Outlier detection for high dimensional data
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
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ICDT '99 Proceedings of the 7th International Conference on Database Theory
Optimal Grid-Clustering: Towards Breaking the Curse of Dimensionality in High-Dimensional Clustering
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
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Computational Intelligence and Neuroscience
Kernel fuzzy c-means with automatic variable weighting
Fuzzy Sets and Systems
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High dimensions have a devastating effect on the FCM algorithm and similar algorithms. One effect is that the prototypes run into the centre of gravity of the entire data set. The objective function must have a local minimum in the centre of gravity that causes FCM's behaviour. In this paper, examine this problem. This paper answers the following questions: How many dimensions are necessary to cause an ill behaviour of FCM? How does the number of prototypes influence the behaviour? Why has the objective function a local minimum in the centre of gravity? How must FCM be initialised to avoid the local minima in the centre of gravity? To understand the behaviour of the FCM algorithm and answer the above questions, the authors examine the values of the objective function and develop three test environments that consist of artificially generated data sets to provide a controlled environment. The paper concludes that FCM can only be applied successfully in high dimensions if the prototypes are initialized very close to the cluster centres.