C-means algorithm

Ischemia in the forearm was studied by Mansfield et al. in 1997 [38], In this study, the workers used fuzzy C means clustering and principal component analysis (PCA) of time series from the NIR imaging of volunteers forearms. They attempted predictions of blood depletion and increase without a priori values for calibration. For those with a mathematical bent, this paper does a very nice job describing the theory behind the PCA and fuzzy C means algorithms. 

Lin, T.-H., Wang, G.-M. and Hsu, Y.-H. (2002) Classification of some active HlV-1 protease inhibitors and their inactive analogues using some uncorrelated three-dimensional molecular descriptors and a fuzzy c-means algorithm. 

Commonly in nonhierarchical cluster analysis, one starts with an initial partitioning of objects to the different clusters. After that, the membership of the objects to the clusters, for example, to the cluster centroids, is determined and the objects are newly partitioned. We consider here a general method for nonhierarchical clustering that can be used for both crisp (classical) and fuzzy clustering, the c-means algorithm. 

We have already discussed an example iot grouping data on the basis of unsupervised learning with respect to fuzzy cluster analysis by the c-means algorithm (Section 5.2). 

With the c-means algorithm a mean vector is taken as representing a cluster and for asymmetric shaped clusters this will be inadequate. The algorithm can readily be generalized to more sophisticated models so that a cluster is represented not by a single point (such as described by a mean vector) but rather by a function describing some attribute of the cluster s shape in pattern space. 

Most of the applications of fuzzy cluster analysis in chemistry apply the fuzzy-c-means algorithm. It relies on the general least-squares error functional... 

A comparison of both the methods, the fuzzy-c-means algorithm and the k-means algorithm, has been performed under practical considerations for interpretation of aluminosilicate glasses analyzed by Si NMR. The results obtained showed that the fuzzy-c-means algorithm verified a great part of the results obtained by the classical version. The results gave additional information on the data structure, especially with respect to hybrids and outliers. 

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