A new unsupervised approach for fuzzy clustering

In this paper, a new level-based (hierarchical) approach to the fuzzy clustering problem for spatial data is proposed. In this approach each point of the initial set is handled as a fuzzy point of the multidimensional space. Fuzzy point conical form, fuzzy α-neighbor points, fuzzy α-joint points are defined and their properties are explored. It is known that in classical fuzzy clustering the matter of fuzziness is usually a possibility of membership of each element into different classes with different positive degrees from [0,1]. In this study, the fuzziness of clustering is evaluated as how much in detail the properties of classified elements are investigated. In this extent, a new Fuzzy Joint Points (FJP) method which is robust through noises is proposed. Algorithm of FJP method is developed and some properties of the algorithm are explored. Also sufficient condition to recognize a hidden optimal structure of clusters is proven. The main advantage of the FJP algorithm is that it combines determination of initial clusters, cluster validity and direct clustering, which are the fundamental stages of a clustering process. It is possible to handle the fuzzy properties with various level-degrees of details and to recognize individual outlier elements as independent classes by the FJP method. This method could be important in biological, medical, geographical information, mapping, etc. problems.