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Effects of Irrelevant Attributes in Fuzzy Clustering

Effects of Irrelevant Attributes in Fuzzy Clustering

引用

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： C. Doring C. Borgelt R. Kruse Department of Knowledge Processing and Language Engineering Otto-von-Guericke University of Magdeburg Magdeburg Germany

In fuzzy clustering soft cluster partitions are formed based on the similarity of data points to the respective cluster prototypes. Similarity is defined in terms of simultaneous closeness regarding all attributes. In some applications the values of many attributes have been measured, but a natural clustering, if it exists, occurs within a (small) subset of attributes. The remaining dimensions can be considered irrelevant. They can obscure an existing grouping and make it harder to discover the cluster structure. In probabilistic fuzzy clustering irrelevant attributes can lead to coincidental cluster centers in the worst case. We study this effect in detail as well as the robustness of different similarity functions and their possible parameterizations against irrelevant input dimensions. Empirical evidence is given for the different properties of the membership functions

关键词： Fuzzy sets Clustering algorithms Partitioning algorithms Iterative algorithms Shape measurement Data engineering Design engineering knowledge engineering Prototypes Robustness

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Fuzzy frequent pattern discovering based on recursive elimination

Fuzzy frequent pattern discovering based on recursive elimin...

引用

International Conference on Machine Learning and Applications (ICMLA)

作者： Xiaomeng Wang C. Borgelt R. Kruse Department of Knowledge Processing and Language Engineering Otto-von-Guericke University of Magdeburg Magdeburg Germany

Real life transaction data often miss some occurrences of items that are actually present. As a consequence some potentially interesting frequent patterns cannot be discovered, since with exact matching the number of supporting transactions may be smaller than the user-specified minimum. In order to allow approximate matching during the mining process, we propose an approach based on transaction editing. Our recursive algorithm relies on a step by step elimination of items from the transaction database together with a recursive processing of transaction subsets. This algorithm works without complicated data structures and allows us to find fuzzy frequent patterns easily.

关键词： Costs Transaction databases Pattern matching Data structures Data engineering knowledge engineering Computer science Delay effects Association rules Fuzzy sets

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Fuzzy Learning Vector Quantization with Size and Shape Parameters

Fuzzy Learning Vector Quantization with Size and Shape Param...

引用

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： C. Borgelt A. Nurnberger R. Kruse Department of Knowledge Processing and Language Engineering Otto-von-Guericke University of Magdeburg Magdeburg Germany

We study an extension of fuzzy learning vector quantization that draws on ideas from the more sophisticated approaches to fuzzy clustering, enabling us to find fuzzy clusters of ellipsoidal shape and differing size 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 document collections, which are, in general, difficult to cluster due to the high number of dimensions and the special distribution characteristics of the data

关键词： Vector quantization Shape Clustering algorithms Fuzzy sets Covariance matrix Partitioning algorithms knowledge engineering Maximum likelihood estimation Web pages

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Fuzzy clustering of quantitative and qualitative data

Fuzzy clustering of quantitative and qualitative data

引用

Conference of the North American Fuzzy Information processing Society - NAFIPS

作者： C. Doring C. Borgelt R. Kruse Department of Knowledge Processing and Language Engineering Otto-von-Guericke University of Magdeburg Magdeburg Germany

In many applications the objects to cluster are described by quantitative as well as qualitative features. A variety of algorithms has been proposed for unsupervised classification if fuzzy partitions and descriptive cluster prototypes are desired. However, most of these methods are designed for data sets with variables measured in the same scale type (only categorical, or only metric). We propose a new fuzzy clustering approach based on a probabilistic distance measure. Thus a major drawback of present methods can be avoided which ties in the vulnerability to favor one type of attributes.

关键词： Clustering algorithms Prototypes Partitioning algorithms Data analysis Data engineering Design engineering knowledge engineering Design methodology Frequency Fuzzy sets

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Adaptable Markov models in industrial planning

Adaptable Markov models in industrial planning

引用

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： J. Gebhardt F. Rugheimer H. Detmer R. Kruse Intelligent Systems Consulting Celle Germany Department of Knowledge Processing and Language Engineering Otto-von-Guericke University of Magdeburg Magdeburg Germany Volkswagen Group Wolfsburg Germany

A significant number of scientific and economic problems is characterised by a large number of interrelated variables. But with larger variable number, the domain under consideration may grow fast, so that analyses and reasoning become increasingly difficult. Graphical models allow to represent the combined distributions compactly and are suitable for dealing with uncertain and incomplete information. We describe their application to a problem of industrial planning. We also demonstrate how the iterative planning process can be supported by allowing the users to adapt the model using revision and updating operators. Moreover we discuss the problem of inconsistent inputs.

关键词： Graphical models Educational institutions Algae Intelligent systems knowledge engineering Process planning Data preprocessing Bayesian methods Markov random fields Probability distribution

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Speeding up fuzzy clustering with neural network techniques

Speeding up fuzzy clustering with neural network techniques

引用

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： C. Borgelt R. Kruse Research Group Neural Networks and Fuzzy Systems Department of Knowledge Processing and Language Engineering School of Computer Science Otto-von-Guericke University of Magdeburg Germany

We explore how techniques that were developed to improve the training process of artificial neural networks can be used to speed up fuzzy clustering. The basic idea of our approach is to regard the difference between two consecutive steps of the alternating optimization scheme of fuzzy clustering as providing a gradient, which may be modified in the same way as the gradient of neural network back-propagation is modified in order to improve training. Our experimental results show that some methods actually lead to a considerable acceleration of the clustering process.

关键词： Fuzzy neural networks Neural networks Artificial neural networks Backpropagation Fuzzy systems knowledge engineering Computer science Electronic mail Acceleration Multilayer perceptrons

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A modification to improve possibilistic fuzzy cluster analysis

A modification to improve possibilistic fuzzy cluster analys...

引用

IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

作者： H. Timm R. Kruse Department of Knowledge Processing and Language Engineering Otto von Guericke University Magdeburg Magdeburg Germany

We explore an approach to possibilistic fuzzy clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical. Our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters, so that they are forced away from each other. We develop this approach for the possibilistic fuzzy c-means algorithm and the Gustafson-Kessel algorithm.

关键词： Clustering algorithms Prototypes knowledge engineering Fuzzy sets Humans Zinc Euclidean distance Covariance matrix

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An extension of partially supervised fuzzy cluster analysis

An extension of partially supervised fuzzy cluster analysis

引用

Conference of the North American Fuzzy Information processing Society - NAFIPS

作者： H. Timm F. Klawonn R. Kruse Department of Knowledge Processing and Language Engineering Otto-von-Guericke University of Magdeburg Germany Department of Computer Science University of Applied Sciences Braunschweig Wolfenbuttel Germany

We propose an approach to handling class information in fuzzy cluster analysis, where a class can consist of several clusters. The approach is based on a penalty term for clusters comprising several clusters.

关键词： Prototypes Information analysis Clustering algorithms Fuzzy sets Zinc Computer science Equations Shape

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An empirical investigation of the k2 metric 6

引用

6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2001

作者： Borgelt, Christian Kruse, Rudolf Department of Knowledge Processing and Language Engineering Otto-von-Guericke-University of Magdeburg Universitatsplatz 2 MagdeburgD-39106 Germany

ISBN: (纸本)9783540424642

The K2 metric is a well-known evaluation measure (or scoring function) for learning Bayesian networks from data [7]. It is derived by assuming uniform prior distributions on the values of an attribute for each possible instantiation of its parent attributes. This assumption introduces a tendency to select simpler network structures. In this paper we modify the K2 metric in three different ways, introducing a parameter by which the strength of this tendency can be controlled. Our experiments with the ALARM network [2] and the BOBLO network [17] suggest that—somewhat contrary to our expectations—a slightly stronger tendency towards simpler structures may lead to even better results. © Springer-Verlag Berlin Heidelberg 2001.

关键词： Bayesian networks

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Fuzzy cluster analysis of classified data

Fuzzy cluster analysis of classified data

引用

Conference of the North American Fuzzy Information processing Society - NAFIPS

作者： H. Timm Department of Knowledge Processing and Language Engineering Otto von Guericke University Magdeburg Magdeburg Germany

Fuzzy cluster analysis is a method for unsupervised clustering. However sometimes class information is available for the given dataset, i.e., only the number of clusters per class is unknown. In this paper it is discussed how class information can be exploited. Some common approaches are reviewed and a new approach is suggested, which integrates class information into fuzzy cluster analysis.

关键词： Data analysis Prototypes Information analysis knowledge engineering Humans Clustering algorithms

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