{"id":357,"date":"2013-12-06T14:49:10","date_gmt":"2013-12-06T19:49:10","guid":{"rendered":"http:\/\/homepages.uc.edu\/~yaozo\/wordpress\/?p=357"},"modified":"2013-12-06T14:49:10","modified_gmt":"2013-12-06T19:49:10","slug":"matlab-fuzzy-clustering","status":"publish","type":"post","link":"https:\/\/zhuoyao.net\/index.php\/2013\/12\/06\/matlab-fuzzy-clustering\/","title":{"rendered":"Matlab Fuzzy Clustering"},"content":{"rendered":"
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What Is Data Clustering?<\/h3>\n

Clustering of numerical data forms the basis of many classification and system modeling algorithms. The purpose of\u00a0<\/a>clustering is to identify natural groupings of data from a large data set to produce a concise representation of a system’s behavior.<\/p>\n

Fuzzy Logic Toolbox\u2122 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,\u00a0genfis2<\/tt>\u00a0to automatically accomplish this type of FIS generation.<\/p>\n

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References<\/h4>\n

<\/a>[1] Bezdec, J.C.,\u00a0Pattern Recognition with Fuzzy Objective Function Algorithms,\u00a0<\/i>Plenum Press, New York, 1981.<\/p>\n

<\/a>[2] Chiu, S., “Fuzzy Model Identification Based on Cluster Estimation,”\u00a0Journal of Intelligent & Fuzzy Systems<\/i>, Vol. 2, No. 3, Spet. 1994.<\/p>\n<\/div>\n

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Fuzzy C-Means Clustering<\/h3>\n

Fuzzy c-means<\/em>\u00a0(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[1]<\/a>\u00a0as 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.<\/p>\n

Fuzzy Logic Toolbox command line function\u00a0fcm<\/tt>\u00a0starts 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,\u00a0fcm<\/tt>\u00a0assigns every data point a membership grade for each cluster. By iteratively updating the cluster centers and the membership grades for each data point,\u00a0fcm<\/tt>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.<\/p>\n

The command line function\u00a0fcm<\/tt>\u00a0outputs a list of cluster centers and several membership grades for each data point. You can use the information returned by\u00a0fcm<\/tt>\u00a0to help you build a fuzzy inference system by creating membership functions to represent the fuzzy qualities of each cluster.<\/p>\n<\/div>\n

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Cluster Quasi-Random Data Using Fuzzy C-Means Clustering<\/h3>\n

You can use quasi-random two-dimensional data to illustrate how FCM clustering works. To load the data set and plot it, type the following commands:<\/p>\n

load fcmdata.dat\nplot(fcmdata(:,1),fcmdata(:,2),'o')<\/pre>\n
\"\"<\/p>\n
Next, invoke the command-line function\u00a0fcm<\/tt>\u00a0to find two clusters in this data set until the objective function is no longer decreasing much at all.<\/p>\n
[center,U,objFcn] = fcm(fcmdata,2);<\/pre>\n
Here, the variable\u00a0center<\/tt>\u00a0contains the coordinates of the two cluster centers,\u00a0U<\/tt>\u00a0contains the membership grades for each of the data points, and\u00a0objFcn<\/tt>\u00a0contains a history of the objective function across the iterations.<\/p>\n
This command returns the following result:<\/p>\n
Iteration count = 1, obj. fcn = 8.794048\nIteration count = 2, obj. fcn = 6.986628\n.....\nIteration count = 12, obj. fcn = 3.797430<\/pre>\n
The\u00a0fcm<\/tt>\u00a0function is an iteration loop built on top of the following routines:<\/p>\n