optics算法matlab实现,OPTICS聚类算法的matlab实现

下面是一个简单的 OPTICS 聚类算法的 Matlab 实现：

function [RD,CD,order]=optics(X,MinPts)
% Implementation of the OPTICS clustering algorithm
% INPUTS:
% X: data set (n x p matrix)
% MinPts: minimum number of points to form a cluster
% OUTPUTS:
% RD: vector of reachability distances
% CD: vector of core distances
% order: vector specifying the order in which points were processed

[n,p]=size(X);

% Calculate distance matrix
D=pdist2(X,X);

% Initialize reachability and core distance vectors
RD=Inf*ones(n,1);
CD=Inf*ones(n,1);

% Initialize order vector
order=zeros(n,1);

% Initialize processed flag
processed=false(n,1);

% Initialize index variable
ind=0;

% Loop through all points
for i=1:n
    
    % If point has not been processed yet, expand cluster order
    if ~processed(i)
        ind=ind+1;
        order(ind)=i;
        processed(i)=true;
        
        % Find neighbors of point
        neighbors=find(D(i,:)<=eps);
        nneighbors=length(neighbors);
        
        % If point is a core point, update reachability and core distance of neighbors
        if nneighbors>=MinPts
            CD(i)=max(D(i,neighbors));
            for j=1:nneighbors
                if ~processed(neighbors(j))
                    newRD=max(CD(i),D(i,neighbors(j)));
                    if newRD<RD(neighbors(j))
                        RD(neighbors(j))=newRD;
                    end
                end
            end
            
            % Process neighbors
            while ~isempty(neighbors)
                % Get next unprocessed neighbor
                k=neighbors(1);
                neighbors=neighbors(2:end);
                if ~processed(k)
                    ind=ind+1;
                    order(ind)=k;
                    processed(k)=true;
                    
                    % Find neighbors of neighbor
                    kn=find(D(k,:)<=eps);
                    knneighbors=length(kn);
                    
                    % If neighbor is a core point, update reachability and core distance of its neighbors
                    if knneighbors>=MinPts
                        newCD=max(D(k,kn));
                        CD(k)=newCD;
                        for j=1:knneighbors
                            if ~processed(kn(j))
                                newRD=max(newCD,D(k,kn(j)));
                                if newRD<RD(kn(j))
                                    RD(kn(j))=newRD;
                                end
                                neighbors=[neighbors,kn(j)];
                            end
                        end
                    end
                end
            end
        end
    end
end

% Remove extra zeros from order vector
order=order(1:ind);
end

这个函数的输入参数是数据集 X 和最小点数 MinPts，输出是 reachability distances、core distances 和 order。下面是一个简单的例子：

% Generate sample data
X=[randn(100,2);2+randn(100,2)];

% Perform OPTICS clustering
[RD,CD,order]=optics(X,5);

% Plot reachability distances
figure;
plot(order,RD(order),'LineWidth',2);
xlabel('Point Index');
ylabel('Reachability Distance');
ylim([0,max(RD)]);

这个代码将生成一个包含两个高斯分布的二维数据集，并使用 OPTICS 算法将其聚类。最终，它会绘制出 reachability distances。