Download A Heuristic Approach to Possibilistic Clustering: Algorithms by Dmitri A. Viattchenin PDF

By Dmitri A. Viattchenin

The current ebook outlines a brand new method of possibilistic clustering within which the sought clustering constitution of the set of gadgets is predicated without delay at the formal definition of fuzzy cluster and the possibilistic memberships are decided at once from the values of the pairwise similarity of gadgets. The proposed technique can be utilized for fixing diversified category difficulties. the following, a few suggestions that would be worthy at this function are defined, together with a strategy for developing a suite of categorized gadgets for a semi-supervised clustering set of rules, a strategy for lowering analyzed characteristic house dimensionality and a equipment for uneven info processing. additionally, a method for developing a subset of the main applicable possible choices for a suite of susceptible fuzzy choice kinfolk, that are outlined on a universe of possible choices, is defined intimately, and a mode for speedily prototyping the Mamdani’s fuzzy inference platforms is brought. This ebook addresses engineers, scientists, professors, scholars and post-graduate scholars, who're drawn 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

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So, the set of (φ ,ϕ ) -cores X (φϕ ) , l = 1, , c and a residual data set X R l containing all remaining elements of the data set X can be obtained. 101) represents the significant structure, and the second part corresponds to the insignificant structure of the data set X . 36 1 Introduction Thus, the cores of the fuzzy clusters controlled independently by the thresholds ϕ and φ generate a hierarchical structure of analytical representations of (φ ,ϕ ) cores. The notion of the core structure of the fuzzy cluster seems as an effective tool for transparent interpretation of fuzzy clustering results.

Some other validity measures for the FNM-algorithm were proposed by Libert and Roubens [72] and [73]. 91) is appropriate for the ARCA-algorithm, because the ARCA-algorithm, though being a relational clustering algorithm, generates prototypes. In general, the problem of cluster validity of the relational data is considered in detail by Sledge, Havens, Bezdek and Keller [103]. The basic idea of unsupervised fuzzy clustering is to define an upper bound for the number of clusters c max and carry out the clustering for each number of fuzzy clusters c ∈{2,, cmax } .

72) l =1 i =1 where u li , l = 1,  , c , i = 1,  , n is the membership degree, xi , i ∈ {1,  , n} is the data point, Τ = {τ 1 ,  , τ c } is the set fuzzy clusters prototypes, γ > 1 is the weighting exponent, and d 2 ( xi ,τ l ) is the squared Euclidean distance between xi and τ l : 2 d 2 ( xi , τ l ) = xi − τ l . 72). 72) is the most popular form of the objective function in case of fuzzy clustering. Special forms of objective functions depend on the choice of a suitable distance measure. For example, the so-called alternative fuzzy c -means was proposed by Wu and Yang [156].

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