Hi,This is Fuzzy C-means clustering related question.I was wondering if any one had some suggestions/mechanism on coming up with (1) the ideal degree of fuziness(2) defining the the threshold for the membership value in order to determine the existence of a particular object in a given cluster.Any kind of input will be greatly appreciated.Thanks

With regard to your second question: In fuzzy c-means clustering, individual items belong, by definition, to all clusters to some degree. If it is neccessary to force an item into a single cluster, I'd suggest selecting the cluster in which the item has the greatest membership.-W. Dwinnellhttp://will.dwinnell.com

1) This value is data dependent, you have to test various values to see which works well on average for the data set2) I am confused with your question here. You assign object membership to the cluster with the corresponding highest membership value. You do not need any threshold for this.Theoretically FCM is on shaky grounds. The simpler k-means algorithm works better most of the time.

(1) The ideal degree of fuzziness: the "fuzziness" of the clustering is determined by the exponent m. In older research, you will see the unstated assumption that m = 2. In practice you must perform a grid search over values of m between 1 and infinity, and you must also perform a grid search over the hyperparameter c (number of centers in the fuzzy c-means algorithm). In order to decide on an optimizer in the grid search you must use some cluster validity index as your performance measure.(2) In order to convert the c fuzzy clusters into k "crisp" clusters you can assign the each point to the cluster for which the point's fuzzy membership is greatest. In cases where a point's fuzzy membership is equal for two or more clusters you must make an "arbitrary" decision which depends on your application.I don't understand alvinkam's comment regarding fuzzy clustering being on shaky grounds. There is a great deal of theoretical work on fuzzy c-means in the literature. I don't think the k-modes clustering algorithm is on any better grounds - after all, a metric has to be arbitrarily chosen. Which algorithm works better depends on your particular application. It is true that the simplicity of the k-modes algorithm makes it attractive and if you are completely throwing away the fuzzy sets by converting to "crisp" sets then you might as well not bother with fuzzy logic and just use k-modes.

QuoteOriginally posted by: Pannini(1) The ideal degree of fuzziness: the "fuzziness" of the clustering is determined by the exponent m. In older research, you will see the unstated assumption that m = 2. In practice you must perform a grid search over values of m between 1 and infinity, and you must also perform a grid search over the hyperparameter c (number of centers in the fuzzy c-means algorithm). In order to decide on an optimizer in the grid search you must use some cluster validity index as your performance measure.I would say rather that one may perform such a search. If an arbitrarily chosen fuzziness and number of clusters solve a problem, there may be no need to find the absolute best such parameters. My experience indicates that separation degrades gracefully with too many or too few clusters when using fuzzy c-means. As a simple example, see this article, which was published in PC AI magazine some years ago:http://will.dwinnell.com/will/Modeling% ... dels.DOC-W. Dwinnellhttp://will.dwinnell.com