A probabilistic clustering method for data elements with normal distributed attributes

ABSTRACT

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.

KEYWORDS:

• Black hole algorithm
• Imperialist competitive algorithm
• Membership probability
• Normal probability distribution
• Probabilistic clustering

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-XX
• 62HXX
• 62H30
• 90-XX
• 90CXX
• 90C59