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Wai-Ho Au and Keith C. C. Chan.
Mining Fuzzy Association Rules in a Bank-Account Database.
TFS,
11(2):238--248,
2003.
Keywords:
Association Rules.
| Abstract: |
This paper describes how we applied a fuzzy technique to a data-mining task involving a large database that was provided by an international bank with offices in Hong Kong. [...] To help the bank achieve its goal, we developed a fuzzy technique, called Fuzzy Association Rule Mining II (FARM II), which can mine fuzzy association rules. FARM II is able to handle both relational and transactional data. It can also handle fuzzy data. The former type of data allows FARM II to discover multidimensional association rules, whereas the latter allows some of the patterns to be more easily revealed and expressed. To effectively uncover the hidden associations in the bank-account database, FARM II performs several steps. First, it combines the relational and transactional data together by performing data transformations. Second, it identifies fuzzy attributes and performs fuzzification so that linguistic terms can be used to represent the uncovered patterns. Third, it makes use of an efficient rule-search process that is guided by an objective interestingness measure. This measure is defined in terms of fuzzy confidence and support measure, which reflect the differences in the actual and the expected degrees to which a customer is characterized by different linguistic terms. [...] |
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Yonatan Aumann and Lindell Yehuda.
A Statistical Theory for Quantitative Association Rules.
JIIS,
20(3):255-283,
2003.
Keywords:
Association Rules.
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Steven Eschrich,
Jingwei Ke,
Lawrence O. Hall,
and Dmitry B. Goldgof.
Fast Accurate Fuzzy Clustering Through Data Reduction.
TFS,
11(2):262--270,
2003.
Keywords:
Clustering,
Fuzzy Clustering,
Fuzzy c-Means,
Image Data,
Speed-up Issues.
| Abstract: |
Clustering is a useful approach in image segmentation, data mining, and other pattern recognition problems for which unlabeled data exist. Fuzzy clustering using fuzzy c-means or variants of it can provide a data prartition that is both better and more meaningful than hard clustering approaches. The clustering process can be quite slow when there are many objects or patterns to be clustered. This paper discusses an algorithm brFCM, which is able to reduce the number of distinct pattern which must be clustered without adversely affecting partition quality. The reduction is done by aggreating similar examples and then using a weighted exemplar in the clustering process. The reduction in the amount of clustering data allows a partition of the data to be produced faster. The alorithm is applied to the problem of segmenting 32 magnetic resonance images into different tissue types and the problem of segmenting 172 infrared images into trees, grass and target. Average speed-ups of as much as 59-290 times a traditional implementation of fuzzy c-means were obtained by using brFCM, while producing partitions that are equivalent to those produced by fuzzy c-means. |
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Frank Höppner and Frank Klawonn.
A Contribution to Convergence Theory of Fuzzy c-Means and Derivatives.
TFS,
11(5):682--694,
2003.
Keywords:
Clustering,
Fuzzy Clustering,
Fuzzy c-Means.
| Abstract: |
In this paper we revisit the convergence and optimization properties of fuzzy clustering algorithms in general and the fuzzy c-means (FCM) algorithm in particular. Our investigation includes probabilistic and (a slightly modified implementation of) possibilistic memberships, which will be discussed under a unified view. We give a convergence proof for the axis-parallel variant of the algorithm by Gustafson and Kessel, that can be generalized to other algorithms more easily than in the usual approach. Using reformulated fuzzy clustering algorithms we apply Banach's classical contraction principle and establish a relationship between saddle points and attractive fixed points. For the special case of FCM we derive a sufficient condition for fixed points to be attractive, allowing identification of them as (local) minima of the objective function (excluding the possibility of a saddle point). |
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Frank Höppner and Frank Klawonn.
Improved Fuzzy Partitions for Fuzzy Regression Models.
IJAR,
32:85--102,
2003.
[ PDF
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Keywords:
Clustering,
Fuzzy Clustering,
Fuzzy c-Means,
Fuzzy Models,
Sequential/Temporal Data,
Regression.
| Abstract: |
Fuzzy clustering algorithms like the popular fuzzy c-means algorithm (FCM) are frequently used to automatically divide up the data space into fuzzy granules. When the fuzzy clusters are used to derive membership functions for a fuzzy rule-based system, then the corresponding fuzzy sets should fulfill some requirements like boundedness of support or unimodality. Problems may also arise in the case, when the fuzzy partition induced by the clusters is intended as a basis for local function approximation. In this case, a local model (function) is assigned to each cluster. Taking the fuzziness of the partition into account, continuous transitions between the single local models can be obtained easily. However, unless the overlapping of the clusters is very small, the local models tend to mix and no local model is actually valid. \newline By rewarding crisp membership degrees, we modify the objective function used in fuzzy clustering and obtain different membership functions that better suit these purposes. We show that the modification can be interpreted as standard FCM using distances to the Voronoi cell of the cluster rather than using distances to the cluster prototypes. In consequence, the resulting partitions of the modified algorithm are much closer to those of the crisp original methods. The membership functions can be generalized to a fuzzified minimum function. We give some bounds on the approximation quality of this fuzzification. \newline We apply this modified fuzzy clustering approach to building fuzzy models of the Takagi-Sugeno (TS) type automatically from data. |
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S. Miyamoto.
Information clustering based on fuzzy multisets.
Information Processing and Management,
39(2):195--213,
2003.
Keywords:
Clustering.
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S. Miyamoto,
D. Suizu,
and O. Takata.
Methods of Fuzzy c-Means and Possibilistic Clustering using a Quadratic Term.
Scientiae Mathematicae Japonicae,
9:17--33,
2003.
Keywords:
Clustering,
Fuzzy Clustering,
Fuzzy c-Means.
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