Robert Ehrlich <bobehrlich@home.com> writes:> I have used fuzzy k-means. Aside from the ever present cluster validity problem > it seems to seve the purpose. Among other things I used it for a pixel by pixle > classification of multispectral images. The nice thing was that the memberships > could be expressed a functions of the original image.
Interesting. I suspect that different methods will develop in application areas to fit the sorts of data found there. In my case, datasets are usually relatively wide (several variables) and shallow (moderate number of cases). Each fuzzy set summarizes the variability in several (three to six) categorical items, which can be analyzed subsequently. Dual scaling is designed for this sort of situation already. To quote: "The notion of 'maturity' plays a rather special role in physical anthropometry. Most measurements of growing children, though possibily difficult to make in a standard and reproducible manner, do not present problems of definition. Maturity, on the other hand, though its general meaning is fairly clear, does not possess an obvious definition and in particular it is not obvious how it should be measured. What are available in practice are a large number of attributes of a growing child which pass through several well-defined stages or categories as the child's maturity increases...; these include secondary sex characteristics, the teeth and the bones of various joints including the wrist and the knee. For any one of these attributes it is possible to make unequivocal comparisons between two children: child A is more mature than child B for a specific attribute if he, or she, exhibits a later occurring stage of that attribute. In practice, of course, if child A is more mature than child B for one attribute, he is usually so for many others and it is just this fact that leads us to the notion of a single underlying maturity value for each child, a value which is reflected in the stages of all the different attributes." M. J. R. Healy and H. Goldstein (1976). "An approach to the scaling of categorized attributes," Biometrika, 63(2), pp. 219-229. Fuzzy really only changes some identification constraints and, of course, the interpretation of the scores generated. I do wish there was more attention payed to this topic--I think in my own area (social science) this is one of the barriers to more widespread adoption of fuzzy methods. Jay -- J. Verkuilen jayv@uiuc.edu "Depend upon it, sir, when a man knows he is to be hanged in a fortnight, it concentrates his mind wonderfully." --Dr. Samuel Johnson Dissertation pages written: 62