Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization |
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Authors: | Roelof K Brouwer Albert Groenwold |
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Affiliation: | (1) Department of Mechanical and Mechatronics Engineering, University of Stellenbosch, Private Bag X1, Matieland, 7602, Stellenbosch, South Africa;(2) Department of Computing Science, Thompson Rivers University, 900 McGill Road, Kamloops, BC, V2C 5N3, Canada |
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Abstract: | The first stage of knowledge acquisition and reduction of complexity concerning a group of entities is to partition or divide
the entities into groups or clusters based on their attributes or characteristics. Clustering algorithms normally require
both a method of measuring proximity between patterns and prototypes and a method for aggregating patterns. However sometimes
feature vectors or patterns may not be available for objects and only the proximities between the objects are known. Even
if feature vectors are available some of the features may not be numeric and it may not be possible to find a satisfactory
method of aggregating patterns for the purpose of determining prototypes. Clustering of objects however can be performed on
the basis of data describing the objects in terms of feature vectors or on the basis of relational data. The relational data
is in terms of proximities between objects. Clustering of objects on the basis of relational data rather than individual object
data is called relational clustering. The premise of this paper is that the proximities between the membership vectors, which
are obtained as the objective of clustering, should be proportional to the proximities between the objects. The values of
the components of the membership vector corresponding to an object are the membership degrees of the object in the various
clusters. The membership vector is just a type of feature vector. Based on this premise, this paper describes another fuzzy
relational clustering method for finding a fuzzy membership matrix. The method involves solving a rather challenging optimization
problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle
swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort,
a Bayesian stopping criterion is used in combination with a multi-start strategy for the PSO. Other relational clustering
methods generally find local optimum of their objective function. |
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Keywords: | Fuzzy relational clustering Fuzzy clustering Optimization Particle swarm algorithm Membership matrix |
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