Advances in Fuzzy Clustering and its Applications - download pdf or read online

By Jose Valente de Oliveira, Witold Pedrycz

ISBN-10: 0470027606

ISBN-13: 9780470027608

A complete, coherent, and extensive presentation of the state-of-the-art in fuzzy clustering .

Fuzzy clustering is now a mature and colourful quarter of analysis with hugely leading edge complicated purposes. Encapsulating this via featuring a cautious choice of study contributions, this e-book addresses well timed and correct suggestions and strategies, while picking out significant demanding situations and up to date advancements within the quarter. cut up into 5 transparent sections, basics, Visualization, Algorithms and Computational points, Real-Time and Dynamic Clustering, and functions and Case stories, the booklet covers a wealth of novel, unique and completely up to date fabric, and specifically bargains:

  • a specialize in the algorithmic and computational augmentations of fuzzy clustering and its effectiveness in dealing with excessive dimensional difficulties, dispensed challenge fixing and uncertainty administration.
  • presentations of the real and correct levels of cluster layout, together with the function of knowledge granules, fuzzy units within the consciousness of human-centricity side of knowledge research, in addition to procedure modelling
  • demonstrations of the way the implications facilitate additional designated improvement of types, and increase interpretation features
  • a rigorously equipped illustrative sequence of purposes and case reviews during which fuzzy clustering performs a pivotal position

This ebook could be of key curiosity to engineers linked to fuzzy keep watch over, bioinformatics, information mining, snapshot processing, and development acceptance, whereas computing device engineers, scholars and researchers, in so much engineering disciplines, will locate this a useful source and learn device.

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Extra resources for Advances in Fuzzy Clustering and its Applications

Sample text

It is not explicitly associated to a prototype, but directly to the distance between an implicit prototype and the data points: the center of the noise cluster is considered to be at a constant distance, , from all data points. This means that all points have a priori the same ‘probability’ of belonging to the noise cluster. During the optimization process, this ‘probability’ is then adapted as a function of the probability according to which points belong to normal clusters. m c X n n c X X X 2 2 J¼ um d þ  1 À u : ð1:26Þ ik ij ij i¼1 j¼1 k¼1 i¼1 The added term is similar to the terms in the first sum: the distance to the cluster prototype is replaced by  and the membership degree to this cluster is defined as the complement to 1 of the sum of all membership degrees to the standard clusters.

Since all data points have the same fixed amount of membership to share between clusters, the normalization condition implements the known partitioning property of any probabilistic fuzzy clustering algorithm. The parameter m; m > 1, is called the fuzzifier or weighting exponent. 1)). The actual value of m then determines the ‘fuzziness’ of the classification. , they are not constrained in {0, 1} (Dunn, 1974b). For achieving the desired fuzzification of the resulting probabilistic data partition the function gðuij Þ ¼ u2ij has been proposed first (Dunn, 1974b).

Thus, in order to balance the two terms, no matter how large dij2 and how small dkj2 are, uij cannot be 0. Therefore, they proposed replaceing the standard g function with other ones. The conditions g must satisfy are gð0Þ ¼ 0 and gð1Þ ¼ 1, increasing and differentiable. Further, the derivative g0 must be OBJECTIVE FUNCTION VARIANTS 23 increasing and must satisfy g0 ð0Þ 6¼ 0. , gðuÞ ¼ au2 þ ð1 À aÞu. Gaussian functions gðuÞ ¼ ðeau À 1Þ=ðea À 1Þ were also suggested, since the parameter a has a similar effect to the fuzzifier m in the standard fuzzy clustering: the smaller the a, the crisper the partition tends to be (Klawonn and Ho¨ppner, 2003a).

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Advances in Fuzzy Clustering and its Applications by Jose Valente de Oliveira, Witold Pedrycz

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