Fuzzy C-means

Y. Chtioui, D. Bertrand, D. Barba and Y. Dattee, Application of fuzzy C-means clustering for seed discrimination by artificial vision. Chemom. Intell. Lab. Syst., 38 (1997) 75-87. 

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). 

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. 

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... 

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. 

J. R. Mansfield et al., Fuzzy C-Means Clustering and Principal Component Analysis of Time Series from Near-Infrared Imaging of Forearm Ischemia, Computerized Med. Imaging and Graphics, 21(5), 299 (1997). 

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. 

Dembele, D., and Kastner, P. (2003). Fuzzy C-means for clustering microarray data. Bioinformatics, 19 973-980. 

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. 

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-... 

Chen W, Giger ML, Bick U et al (2006) A fuzzy c-means (FCM)-based approach for computerized segmentation of breast lesions in dynamic contrast-enhanced MR images. Acad Radiol 13 63-72... 

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