This example shows how FCM clustering works using quasi-random two-dimensional data.
Load the data set and plot it.
load fcmdata.dat plot(fcmdata(:,1),fcmdata(:,2),'o')
Next, invoke the command-line function,
fcm, to find two clusters in this data set until the objective function is no longer decreasing much at all.
[center,U,objFcn] = fcm(fcmdata,2);
Iteration count = 1, obj. fcn = 8.970479 Iteration count = 2, obj. fcn = 7.197402 Iteration count = 3, obj. fcn = 6.325579 Iteration count = 4, obj. fcn = 4.586142 Iteration count = 5, obj. fcn = 3.893114 Iteration count = 6, obj. fcn = 3.810804 Iteration count = 7, obj. fcn = 3.799801 Iteration count = 8, obj. fcn = 3.797862 Iteration count = 9, obj. fcn = 3.797508 Iteration count = 10, obj. fcn = 3.797444 Iteration count = 11, obj. fcn = 3.797432 Iteration count = 12, obj. fcn = 3.797430
center contains the coordinates of the two cluster centers,
U contains the membership grades for each of the data points, and
objFcn contains a history of the objective function across the iterations.
fcm function is an iteration loop built on top of the following routines:
initfcm - initializes the problem
distfcm - performs Euclidean distance calculation
stepfcm - performs one iteration of clustering
To view the progress of the clustering, plot the objective function.
figure plot(objFcn) title('Objective Function Values') xlabel('Iteration Count') ylabel('Objective Function Value')
Finally, plot the two cluster centers found by the
fcm function. The large characters in the plot indicate cluster centers.
maxU = max(U); index1 = find(U(1,:) == maxU); index2 = find(U(2,:) == maxU); figure line(fcmdata(index1,1), fcmdata(index1,2), 'linestyle',... 'none','marker', 'o','color','g') line(fcmdata(index2,1),fcmdata(index2,2),'linestyle',... 'none','marker', 'x','color','r') hold on plot(center(1,1),center(1,2),'ko','markersize',15,'LineWidth',2) plot(center(2,1),center(2,2),'kx','markersize',15,'LineWidth',2)
Note: Every time you run this example, the
fcm function initializes with different initial conditions. This behavior swaps the order in which the cluster centers are computed and plotted.