DBSCAN聚类算法三部分：
1、DBSCAN原理、流程、参数设置、优缺点以及算法；
/zhouxianen1987/article/details/68945844
2、matlab代码实现；
blog：/zhouxianen1987/article/details/68946169
code：/detail/zhouxianen1987/9789230
3、C++代码实现及与matlab实例结果比较。
blog：/zhouxianen1987/article/details/68946278
code：/detail/zhouxianen1987/9789231
摘要：介绍DBSCAN原理、流程、参数设置、优缺点以及算法的matlab和C++代码实例。
matlab代码测试实验(代码从matlab官方网站[8]下载)：
下载的代码主要包括一个测试数据集合mydata.mat,main.m，DBSCAN.m和PlotClusterinResult.m共4个文件，我们在测试实验实验中做了两个方面更改：1)更换了另外一个测试数据，测试数据来源于[13]（取其中的一部分）,2)添加了个K距离图部分代码(均在如下主程序代码中给出)，代码按照个人对k-distance graph的理解编写，如有错误之处，望大家指正，3）改变参数Eps值大小，输出结果并显示。
所有测试代码在下文给出，包括DBSCAN.m和PlotClusterinResult.m子函数。
（所有测试代码下载：）
%main function：主函数%all codes and test data downlown: /255/ypml110-dbscan-clustering % Copyright (c) , Yarpiz ()% All rights reserved. Please read the "license.txt" for license terms.%% Project Code: YPML110% Project Title: Implementation of DBSCAN Clustering in MATLAB% Publisher: Yarpiz ()% % Developer: S. Mostapha Kalami Heris (Member of Yarpiz Team)% % Contact Info: sm.kalami@, info@clc;clear;close all;%% test Data%数据下载网站：http://archive.ics.uci.edu/ml/machine-learning-databases/iris/%这里使用的iris数据的一部分，由于第3维和第4为数据数据区分度好，因此用3、4维数据测试X1 =[5.1,3.5,1.4,0.2;%,Iris-setosa4.9,3.0,1.4,0.2;4.7,3.2,1.3,0.2;4.6,3.1,1.5,0.2;5.1,3.7,1.5,0.4;4.6,3.6,1.0,0.2;5.1,3.3,1.7,0.5;5.0,3.6,1.4,0.2;5.4,3.9,1.7,0.4;4.6,3.4,1.4,0.3;5.0,3.4,1.5,0.2;4.4,2.9,1.4,0.2;4.9,3.1,1.5,0.1;5.4,3.7,1.5,0.2;4.8,3.4,1.6,0.2;4.8,3.0,1.4,0.1;4.3,3.0,1.1,0.1;5.8,4.0,1.2,0.2;5.7,4.4,1.5,0.4;5.4,3.9,1.3,0.4;5.1,3.5,1.4,0.3;5.7,3.8,1.7,0.3;5.1,3.8,1.5,0.3;5.4,3.4,1.7,0.2;6.4,3.2,4.5,1.5;%Iris-versicolor6.9,3.1,4.9,1.5;5.5,2.3,4.0,1.3;6.5,2.8,4.6,1.5;5.7,2.8,4.5,1.3;6.3,3.3,4.7,1.6;4.9,2.4,3.3,1.0;4.9,2.4,3.3,1.0;6.6,2.9,4.6,1.3;5.2,2.7,3.9,1.4;5.0,2.0,3.5,1.0;5.9,3.0,4.2,1.5;6.0,2.2,4.0,1.0];X=X1(:,3:4);%%KNN k distance graph, to determine the epsilonA=X;numData=size(A,1);Kdist=zeros(numData,1);[IDX,Dist]=knnsearch(A(2:numData,:),A(1,:));Kdist(1)=Dist;for i=2:size(A,1)[IDX,Dist] = knnsearch(A([1:i-1,i+1:numData],:),A(i,:));Kdist(i)=Dist;end[sortKdist,sortKdistIdx]=sort(Kdist,'descend');distX=[1:numData]';plot(distX,sortKdist,'r+-','LineWidth',2);set(gcf,'position',[1000 340 350 350]);grid on;%% Run DBSCAN Clustering Algorithmepsilon= 0.15 ;MinPts= 3 ;IDX1=DBSCAN(X,epsilon,MinPts);%% Plot Resultsfigure;PlotClusterinResult(X, IDX1);title(['DBSCAN Clustering (\epsilon = ' num2str(epsilon) ', MinPts = ' num2str(MinPts) ')']);set(gcf,'position',[30 -10 500 500]); epsilon= 0.25 ;MinPts= 3 ;IDX2=DBSCAN(X,epsilon,MinPts);%% Plot Resultsfigure;PlotClusterinResult(X, IDX2);title(['DBSCAN Clustering (\epsilon = ' num2str(epsilon) ', MinPts = ' num2str(MinPts) ')']);set(gcf,'position',[530 -10 500 500]);epsilon= 0.5 ;MinPts= 3 ;IDX3=DBSCAN(X,epsilon,MinPts);%% Plot Resultsfigure;PlotClusterinResult(X, IDX3);title(['DBSCAN Clustering (\epsilon = ' num2str(epsilon) ', MinPts = ' num2str(MinPts) ')']);set(gcf,'position',[30 380 500 500]);%DBSCAN算法子函数，需另外创建.m文件保存% Copyright (c) , Yarpiz ()% All rights reserved. Please read the "license.txt" for license terms.%% Project Code: YPML110% Project Title: Implementation of DBSCAN Clustering in MATLAB% Publisher: Yarpiz ()% % Developer: S. Mostapha Kalami Heris (Member of Yarpiz Team)% % Contact Info: sm.kalami@, info@function [IDX, isnoise]=DBSCAN(X,epsilon,MinPts)C=0;n=size(X,1);IDX=zeros(n,1);D=pdist2(X,X);visited=false(n,1);isnoise=false(n,1);for i=1:nif ~visited(i)visited(i)=true;Neighbors=RegionQuery(i);if numel(Neighbors)<MinPts% X(i,:) is NOISEisnoise(i)=true;elseC=C+1;ExpandCluster(i,Neighbors,C);endendendfunction ExpandCluster(i,Neighbors,C)IDX(i)=C;k = 1;while truej = Neighbors(k);if ~visited(j)visited(j)=true;Neighbors2=RegionQuery(j);if numel(Neighbors2)>=MinPtsNeighbors=[Neighbors Neighbors2]; %#okendendif IDX(j)==0IDX(j)=C;endk = k + 1;if k > numel(Neighbors)break;endendendfunction Neighbors=RegionQuery(i)Neighbors=find(D(i,:)<=epsilon);endend%结果显示子函数，需另外创建.m文件保存% Copyright (c) , Yarpiz ()% All rights reserved. Please read the "license.txt" for license terms.%% Project Code: YPML110% Project Title: Implementation of DBSCAN Clustering in MATLAB% Publisher: Yarpiz ()% % Developer: S. Mostapha Kalami Heris (Member of Yarpiz Team)% % Contact Info: sm.kalami@, info@function PlotClusterinResult(X, IDX)k=max(IDX);Colors=hsv(k);Legends = {};for i=0:kXi=X(IDX==i,:);if i~=0Style = 'x';MarkerSize = 8;Color = Colors(i,:);Legends{end+1} = ['Cluster #' num2str(i)];elseStyle = 'o';MarkerSize = 6;Color = [0 0 0];if ~isempty(Xi)Legends{end+1} = 'Noise';endendif ~isempty(Xi)plot(Xi(:,1),Xi(:,2),Style,'MarkerSize',MarkerSize,'Color',Color);endhold on;endhold off;axis equal;grid on;legend(Legends);legend('Location', 'NorthEastOutside');end
运行结果：
观察当Eps由小到大变化时候，当Eps=0.15时，数据分成2类，噪音点有9个，当Eps=0.25时，数据分成3来，噪音点4个，Eps=0.15时，被分成2类，无噪音点，而根据k距离图大致确定0.15为较适合的Eps参数值，但是这不能很好的将这两类数据分开（数据来源：http://archive.ics.uci.edu/ml/machine-learning-databases/iris/，数据详细说明可到上述网站查看），这可能是数据密度分布不均匀，导致参数Eps不太容易确定，在这种时候按照参数设置的指导原则不能选取较好的参数，而是需要根据具体应用先验进行参数适当调整。
有关matlab版本的DBSCAN算法代码，除了matlab官网可以下载DBSCAN算法代码知网,[9]也给出一个最原始的DBSCAN的matlab实现，只能处理小规模的数据。
参考资料：
[1] /wiki/DBSCAN
[2]Ester,Martin;Kriegel, Hans-Peter; Sander,Jörg; Xu, Xiaowei (1996). Simoudis, Evangelos; Han, Jiawei; Fayyad, Usama M.,eds.Adensity-based algorithm for discovering clusters in large spatial databaseswith noise. Proceedings of the Second International Conference on KnowledgeDiscovery and Data Mining (KDD-96).AAAI Press.pp.226–231.CiteSeerX10.1.1.121.9220.ISBN1-57735-004-9.
[3]各种聚类算法的比较
/qianshch@126/blog/static/4897252292254141315/
[4]/chaosimple/p/3164775.html
[5]/view/ce3e324aa8956bec0975e3d5.html
[6]/itplus/article/details/10088625
[7]/articles/euAZneu
[8] /matlabcentral/fileexchange/52905-dbscan-clustering-algorithm
[9] /snnxb/article/details/29880387
[10] 聚类算法-DBSCAN-C++实现,/k76853/article/details/50440182
[11] DBSCAN聚类算法C++实现,/u011367448/article/details/18549823
[12] DBSCAN 算法介绍以及C++实现，/u011557212/article/details/53203323
[13] /siddharth-agrawal/DBSCAN
[14] /download/piaominnan/8480767
