Fuzzy clustering technique

Bandemer considered the role of fuzzy set theory in analytical chemistry. The applications they described focused on pattern recognition problems, the calibration of analytical methods,quality control, and component identification and mixture evaluation. Gordon and Somorjai applied a fuzzy clustering technique to the detection of similarities among protein substructures. A molecular dynamics trajectory of a protein fragment was analyzed. In the following subsections, some applications based on the hierarchical fuzzy clustering techniques presented in this chapter are reviewed. 

The small clusters (< 5 members) were extracted and reclustered. When the results were checked by medicinal chemists, this strategy seemed to have reduced the number of singletons to an acceptable level. An alternative approach developed by Doman et al.i" employed a fuzzy clustering technique combined with the Jarvis-Patrick method. " The methodology has no user-defined parameters and allows compounds to belong to more than one cluster. 

Pollution VI, C. A. Brebbia, C. F. Ratto, and H. Power, Eds., WIT Press, Southampton, UK, 1998, pp. 257-266. Forecasting High SO2 Concentration Levels with Fuzzy Clustering Techniques. 

A, 36, 153 (2001). Statistical Evaluation of PCDD/F Emission Data During Solid Waste Combustion by Fuzzy Clustering Techniques. 

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. 

Comput. Sci., 36 (6), 1195 (1996). Algorithm5 A Technique for Fuzzy Clustering of Chemical Inventories. 

In addition to fuzzy logic, we will concentrate on the Self-Organizing Map (SOM) algorithm, since it has properties that make it both a data visualization and a clustering technique. We present this method in relation to other... 

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. 

The outcome of agglomerative hierarchical cluster analysis is a crisp cluster membership function, which can take only the values 0 (no membership) or 1 (membership). Other non-hierarchical clustering techniques such as k-means cluster (KMC) analysis still follow this concept, whereas fuzzy C-means (FCM) clustering returns fuzzy class memberships. The latter method thus departs from the classical (0 or 1) two-valued logic and uses soft linguistic system variables, i.e. degrees of class membership values varying between 0 and 1. 

Yoshinari, Y., Pedrycz, W. and Hirota, K. (1993) Construction of fuzzy models through clustering techniques. Fuzzy Sets and Systems, 54,157-65. 

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