Classification fuzzy clustering

Kavuri, S. N., and Venkatasubramanian, V., Using fuzzy clustering with ellipsoidal units in neural networks for robust fault classification, Comput. Chem. Eng. 17(8), 765 (1993). 

Fuzzy clustering methods that have recently become popular are distinct from traditional clustering techniques in that molecules are permitted to belong to multiple clusters or have fractional membership in all clusters. A potential advantage of such classification schemes is that more than one similarity relationship can be established by cluster analysis. 

Zadeh LA (1977) Fuzzy sets and their applications to classification and clustering. In Ryzin JV (ed) Classification and clustering. Academic, NY, pp 251-299... 

As is well known, Cluster Analysis involves the classification of objects into categories. Since most categories have vague boundaries, and may even overlap, the necessity of introducing fuzzy sets is obvious. A discussion of Fuzzy Clustering must refer to the following issues ... 

Due to the large number of characteristics, there is a need to extract the most relevant characteristics from the input data, so that the amount of information lost is minimal, and the classification realized with the projected data set is relevant with respect to the original data. In order to achieve this feature extraction, different statistical techniques, as well as the fuzzy clustering algorithms outlined here, may be used. 

Xu et al. [13] demonstrated the use of ANN and fuzzy clustering method for the identification of various types of trash based on their color and shape parameters. Three color parameters, namely lightness (Z), redness a) and yellowness (+i) and one shape parameter in the form of roimdness were used as inputs. The outputs were four trash categories, namely leaf, bark, hairy seed coat and smooth seed coat. The classification accuracy was higher for ANN clustering than the fuzzy clustering. 

Supervised and unsupervised classification for example PCA, K-means and fuzzy clustering, linear discriminant analysis (LDA), partial least squares-discriminant analysis (PLS-DA), fisher discriminant analysis (FDA), artificial neural networks (ANN). 

Examples of nonhierarchical clustering [22] methods include Gaussian mixture models, means, and fuzzy C means. They can be subdivided into hard and soft clustering methods. Hard classification methods such as means assign pixels to membership of only one cluster whereas soft classifications such as fuzzy C means assign degrees of fractional membership in each cluster. 

Dumitrescu and Kekedy used the FHDC procedure for the classification of mineral waters. Each sample was characterized by the analytical chemical data for eight major components CO2, HCO, Cl , Ca, Mg ", Fe, Na, and mineralization. Tentatively, classifications were made with a smaller number of components. The components present in greater concentration were successively omitted so as to investigate the possible influence on the classification of components present in smaller concentrations. Thus fuzzy hierarchical clustering was performed by considering successively only seven components (mineralization omitted), six constituents (mineralization and HCOj content omitted), or only five constituents (the previous and COj content omitted), respectively. With eight components the FHDC method yielded three clusters. To characterize the three distinct classes of water found, the total hardness (in German... 

Wang, J., Bo, T. H., Jonassen, L and Hovig, E. (2003). Tiimor classification and marker gene prediction by feature selection and fuzzy c-means clustering using microarray data. BMC Bioinformatics, 4 60. 

The fuzzy C-mean (FCM) approach (Udupa and Samarasekera 1996 Bezdek 1948) is able to make unsupervised classification of data in a number of clusters by identifying different tissues in an image without the use of an explicit threshold. The FCM algorithm performs a classification of image data by computing a measure of membership, called fuzzy membership, at each pixel for a specified number of classes. The fuzzy membership function, con-... 

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