George E. Tsekouras

A hierarchical fuzzy-clustering approach to fuzzy modeling

Abstract This paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy-clustering scheme. The method consists of a sequence of steps aiming towards developing a Takagi–Sugeno (TS) fuzzy model of optimal structure, where the fuzzy sets in the premise part are of Gaussian type. Starting from an initial ordinary fuzzy partition of the input space, the algorithm performs a nearest-neighbor search and groups the original input training data into a number of clusters. The centers of these clusters are further processed using an optimal fuzzy clustering technique, which is based on the weighted fuzzy c -means algorithm. The resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters, which in a next step are fine tuned using the well-known gradient-descend algorithm. The proposed method is successfully applied to three test examples, where the produced fuzzy models prove to be very accurate, as well as compact in size.

On the use of the weighted fuzzy c-means in fuzzy modeling

This paper proposes a fuzzy clustering-based algorithm for fuzzy modeling. The algorithm incorporates unsupervised learning with an iterative process into a framework, which is based on the use of the weighted fuzzy c-means. In the first step, the learning vector quantization (LVQ) algorithm is exploited as a data pre-processor unit to group the training data into a number of clusters. Since different clusters may contain different number of objects, the centers of these clusters are assigned weight factors, the values of which are calculated by the respective cluster cardinalities. These centers accompanied with their weights are considered to be a new data set, which is further elaborated by an iterative process. This process consists of applying in sequence the weighted fuzzy c-means and the back-propagation algorithm. The application of the weighted fuzzy c-means ensures that the contribution of each cluster center to the final fuzzy partition is determined by its cardinality, meaning that the real data structure can be easier discovered. The algorithm is successfully applied to three test cases, where the produced fuzzy models prove to be very accurate as well as compact in size.

On training RBF neural networks using input--output fuzzy clustering and particle swarm optimization

This paper elaborates on the use of particle swarm optimization in training Gaussian type radial basis function neural networks under the umbrella of input-output fuzzy clustering. The problem being investigated concerns the selection of basis function centers that contribute most in networks performance, given that the clustering process in the input space is guided by the clustering in the output space. To accomplish this task, we quantify the effect of the input space fuzzy partition upon networks square error in terms of an objective function that describes the ability of the partition to accurately reconstruct the input training samples. We, then, theoretically prove that the minimization of the above function acts to minimize an upper bound of the networks square error. Therefore, the resulting solution corresponds to a minimal square error, while at the same time it maintains the structure of the input data. Due to the peculiarity of the aforementioned objective function, we treat it as the fitness function used by the particle swarm optimizer. The proposed methodology encompasses three design steps. The first step implements an independent fuzzy clustering in the output space to obtain a set of cluster centers. In the second step, unlike other approaches, the above centers are directly involved in the estimation of the membership degrees in the input-output space. In the third step, these membership degrees are used by the particle swarm optimizer in order to obtain optimal values for the centers. To summarize, the novelty of our contribution lies in: (a) the way we handle the information flow from output to input space, and (b) the way we handle the effect of the input space partition upon networks performance. The experiments indicate that the fitness function decreases as the number of hidden node increases. Finally, a comparison between the proposed method and other sophisticated approaches shows its statistically significant superiority.

A mobile agent platform for distributed network and systems management

The mobile agent (MA) technology has been proposed for the management of networks and distributed systems as an answer to the scalability problems of the centralized paradigm. Management tasks may be assigned to an agent, which delegates and executes management logic in a distributed and autonomous fashion. MA-based management has been a subject of intense research in the past few years, reflected on the proliferation of MA platforms (MAPs) expressly oriented to distributed management. However, most of these platforms impose considerable burden on network and system resources and also lack of essential functionality, such as security mechanisms, fault tolerance, strategies for building network-aware MA itineraries and support for user-friendly customization of MA-based management tasks. In this paper, we discuss the design considerations and implementation details of a complete MAP research prototype that sufficiently addresses all the aforementioned issues. Our MAP has been implemented in Java and optimized for network and systems management applications. The paper also presents the evaluation results of our prototype in real and simulated networking environments.

A novel training algorithm for RBF neural network using a hybrid fuzzy clustering approach

This paper introduces a novel clustering-based algorithm to train Gaussian type radial basis function neural networks. In contrast to existing approaches, we develop a specialized learning strategy that combines the merits of fuzzy and crisp clustering. Crisp clustering is a fast process, yet very sensitive to initialization. On the other hand, fuzzy clustering reduces the dependency on initialization; however, it constitutes a slow learning process. The proposed strategy aims to search for a trade-off among these two potentially different effects. The produced clusters possess fuzzy and crisp areas and therefore, the final result is a hybrid partition, where the fuzzy and crisp conditions coexist. The hybrid clusters are directly involved in the estimation process of the neural networks parameters. Specifically, the center elements of the basis functions coincide with cluster centers, while the respective widths are calculated by taking into account the topology of the hybrid clusters. To this end, the networks design becomes a fast and efficient procedure. The proposed method is successfully applied to a number of experimental cases, where the produced networks prove to be highly accurate and compact in size.

A fuzzy vector quantization approach to image compression

The use of fuzzy clustering analysis in the early stages of a vector quantization process is able to make this process less sensitive to initialization. This is justified by the fact that fuzzy clustering provides a framework for the quantitative formulation of the uncertainty typically involved in a training vector space. This paper proposes a fuzzy clustering based vector quantization algorithm, which employs an effective vector assignment strategy for the transition from fuzzy mode, where each training vector is assigned to more than one clusters, to crisp mode, where each training vector is assigned to only one cluster. This transition is controlled by analytical conditions that are obtained by minimizing a modified objective function for the fuzzy c-means algorithm. The application to image compression shows that the proposed approach is able to achieve a very efficient performance, while maintaining the computational capabilities of other methods reported in the literature.

Improved batch fuzzy learning vector quantization for image compression

In this paper, we develop a batch fuzzy learning vector quantization algorithm that attempts to solve certain problems related to the implementation of fuzzy clustering in image compression. The algorithms structure encompasses two basic components. First, a modified objective function of the fuzzy c-means method is reformulated and then is minimized by means of an iterative gradient-descent procedure. Second, the overall training procedure is equipped with a systematic strategy for the transition from fuzzy mode, where each training vector is assigned to more than one codebook vectors, to crisp mode, where each training vector is assigned to only one codebook vector. The algorithm is fast and easy to implement. Finally, the simulation results show that the method is efficient and appears to be insensitive to the selection of the fuzziness parameter.

Cultural applications for mobile devices: Issues and requirements for authoring tools and development platforms

This paper explores requirements that authoring tools and development platforms should satisfy for the development of cultural applications tailored for deployment on Personal Digital Assistants (PDAs) and mobile phones. To effectively determine such requirements the paper reviews the use of mobile technologies in the context of cultural organizations and tourism and examines three â real worldâ case studies that focus on the use of PDAs and mobile phones for providing cultural and tourist information, keeping the visitorsâ interest and attention, as well as promoting various cultural organizations and tourist facilities. This approach allows the extraction of a set of PDA and mobile phone application requirements, the implementation of which is based on the apparatus offered by authoring tools and development platforms. The paper reviews and evaluates the design and development facilities provided by state-of-the-art multimedia application development tools for PDAs and mobile phones: Macromedia Flash Lite, Navipocket, Java 2 Micro Edition and Microsoft .Net platform for the Mobile Web. The paper concludes with a set of recommendations related to the way authoring tools and development platforms should be exploited in order to gratify application and designer needs for developing cultural and tourist applications

A simple algorithm for training fuzzy systems using input-output data

This paper proposes a simple algorithm for training fuzzy systems from numerical data. The main advantage of the method is the lack of complicated iterative mechanisms and therefore, its implementation is carried out easily. The suggested algorithm employs a fuzzy model with simplified rules, assuming a fuzzy partition of the input space into fuzzy subspaces. The output is inferred by expanding the model into fuzzy basis functions (FBFs), where each FBF corresponds to a certain fuzzy subspace. The number of rules and the respective premise parts (fuzzy subspaces) are determined using the nearest neighbor approach. Then, the optimal consequent parameters are obtained by the least-squares method. Finally, simulations show the validity of the method.

Letters: A simple and effective algorithm for implementing particle swarm optimization in RBF network's design using input-output fuzzy clustering

In this paper we investigate the implementation of particle swarm optimization in the design of radial basis function neural networks under the framework of input-output fuzzy clustering. The problem being studied concerns the optimal estimation of the basis function centers, provided that the learning process is guided by the information of the output space. The proposed method encompasses a cost function, which is defined by a reformulated version of the fuzzy c-means applied in the product (i.e. input-output) space. The minimization of this function is accomplished by using the particle swarm optimization, where each particle encodes a set of cluster centers associated to a single fuzzy partition. The algorithm is simple and easy to implement, yet very effective. The performance of the resulting network is tested and verified through a number of experimental cases in terms of a 10-fold cross validation analysis.