By Dmitri A. Viattchenin
The current ebook outlines a brand new method of possibilistic clustering during which the sought clustering constitution of the set of gadgets is predicated at once at the formal definition of fuzzy cluster and the possibilistic memberships are decided at once from the values of the pairwise similarity of items. The proposed strategy can be utilized for fixing various type difficulties. the following, a few recommendations that will be helpful 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 lowering analyzed characteristic area dimensionality and a tools for uneven information processing. in addition, a strategy for developing a subset of the main applicable possible choices for a suite of vulnerable fuzzy choice kinfolk, that are outlined on a universe of choices, is defined intimately, and a style for swiftly prototyping the Mamdani’s fuzzy inference structures 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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Additional resources for A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications
2 Basic Methods of Fuzzy Clustering 25 Xˆ n×m1 = [ xˆ it1 ] , i = 1, , n , t1 = 1, , m1 and the data are called sometimes the two-way data . , xn } is the set of objects. So, the two-way data matrix can be represented as follows: Xˆ n×m1 xˆ11 xˆ 2 = 2 xˆ 1 n xˆ12 xˆ1m1 xˆ 22 xˆ 2m1 . 69) Therefore, the two-way data matrix can be represented as Xˆ = ( xˆ 1 , , xˆ m1 ) using n -dimensional column vectors xˆ 1 , t1 = 1, , m1 , composed of the t elements of the t1 -th column of Xˆ .
The recursive process is terminated when the optimum number of fuzzy clusters is equal one, or when the number of objects in a cluster is smaller than some a priori determined constant multiplied by the number of features. The sum of membership values for each object in all fuzzy clusters is equal to one when the HUFC-algorithm is stopped. Fifth, an unsupervised fuzzy graph clustering (UFGC) method has been developed by Devillez, Billaudel, and Villermain Lecolier and the UFGCalgorithm is described in .
The possibilistic approach to clustering was developed by other researchers too. This approach can be considered as an example of an optimization approach in fuzzy clustering because all methods of possibilistic clustering are objective function-based. Similarly to the fuzzy clustering procedures, the possibilistic clustering algorithms can be divided into two types: object type and relational type. Moreover, hybrid clustering techniques have also been proposed which combine the fuzzy and possibilistic approaches.
A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications by Dmitri A. Viattchenin