Pattern Recognition in Numerical Data Sets and Color Images through the Typicality Based on the GKPFCM Clustering Algorithm

We take the concept of typicality from the field of cognitive psychology, and we apply the meaning to the interpretation of numerical data sets and color images through fuzzy clustering algorithms, particularly the GKPFCM, looking to get better information from the processed data. The Gustafson Kessel Possibilistic Fuzzy c-means (GKPFCM) is a hybrid algorithm that is based on a relative typicality (membership degree, Fuzzy c-means) and an absolute typicality (typicality value, Possibilistic c-means). Thus, using both typicalities makes it possible to learn and analyze data as well as to relate the results with the theory of prototypes. In order to demonstrate these results we use a synthetic data set and a digitized image of a glass, in a first example, and images from the Berkley database, in a second example. The results clearly demonstrate the advantages of the information obtained about numerical data sets, taking into account the different meaning of typicalities and the availability of both values with the clustering algorithm used. This approach allows the identification of small homogeneous regions, which are difficult to find.