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")
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.