A Heuristic Approach to Possibilistic Clustering: Algorithms - download pdf or read online

By Dmitri A. Viattchenin

ISBN-10: 3642355358

ISBN-13: 9783642355356

ISBN-10: 3642355366

ISBN-13: 9783642355363

The current booklet outlines a brand new method of possibilistic clustering within which the sought clustering constitution of the set of items relies without delay at the formal definition of fuzzy cluster and the possibilistic memberships are decided without delay from the values of the pairwise similarity of gadgets. The proposed method can be utilized for fixing diversified category difficulties. the following, a few recommendations that would be valuable at this function are defined, together with a technique for developing a suite of categorised gadgets for a semi-supervised clustering set of rules, a strategy for decreasing analyzed characteristic area dimensionality and a equipment for uneven information processing. in addition, a strategy for developing a subset of the main acceptable choices for a collection of vulnerable fuzzy choice kin, that are outlined on a universe of choices, is defined intimately, and a style for swiftly prototyping the Mamdani’s fuzzy inference platforms is brought. This ebook addresses engineers, scientists, professors, scholars and post-graduate scholars, who're attracted to and paintings with fuzzy clustering and its applications

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Extra resources for A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

Example text

88) and d ( xi , x j ) is the dissimilarity relation between the pair of objects xi and x j , and d ( x j , τ ) is the relation between the prototype τ , l ∈ {1,  , c} and the l l object x j , j ∈ {1,  , n} . For all fuzzy clustering approaches described above the number of clusters has to be specified in advance. However, the most important problem of fuzzy clustering is neither the choice of the numerical procedure nor the distance to use but concerns the number c of fuzzy clusters to look for.

The generated partition is optimal in the sense that the clustering procedure detects all of the existing unimodal fuzzy sets and realizes the maximum separation among them. The order of the objects according to their membership degrees as well as the order according to a distance are used in the algorithm. The algorithm is a systematic procedure which always terminates. , x n } . The method is based on the concept of a stable set internally maximum. The cluster is the stable set internally maximum when a representativeness constraint and a separability constraint are satisfied.

94) should be maximized too. When the initial data are relational, the direct indices are not applicable to the problem of cluster validity. 90) can be used for validation in these cases. On the other hand, the indirect indices can be modified for the relational clustering algorithms in each concrete case. 89) was modified by Roubens [95] as follows: m c n  c   u li2  − n . 95) should be maximized. Some other validity measures for the FNM-algorithm were proposed by Libert and Roubens [72] and [73].

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A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications by Dmitri A. Viattchenin

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