isomap数据降维matlab代码

Sure! Here is an example of Isomap dimensionality reduction implemented in MATLAB:

% Load your data matrix here
data = load('your_data.mat');

% Determine the number of nearest neighbors
k = 10;

% Compute pairwise distances using Euclidean distance
distances = pdist2(data, data);

% Find the k-nearest neighbors for each point
[~, nearest_neighbors] = sort(distances, 2);
nearest_neighbors = nearest_neighbors(:, 2:k+1);

% Create the neighborhood graph
graph = zeros(size(data, 1));
for i = 1:size(data, 1)
    for j = nearest_neighbors(i, :)
        graph(i, j) = distances(i, j);
    end
end

% Apply Floyd-Warshall algorithm to find the shortest path distances
shortest_distances = graph;
for k = 1:size(data, 1)
    for i = 1:size(data, 1)
        for j = 1:size(data, 1)
            if shortest_distances(i, k) + shortest_distances(k, j) < shortest_distances(i, j)
                shortest_distances(i, j) = shortest_distances(i, k) + shortest_distances(k, j);
            end
        end
    end
end

% Compute the Gram matrix
squared_distances = shortest_distances.^2;
gram_matrix = -0.5 * (squared_distances - ...
    sum(squared_distances, 1)/size(data, 1) - ...
    sum(squared_distances, 2)/size(data, 1) + ...
    sum(squared_distances(:))/(size(data, 1)^2));

% Perform singular value decomposition
[V, D] = eig(gram_matrix);
[~, sorted_indices] = sort(diag(D), 'descend');
D_sorted = D(sorted_indices, sorted_indices);
V_sorted = V(:, sorted_indices);

% Choose the number of dimensions for the reduced space
num_dimensions = 2;

% Compute the final lower-dimensional representation
reduced_data = V_sorted(:, 1:num_dimensions) * sqrt(D_sorted(1:num_dimensions, 1:num_dimensions));

% Plot the reduced data
scatter(reduced_data(:, 1), reduced_data(:, 2));
title('Isomap Dimensionality Reduction');
xlabel('Dimension 1');
ylabel('Dimension 2');

Make sure to replace `'your_data.mat'` with the path to your actual data file. Also, feel free to adjust the parameters such as the number of nearest neighbors (`k`) and the number of dimensions in the reduced space (`num_dimensions`) according to your needs.