Fuzzy clustering of probability density functions

ABSTRACT

Basing on L¹-distance and representing element of cluster, the article proposes new three algorithms in Fuzzy Clustering of probability density Functions (FCF). They are hierarchical approach, non-hierarchical approach and the algorithm to determine the optimal number of clusters and the initial partition matrix to improve the qualities of established clusters in non-hierarchical approach. With proposed algorithms, FCF has more advantageous than Non-fuzzy Clustering of probability density Functions. These algorithms are applied for recognizing images from Texture and Corel database and practical problem about studying and training marks of students at an university. Many Matlab programs are established for computation in proposed algorithms. These programs are not only used to compute effectively the numerical examples of this article but also to be applied for many different realistic problems.

KEYWORDS:

• Fuzzy
• clustering
• density function
• distance
• hierarchical approach

MATHEMATICS SUBJECT CLASSIFICATION::

• 62H30
• 68T10

Acknowledgements

The authors wish to thank two anonymous referees for some very pertinent remarks that have led to several improvements on the content and on the presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.