How to perform fuzzy c means clustering using custom initializations (initial fuzzy membership metric, datapoints, cluster centers.. etc)?

% Define the data points as coordinates (X, Y)

Data = [

1, 3;

8, 2;

1, 2;

3, 1

];

% Defining total number of clusters

NumOfClusters = 2;

% Create the initial fuzzy partition matrix (U0)

U0 = [

1, 1, 0, 0;

0, 0, 1, 1

]; % Provided initial partition matrix

% Define initial cluster center values

initial_centers = [

2.0, 2.35;

2.15, 1.9

];

% Fuzzy c-means options

fuzzy_options = [2.0];

% Perform Fuzzy C-Means clustering with initializations

[~, cluster_centers, membership] = fcm(Data', NumOfClusters, fuzzy_options, U0, [], initial_centers);

% Displaying the updated partition matrix

disp('Updated Partition Matrix (Membership):');

disp(membership);

% Plotting the clustered data with different colors for each cluster

colors = distinguishable_colors(NumOfClusters); % Generate distinct colors for clusters

figure;

for i = 1:NumOfClusters

idx = find(membership(i, :) == max(membership));

scatter(Data(idx, 1), Data(idx, 2), 100, colors(i, :), 'filled');

hold on;

end

plot(cluster_centers(:, 1), cluster_centers(:, 2), 'kx', 'MarkerSize', 15, 'LineWidth', 2); % Plot cluster centers

hold off;

% Creating a legend dynamically based on the number of clusters

legend_strings = cell(1, NumOfClusters);

for i = 1:NumOfClusters

legend_strings{i} = ['Cluster ' num2str(i)];

end

legend_strings{NumOfClusters + 1} = 'Cluster Centers';

legend(legend_strings);

title('Fuzzy C-Means Clustering with Initializations');

I want to initialize the datapoints, initial fuzzy partition matrix U0, initial_cluster centers but i am getting the following error:

Error using fcm Too many input arguments. Error in (line 28) [~, cluster_centers, membership] = fcm(Data', NumOfClusters, fuzzy_options, U0, [], initial_centers);

When i remove the initial fuzzy partition matrix U0 and initial cluster centers the code works.