Clustering of numerical data forms the basis of many classification and system modeling algorithms. The purpose of clustering is to identify natural groupings of data from a large data set to produce a concise representation of a system's behavior.
Fuzzy Logic Toolbox™ tools allow you to find clusters in input-output
training data. You can use the cluster information to generate a Sugeno-type
fuzzy inference system that best models the data behavior using a
minimum number of rules. The rules partition themselves according
to the fuzzy qualities associated with each of the data clusters.
Use the command-line function,
genfis2 to automatically
accomplish this type of FIS generation.
Fuzzy c-means (FCM) is a data clustering technique wherein each data point belongs to a cluster to some degree that is specified by a membership grade. This technique was originally introduced by Jim Bezdek in 1981 as an improvement on earlier clustering methods. It provides a method that shows how to group data points that populate some multidimensional space into a specific number of different clusters.
Fuzzy Logic Toolbox command line function
fcm starts with an initial guess for the cluster centers, which are
intended to mark the mean location of each cluster. The initial guess
for these cluster centers is most likely incorrect. Additionally,
fcm assigns every data point a membership grade for each
cluster. By iteratively updating the cluster centers and the membership
grades for each data point,
fcm iteratively moves
the cluster centers to the right location within a data set. This
iteration is based on minimizing an objective function that represents
the distance from any given data point to a cluster center weighted
by that data point's membership grade.
The command line function
fcm outputs a list
of cluster centers and several membership grades for each data point.
You can use the information returned by
help you build a fuzzy inference system by creating membership functions
to represent the fuzzy qualities of each cluster.
If you do not have a clear idea how many clusters there should
be for a given set of data, Subtractive clustering, , is a fast, one-pass algorithm for estimating
the number of clusters and the cluster centers in a set of data. The
cluster estimates, which are obtained from the
subclust function, can be used to initialize iterative optimization-based
clustering methods (
fcm) and model identification
subclust function finds the clusters by using the subtractive clustering
genfis2 function builds upon the
subclust function to provide a fast, one-pass method to
take input-output training data and generate a Sugeno-type fuzzy inference system that
models the data behavior.
 Bezdec, J.C., Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981.
 Chiu, S., "Fuzzy Model Identification Based on Cluster Estimation," Journal of Intelligent & Fuzzy Systems, Vol. 2, No. 3, Spet. 1994.