Cluster Quasi-Random Data Using Fuzzy C-Means Clustering

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")

Using the fcm function, find two clusters in this data set. The clustering algorithm stops when the improvement in the objective function between subsequent iterations is below a threshold.

options = fcmOptions(NumClusters=2);
[center,U,objFcn] = fcm(fcmdata,options);

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
Minimum improvement reached.

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.

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")

Assign each data point to the cluster for which its cluster membership is greatest.

maxU = max(U);
index1 = find(U(1,:) == maxU);
index2 = find(U(2,:) == maxU);

Finally, plot the clustered data along with the two cluster centers found by the fcm function. The large characters in the plot indicate the cluster centers.

figure
plot(fcmdata(index1,1),fcmdata(index1,2),"og")
hold on
plot(fcmdata(index2,1),fcmdata(index2,2),"xr")
plot(center(1,1),center(1,2),"ok",...
    MarkerSize=15,LineWidth=3)
plot(center(2,1),center(2,2),"xk",...
    MarkerSize=15,LineWidth=3)

Every time you run this example, the fcm function initializes with different initial conditions. This behavior can swap the order in which the cluster centers are computed and plotted.