二维DBSCAN聚类算法matlab代码

下面是二维DBSCAN聚类算法的MATLAB代码实现。

function [C, idx] = dbscan(X,epsilon,MinPts)
% DBSCAN Clustering
%
% [C, idx] = dbscan(X,epsilon,MinPts) clusters the points in the n-by-p 
% matrix X using DBSCAN algorithm, where each row represents a point in the
% p-dimensional space. 
%
% Input:
% X: n-by-p data matrix.
% epsilon: the radius of the neighborhood.
% MinPts: the minimum number of points in the neighborhood.
%
% Output:
% C: cluster assignments for each point in X. 0 means noise.
% idx: indices of the core points.
%
% Reference: 
% Martin Ester, Hans-Peter Kriegel, Jorg Sander, and Xiaowei Xu. 1996. 
% A density-based algorithm for discovering clusters in large spatial databases 
% with noise. In Proceedings of the 2nd International Conference on Knowledge 
% Discovery and Data Mining (KDD'96), Evangelos Simoudis, Jiawei Han, and Usama 
% Fayyad (Eds.). AAAI Press 226-231.

n = size(X,1);

% Calculate the distance matrix
D = squareform(pdist(X));

% Initialize the visited and noise flags
visited = false(n,1);
noise = false(n,1);

% Initialize the cluster assignments
C = zeros(n,1);
k = 0;

% Find the core points
for i = 1:n
    % Find the neighbors within the radius
    neighbors = find(D(i,:) <= epsilon);
    
    % If there are less than MinPts neighbors, mark as noise
    if numel(neighbors) < MinPts
        noise(i) = true;
    else
        % Mark as core point
        C(i) = k;
        
        % Mark all neighbors as visited
        visited(i) = true;
        visited(neighbors) = true;
        
        % Find the connected components
        while ~isempty(neighbors)
            j = neighbors(1);
            neighbors(1) = [];
            
            % Add j to the current cluster
            C(j) = k;
            
            % If j is a core point, add its neighbors to the list
            if numel(find(D(j,:) <= epsilon)) >= MinPts
                neighbors = [neighbors find(D(j,:) <= epsilon)];
            end
            
            % Mark j as visited
            visited(j) = true;
        end
        
        % Move to the next cluster
        k = k + 1;
    end
end

% Find the border points
for i = 1:n
    if ~noise(i) && ~visited(i)
        % Find the neighbors within the radius
        neighbors = find(D(i,:) <= epsilon);
        
        % If there is a core point in the neighborhood, assign to that cluster
        for j = neighbors
            if C(j) > 0
                C(i) = C(j);
                break;
            end
        end
    end
end

% Output the indices of the core points
idx = find(~noise);

end

在代码中，输入参数X是数据矩阵，epsilon是邻域半径，MinPts是邻域最小点数。输出参数C是数据点的簇分配，0表示噪声点。idx是核心点的索引。