Fuzzy 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. 

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. 

FIGURE 6.18 Cluster validity V(k), see Equation 6.13, for the algorithms fc-means, fuzzy c-means, and model-based clustering with varying number of clusters. The left picture is the result for the example used in Figure 6.8 (three spherical clusters), the right picture results from the analysis of the data from Figure 6.9 (two elliptical clusters and one spherical cluster). 

With a combined VIS + NIR SI system and a fuzzy-C-means classification algorithm, it was possible to set up a fast, compact, contact-less and non-destructive analytical instrument. As shown in Fig. 7.7, the two-range spectroscopic imager is capable of distinguishing among true turquoises, even if they are set into bedrock (b), treated turquoises (pressed turquoise powder, etc.), synthetic turquoises and nonturquoise materials without sample pre-treatment with high reliability.18... 

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). 

Lim YW, Lee SU (1990) On the color image segmentation algorithm based tm the thresholding and the fuzzy c-means technique. Pattern Recogn 23(9) 935-952... 

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-... 

The other major variant of clustering minimizes some objective function of the intersample distances. The results are also dependent on user-selected parameters (e.g. the number of clusters and the type of the distance measure used). However, these results become more realistic if we allow overlap between clusters, i.e. if we accept that the samples can be fuzzy, having memberships in all clusters. Bezdek s fuzzy c-means clustering algorithm is the most popular of such clustering methods. Neither clustering... 

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