# Research on Improved Weighted Fuzzy Clustering Algorithm Based on Rough Set

22 Jan 2009-Vol. 2, pp 98-102

TL;DR: The rough set is brought into fuzzy cluster by using the methods of attributes contracted in the rough set theory to improve the FCM algorithm; the improved algorithm had been proved a high precise ratio.

Abstract: Clustering is used to find out the objects that resemble each other and compose different groups, cluster analysis is an important job in data mining. Thisarticle brings the rough set into fuzzy cluster, by using the methods of attributes contracted in the rough set theory to improve the FCM algorithm; the improvedalgorithm had been proved a high precise ratio.

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Anna University

^{1}TL;DR: A Novel Weighted Fuzzy C-Means clustering method based on Immune Genetic Algorithm (IGA-NWFCM) is proposed and hence it improves the performance of the existing techniques to solve the high dimensional multi-class problems.

39 citations

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TL;DR: In this article, an interval number is introduced for attribute weighting in the weighted fuzzy c-means (WFCM) clustering, and it is illustrated that interval weighting can obtain appropriate weights more easily from the viewpoint of geometric probability.

Abstract: The fuzzy c-means (FCM) algorithm is a widely applied clustering technique, but the implicit assumption that each attribute of the object data has equal importance affects the clustering performance. At present, attribute weighted fuzzy clustering has became a very active area of research, and numerous approaches that develop numerical weights have been combined into fuzzy clustering. In this paper, interval number is introduced for attribute weighting in the weighted fuzzy c-means (WFCM) clustering, and it is illustrated that interval weighting can obtain appropriate weights more easily from the viewpoint of geometric probability. Moreover, a genetic heuristic strategy for attribute weight searching is proposed to guide the alternating optimization (AO) of WFCM, and improved attribute weights in interval-constrained ranges and reasonable data partition can be obtained simultaneously. The experimental results demonstrate that the proposed algorithm is superior in clustering performance. It reveals that the interval weighted clustering can act as an optimization operator on the basis of the traditional numerical weighted clustering, and the effects of interval weight perturbation on clustering performance can be decreased.

33 citations

01 Jan 2015

TL;DR: The FCM algorithm is implemented and successfully integrate it in WEKA to expand the system functions of the open-source platform, so that users can directly call theFCM algorithm to do fuzzy clustering analysis.

Abstract: Internet has become a vital part of any organization. Sensitive and confidential information is being sent over the network. But with the growth of internet, intrusion and attacks have also increased. Thus, there arises a need of robust and powerful intrusion detection systems which can detect the attacks. Recently, many novel methods are experimented to build strong IDSs. The aim of this paper is to present a methodology that can recognise and detect attacks efficiently. In this paper, we implement the FCM algorithm and successfully integrate it in WEKA to expand the system functions of the open-source platform, so that users can directly call the FCM algorithm to do fuzzy clustering analysis. Besides, considering the shortcoming of the classical FCM algorithm in selecting the initial cluster centers, we represent an improved FCM algorithm which adopts a new strategy to optimize the selection of original cluster centers. A novel classification via dynamic fuzzy c means clustering algorithm has been proposed to build an efficient anomaly based network intrusion detection model. A subset of KDDCup 1999 intrusion detection benchmark dataset has been used for the experiment. The proposed novel concept will be efficient in terms of detection accuracy, low false positive rate in comparison to the other existing methods.

### Cites methods from "Research on Improved Weighted Fuzzy..."

...Li Jian-guo, et al [9] proposed an improved weighted fuzzy clustering algorithm based on rough set by using the methods of attributes contracted in the rough set theory to improve the FCM algorithm....

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##### References

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01 Oct 1987TL;DR: In this paper, a counterexample to the original incorrect convergence theorem for the fuzzy c-means (FCM) clustering algorithms is provided, which establishes the existence of saddle points of the FCM objective function at locations other than the geometric centroid of fuzzy partition space.

Abstract: A counterexample to the original incorrect convergence theorem for the fuzzy c-means (FCM) clustering algorithms (see J.C. Bezdak, IEEE Trans. Pattern Anal. and Math. Intell., vol.PAMI-2, no.1, pp.1-8, 1980) is provided. This counterexample establishes the existence of saddle points of the FCM objective function at locations other than the geometric centroid of fuzzy c-partition space. Counterexamples previously discussed by W.T. Tucker (1987) are summarized. The correct theorem is stated without proof: every FCM iterate sequence converges, at least along a subsequence, to either a local minimum or saddle point of the FCM objective function. Although Tucker's counterexamples and the corrected theory appear elsewhere, they are restated as a caution not to further propagate the original incorrect convergence statement.

476 citations

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TL;DR: It is shown that fixed points of the algorithm are stationary points of The fuzzy c-means/ISODATA algorithm, and vice versa, and with respect to minimizing the fuzzy objective functional, the algorithm based on the empirical distribution is asymptotically at least as good as the algorithmbased on the true distribution.

Abstract: The fuzzy c-means/ISODATA algorithm is usually described in terms of clustering a finite data set. An equivalent point of view is that the algorithm clusters the support points of a finite-support probability distribution. Motivated by recent work on the hard version of the algorithm, this paper extends the definition to arbitrary distributions and considers asymptotic properties. It is shown that fixed points of the algorithm are stationary points of the fuzzy objective functional, and vice versa. When the algorithm is iteratively applied to an initial prototype set, the sequence of prototype sets produced approaches the set of fixed points. If an unknown distribution is approximated by the empirical distribution of stationary, ergodic observations, then as the number of observations grows large, fixed points of the algorithm based on the empirical distribution approach fixed points of the algorithm based on the true distribution. Furthermore, with respect to minimizing the fuzzy objective functional, the algorithm based on the empirical distribution is asymptotically at least as good as the algorithm based on the true distribution.

65 citations

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TL;DR: This paper provides a theoretical framework in which currently used geometrical fuzzy clustering algorithms become special cases and a family of functions called feasible are defined which can be used to construct such algorithms and convergence results are obtained.

63 citations

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TL;DR: The notions of reduced objective function and improving and feasible directions are used and the properties of the underlying optimization problem are explored to explore the conjecture that two sets of conditions are necessary and sufficient for a local minimum point.

Abstract: The convergence of the fuzzy ISODATA clustering algorithm was proved by Bezdek [3]. Two sets of conditions were derived and it was conjectured that they are necessary and sufficient for a local minimum point. In this paper, we address this conjecture and explore the properties of the underlying optimization problem. The notions of reduced objective function and improving and feasible directions are used to examine this conjecture. Finally, based on the derived properties of the problem, a new stopping criterion for the fuzzy ISODATA algorithm is proposed.

50 citations

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TL;DR: This paper presents convergence properties of the generalized FCM clustering algorithms, which are global convergence, local convergence, and its rate of convergence.

Abstract: Fuzzy c-means (FCM) clustering algorithms have been widely used to solve clustering problems. Yang and Yu [1] extended these to optimization procedures with respect to any probability distribution. They showed that the optimal cluster centers are the fixed points of these generalized FCM clustering algorithms. The convergence properties of algorithms are the important theoretical issue. In this paper, we present convergence properties of the generalized FCM clustering algorithms. These are global convergence, local convergence, and its rate of convergence.

26 citations