The Experts below are selected from a list of 39813 Experts worldwide ranked by ideXlab platform
Rudolf Kruse - One of the best experts on this subject based on the ideXlab platform.
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SMPS - Agglomerative Fuzzy Clustering
Advances in Intelligent Systems and Computing, 2016Co-Authors: Christian Borgelt, Rudolf KruseAbstract:The term Fuzzy Clustering usually refers to prototype-based methods that optimize an objective function in order to find a (Fuzzy) partition of a given data set and are inspired by the classical c-means Clustering algorithm. Possible transfers of other classical approaches, particularly hierarchical agglomerative Clustering, received much less attention as starting points for developing Fuzzy Clustering methods. In this chapter we strive to improve this situation by presenting a (hierarchical) agglomerative Fuzzy Clustering algorithm. We report experimental results on two well-known data sets on which we compare our method to classical hierarchical agglomerative Clustering.
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Fuzzy Clustering
Fuzzy Sets and Systems, 2015Co-Authors: Frank Klawonn, Rudolf Kruse, Roland WinklerAbstract:The initial idea of extending the classical k-means Clustering technique to an algorithm that uses membership degrees instead of crisp assignments of data objects to clusters led to the invention of a large variety of new Fuzzy Clustering algorithms. However, most of these algorithms are concerned with cluster shapes or outliers and could have been defined without any problems in the context of crisp assignments of data objects to clusters. In this paper, we demonstrate that the use of membership degrees for these algorithms - although it is not necessary from the theoretical point of view - is essential for these algorithms to function in practice. With crisp assignments of data objects to clusters these algorithms would get stuck most of the time in a local minimum of their underlying objective function, leading to undesired Clustering results. In other contributions it was shown that the use of membership degrees can avoid this problem of local minima but it also introduces new problems, especially for clusters with varying density and for high-dimensional data, at least if Fuzzy Clustering is carried out with the simple standard fuzzifier.
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Handling noise and outliers in Fuzzy Clustering
2015Co-Authors: Christian Borgelt, Christian Braune, Marie-jeanne Lesot, Rudolf KruseAbstract:Since it is an unsupervised data analysis approach, Clustering relies solely on the location of the data points in the data space or, alternatively, on their relative distances or similarities. As a consequence, Clustering can suffer from the presence of noisy data points and outliers, which can obscure the structure of the clusters in the data and thus may drive Clustering algorithms to yield suboptimal or even misleading results. Fuzzy Clustering is no exception in this respect, although it features an aspect of robustness, due to which outliers and generally data points that are atypical for the clusters in the data have a lesser influence on the cluster parameters. Starting from this aspect, we provide in this paper an overview of different approaches with which Fuzzy Clustering can be made less sensitive to noise and outliers and categorize them according to the component of standard Fuzzy Clustering they modify.
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Data analysis with Fuzzy Clustering methods
Computational Statistics & Data Analysis, 2006Co-Authors: Christian Döring, Marie-jeanne Lesot, Rudolf KruseAbstract:An encompassing, self-contained introduction to the foundations of the broad field of Fuzzy Clustering is presented. The Fuzzy cluster partitions are introduced with special emphasis on the interpretation of the two most encountered types of gradual cluster assignments: the Fuzzy and the possibilistic membership degrees. A systematic overview of present Fuzzy Clustering methods is provided, highlighting the underlying ideas of the different approaches. The class of objective function-based methods, the family of alternating cluster estimation algorithms, and the Fuzzy maximum likelihood estimation scheme are discussed. The latter is a Fuzzy relative of the well-known expectation maximization algorithm and it is compared to its counterpart in statistical Clustering. Related issues are considered, concluding with references to selected developments in the area.
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Automatic generation of Fuzzy controllers by Fuzzy Clustering
1995 IEEE International Conference on Systems Man and Cybernetics. Intelligent Systems for the 21st Century, 1Co-Authors: Frank Klawonn, Rudolf KruseAbstract:This paper describes techniques for deriving Fuzzy if-then rules based on special modified Fuzzy Clustering algorithms. The basic idea is that each Fuzzy cluster induces a rule. The Fuzzy sets appearing in a rule associated with a Fuzzy cluster are obtained by projecting the cluster to the one-dimensional coordinate spaces. In order to allow clusters of varying shape and size the authors derive special Fuzzy Clustering algorithms which are searching for clusters in the form of axes-parallel hyper-ellipsoids.
Christian Borgelt - One of the best experts on this subject based on the ideXlab platform.
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SMPS - Agglomerative Fuzzy Clustering
Advances in Intelligent Systems and Computing, 2016Co-Authors: Christian Borgelt, Rudolf KruseAbstract:The term Fuzzy Clustering usually refers to prototype-based methods that optimize an objective function in order to find a (Fuzzy) partition of a given data set and are inspired by the classical c-means Clustering algorithm. Possible transfers of other classical approaches, particularly hierarchical agglomerative Clustering, received much less attention as starting points for developing Fuzzy Clustering methods. In this chapter we strive to improve this situation by presenting a (hierarchical) agglomerative Fuzzy Clustering algorithm. We report experimental results on two well-known data sets on which we compare our method to classical hierarchical agglomerative Clustering.
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Handling noise and outliers in Fuzzy Clustering
2015Co-Authors: Christian Borgelt, Christian Braune, Marie-jeanne Lesot, Rudolf KruseAbstract:Since it is an unsupervised data analysis approach, Clustering relies solely on the location of the data points in the data space or, alternatively, on their relative distances or similarities. As a consequence, Clustering can suffer from the presence of noisy data points and outliers, which can obscure the structure of the clusters in the data and thus may drive Clustering algorithms to yield suboptimal or even misleading results. Fuzzy Clustering is no exception in this respect, although it features an aspect of robustness, due to which outliers and generally data points that are atypical for the clusters in the data have a lesser influence on the cluster parameters. Starting from this aspect, we provide in this paper an overview of different approaches with which Fuzzy Clustering can be made less sensitive to noise and outliers and categorize them according to the component of standard Fuzzy Clustering they modify.
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Accelerating Fuzzy Clustering
Information Sciences, 2009Co-Authors: Christian BorgeltAbstract:This paper extends earlier work [C. Borgelt, R. Kruse, Speeding up Fuzzy Clustering with neural network techniques, in: Proceedings of the 12th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE'03, St. Louis, MO, USA), IEEE Press, Piscataway, NJ, USA, 2003] on an approach to accelerate Fuzzy Clustering by transferring methods that were originally developed to speed up the training process of (artificial) neural networks. The core idea is to consider the difference between two consecutive steps of the alternating optimization scheme of Fuzzy Clustering as providing a gradient. This ''gradient'' may then be modified in the same way as a gradient is modified in error backpropagation in order to enhance the training. Even though these modifications are, in principle, directly applicable, carefully checking and bounding the update steps can improve the performance and can make the procedure more robust. In addition, this paper provides a new and much more detailed experimental evaluation that is based on Fuzzy cluster comparison measures [C. Borgelt, Resampling for Fuzzy Clustering, Int. J. Uncertainty, Fuzziness Knowledge-based Syst. 15 (5) (2007), 595-614], which can be used nicely to study the convergence speed.
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Fast Fuzzy Clustering of Web Page Collections
2004Co-Authors: Christian Borgelt, Andreas NürnbergerAbstract:We study an extension of learning vector quantization that draws on ideas from Fuzzy Clustering, enabling us to find Fuzzy clusters of ellipsoidal shape with a competitive learning scheme. This approach may be seen as a kind of online Fuzzy Clustering, which can have advantages w.r.t. the execution time of the Clustering algorithm. We demonstrate the usefulness of our approach by applying it to web page collections, which are, in general, difficult to cluster due to the high number of dimensions and the special distribution characteristics of the data.
Le Hoang Son - One of the best experts on this subject based on the ideXlab platform.
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Picture Fuzzy Clustering for complex data
Engineering Applications of Artificial Intelligence, 2016Co-Authors: Pham Huy Thong, Le Hoang SonAbstract:Abstract Fuzzy Clustering is a useful segmentation tool which has been widely used in many applications in real life problems such as in pattern recognition, recommender systems, forecasting, etc. Fuzzy Clustering algorithm on picture Fuzzy set (FC-PFS) is an advanced Fuzzy Clustering algorithm constructed on the basis of picture Fuzzy set with the appearance of three membership degrees namely the positive, the neutral and the refusal degrees combined within an entropy component in the objective function to handle the problem of incomplete modeling in Fuzzy Clustering. A disadvantage of FC-PFS is its capability to handle complex data which include mix data type (categorical and numerical data) and distinct structured data. In this paper, we propose a novel picture Fuzzy Clustering algorithm for complex data called PFCA-CD that deals with both mix data type and distinct data structures. The idea of this method is the modification of FC-PFS, using a new measurement for categorical attributes, multiple centers of one cluster and an evolutionary strategy – particle swarm optimization. Experiments indicate that the proposed algorithm results in better Clustering quality than others through Clustering validity indices.
Le Hoang Son - One of the best experts on this subject based on the ideXlab platform.
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dpfcm a novel distributed picture Fuzzy Clustering method on picture Fuzzy sets
Expert Systems With Applications, 2015Co-Authors: Le Hoang SonAbstract:Abstract Fuzzy Clustering is considered as an important tool in pattern recognition and knowledge discovery from a database; thus has been being applied broadly to various practical problems. Recent advances in data organization and processing such as the cloud computing technology which are suitable for the management, privacy and storing big datasets have made a significant breakthrough to information sciences and to the enhancement of the efficiency of Fuzzy Clustering. Distributed Fuzzy Clustering is an efficient mining technique that adapts the traditional Fuzzy Clustering with a new storage behavior where parts of the dataset are stored in different sites instead of the centralized main site. Some distributed Fuzzy Clustering algorithms were presented including the most effective one – the CDFCM of Zhou et al. (2013). Based upon the observation that the communication cost and the quality of results in CDFCM could be ameliorated through the integration of a distributed picture Fuzzy Clustering with the facilitator model, in this paper we will present a novel distributed picture Fuzzy Clustering method on picture Fuzzy sets so-called DPFCM. Experimental results on various datasets show that the Clustering quality of DPFCM is better than those of CDFCM and relevant algorithms.
W. Shitong - One of the best experts on this subject based on the ideXlab platform.
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robust Fuzzy Clustering based image segmentation
Applied Soft Computing, 2009Co-Authors: Zhang Yang, Fu-lai Chung, W. ShitongAbstract:The Fuzzy Clustering algorithm Fuzzy c-means (FCM) is often used for image segmentation. When noisy image segmentation is required, FCM should be modified such that it can be less sensitive to noise in an image. In this correspondence, a robust Fuzzy Clustering-based segmentation method for noisy images is developed. The contribution of the study here is twofold: (1) we derive a robust modified FCM in the sense of a novel objective function. The proposed modified FCM here is proved to be equivalent to the modified FCM given by Hoppner and Klawonn [F. Hoppner, F. Klawonn, Improved Fuzzy partitions for Fuzzy regression models, Int. J. Approx. Reason. 32 (2) (2003) 85-102]. (2) We explore the very applicability of the proposed modified FCM for noisy image segmentation. Our experimental results indicate that the proposed modified FCM here is very suitable for noisy image segmentation.
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Note on the relationship between probabilistic and Fuzzy Clustering
Soft Computing - A Fusion of Foundations Methodologies and Applications, 2004Co-Authors: W. Shitong, Korris Fu-lai Chung, S. Hongbin, Z. RuiqiangAbstract:In this short communication, based on Renyi entropy measure, a new Renyi information based Clustering algorithm A is presented. Algorithm A and the well-known Fuzzy Clustering algorithm FCM have the same Clustering track. This fact builds the very bridge between probabilistic Clustering and Fuzzy Clustering, and fruitful research results on Renyi entropy measure may help us to further understand the essence of Fuzzy Clustering.
