Posted by *santa* on April 16, 20011

In Reply to Re: need help ?? how implementation fuzzy c-means posted by *Math-Man* on March 27, 20011

: : how implementation fuzzy c-means in delphi...,because i do now implementasion algorithm fuzzy c-means in programe dlphi...!!!!

: ------------------

: First a short intro for most readers who never heard of "fuzzy c-means"...

: Fuzzy C-Means (FCM) clustering allows a set of data-points to belong to two or more clusters. Each point has a degree of belonging to the various clusters (between 0 and 1, as in fuzzy logic). Thus, points on the edge of a cluster, may be in the cluster to a lesser degree than points in the center of cluster.

: Clustering is a common technique for statistical data analysis used in many fields, including machine learning, data mining, pattern recognition, image analysis, information retrieval, and bio-informatics.

: FCM partitioning is carried out through an iterative method, where an algorithm is repeated until a calculated value becomes smaller than a given "error value" e (between 0 and one). The smaller e, the greater the precision and the more steps will be needed.

: For each point X we have a coefficient Uk(x) giving the degree of being in the K-th cluster. Usually, the sum of those coefficients for any given X is defined to be 1.

: With FCM, the "centroid" of a cluster is the mean of all points, weighted by their degree of belonging to the cluster ( this degree is related to the inverse of the distance to the cluster center).

: The FCM algorithm is carried out as follows:

: 1. Choose a number of clusters.

: 2. Assign randomly to each point coefficients for being in the clusters.

: 3. Repeat until the algorithm has converged (that is, the coefficients' change between two iterations is no more than e, the given sensitivity threshold):

: 3.1 Compute the centroid for each cluster.

: 3.2 For each point, compute its coefficients of being in the clusters.

: Gimme a few days to come up with an example and some code.

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