difficult to deal with. Therefore, fuzzy logic techniques have been introduced to collaboratively work with the K-means algorithm. Experiments are to be carrying out in order to test and verify the proposed algorithm after the implementation of the software. The proposed algorithm and the software are going to be optimized in the nearly future

Adaptive constrained clustering with application to dynamic image database categorization and visualization.

The advent of larger storage spaces, affordable digital capturing devices, and an ever growing online community dedicated to sharing images has created a great need for efficient analysis methods. In fact, analyzing images for the purpose of automatic categorization and retrieval is quickly becoming an overwhelming task even for the casual user. Initially, systems designed for these applications relied on contextual information associated with images. However, it was realized that this approach does not scale to very large data sets and can be subjective. Then researchers proposed methods relying on the content of the images. This approach has also proved to be limited due to the semantic gap between the low-level representation of the image and the high-level user perception. In this dissertation, we introduce a novel clustering technique that is designed to combine multiple forms of information in order to overcome the disadvantages observed while using a single information domain. Our proposed approach, called Adaptive Constrained Clustering (ACC), is a robust, dynamic, and semi-supervised algorithm. It is based on minimizing a single objective function incorporating the abilities to: (i) use multiple feature subsets while learning cluster independent feature relevance weights; (ii) search for the optimal number of clusters; and (iii) incorporate partial supervision in the form of pairwise constraints. The content of the images is used to extract the features used in the clustering process. The context information is used in constructing a set of appropriate constraints. These constraints are used as partial supervision information to guide the clustering process. The ACC algorithm is dynamic in the sense that the number of categories are allowed to expand and contract depending on the distribution of the data and the available set of constraints. We show that the proposed ACC algorithm is able to partition a given data set into meaningful clusters using an adaptive, soft constraint satisfaction methodology for the purpose of automatically categorizing and summarizing an image database. We show that the ACC algorithm has the ability to incorporate various types of contextual information. This contextual information includes: spatial information provided by geo-referenced images that include GPS coordinates pinpointing their location, temporal information provided by each image\u27s time stamp indicating the capture time, and textual information provided by a set of keywords describing the semantics of the associated images