教你使用 MATLAB 绘制散点密度图(二维核密度)

本文主要是介绍教你使用 MATLAB 绘制散点密度图(二维核密度)，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

效果：

原理也很简单，通过matlab自带的ksdensity获得网格每一点密度，通过密度拟合曲面，再计算每个数据点对应的概率，并将概率映射到颜色即可
为了怕大家找不到函数这次工具函数放到最前面

1工具函数完整代码

function [CData,h,XMesh,YMesh,ZMesh,colorList]=density2C(X,Y,XList,YList,colorList)
[XMesh,YMesh]=meshgrid(XList,YList);
XYi=[XMesh(:) YMesh(:)];
F=ksdensity([X,Y],XYi);
ZMesh=zeros(size(XMesh));
ZMesh(1:length(F))=F;h=interp2(XMesh,YMesh,ZMesh,X,Y);
if nargin<5
colorList=[0.2700         0    0.33000.2700    0.2300    0.51000.1900    0.4100    0.56000.1200    0.5600    0.55000.2100    0.7200    0.47000.5600    0.8400    0.27000.9900    0.9100    0.1300];
end
colorFunc=colorFuncFactory(colorList);
CData=colorFunc((h-min(h))./(max(h)-min(h)));
colorList=colorFunc(linspace(0,1,100)');function colorFunc=colorFuncFactory(colorList)
x=(0:size(colorList,1)-1)./(size(colorList,1)-1);
y1=colorList(:,1);y2=colorList(:,2);y3=colorList(:,3);
colorFunc=@(X)[interp1(x,y1,X,'pchip'),interp1(x,y2,X,'pchip'),interp1(x,y3,X,'pchip')];
end
end

2参数说明

输入：

• X,Y 散点坐标
• XList,YList 用来构造密度曲面网格的序列，其实就是把XLim，YLim分成小份，例如XList=0:0.1:10
• colorList 颜色表mx3数组，用来构造将高度映射到颜色函数的数据表

输出：

• CData各个点对应颜色
• h 各个点对应核密度
• XMesh,YMesh,ZMesh 核密度曲面数据
• colorList 插值后更细密的颜色表

3使用方式

假如编写了如下程序：

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];
scatter(PntSet(:,1),PntSet(:,2),'filled');

结果：

3.1散点赋色

将上面那段代码改写

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];CData=density2C(PntSet(:,1),PntSet(:,2),-2:0.1:15,-2:0.1:15);
scatter(PntSet(:,1),PntSet(:,2),'filled','CData',CData);

3.2等高线图

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];[~,~,XMesh,YMesh,ZMesh,colorList]=density2C(PntSet(:,1),PntSet(:,2),-2:0.1:12,-2:0.1:12);
colormap(colorList)
contourf(XMesh,YMesh,ZMesh,10)

3.3带直方图的散点图

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];colorList=[0.9400    0.9700    0.96000.8900    0.9300    0.92000.8200    0.9100    0.88000.6900    0.8500    0.77000.5900    0.7800    0.69000.5500    0.7500    0.65000.4500    0.6500    0.56000.4000    0.5800    0.49000.3500    0.5100    0.42000.2500    0.3600    0.31000.1300    0.1700    0.1400];
CData=density2C(PntSet(:,1),PntSet(:,2),-2:0.1:15,-2:0.1:15,colorList);set(gcf,'Color',[1 1 1]);% 主分布图
ax1=axes('Parent',gcf);hold(ax1,'on')
scatter(ax1,PntSet(:,1),PntSet(:,2),'filled','CData',CData);
ax1.Position=[0.1,0.1,0.6,0.6];% X轴直方图
ax2=axes('Parent',gcf);hold(ax2,'on')
histogram(ax2,PntSet(:,1),'FaceColor',[0.78 0.88 0.82],...'EdgeColor','none','FaceAlpha',0.7)
ax2.Position=[0.1,0.75,0.6,0.15];
ax2.YColor='none';
ax2.XTickLabel='';
ax2.TickDir='out';
ax2.XLim=ax1.XLim;% Y轴直方图
ax3=axes('Parent',gcf);hold(ax3,'on')
histogram(ax3,PntSet(:,2),'FaceColor',[0.78 0.88 0.82],...'EdgeColor','none','FaceAlpha',0.7,'Orientation','horizontal')
ax3.Position=[0.75,0.1,0.15,0.6];
ax3.XColor='none';
ax3.YTickLabel='';
ax3.TickDir='out';
ax3.YLim=ax1.YLim;

3.4带直方图的等高线图

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];
colorList=[0.9300    0.9500    0.97000.7900    0.8400    0.91000.6500    0.7300    0.85000.5100    0.6200    0.79000.3700    0.5100    0.73000.2700    0.4100    0.63000.2100    0.3200    0.49000.1500    0.2200    0.35000.0900    0.1300    0.21000.0300    0.0400    0.0700];
[~,~,XMesh,YMesh,ZMesh,colorList]=density2C(PntSet(:,1),PntSet(:,2),-2:0.1:13,-2:0.1:13,colorList);set(gcf,'Color',[1 1 1]);
% 主分布图
ax1=axes('Parent',gcf);hold(ax1,'on')
colormap(colorList)
contourf(XMesh,YMesh,ZMesh,10,'EdgeColor','none')
ax1.Position=[0.1,0.1,0.6,0.6];
ax1.TickDir='out';% X轴直方图
ax2=axes('Parent',gcf);hold(ax2,'on')
[f,xi]=ksdensity(PntSet(:,1));
fill([xi,xi(1)],[f,0],[0.34 0.47 0.71],'FaceAlpha',...0.3,'EdgeColor',[0.34 0.47 0.71],'LineWidth',1.2)
ax2.Position=[0.1,0.75,0.6,0.15];
ax2.YColor='none';
ax2.XTickLabel='';
ax2.TickDir='out';
ax2.XLim=ax1.XLim;% Y轴直方图
ax3=axes('Parent',gcf);hold(ax3,'on')
[f,yi]=ksdensity(PntSet(:,2));
fill([f,0],[yi,yi(1)],[0.34 0.47 0.71],'FaceAlpha',...0.3,'EdgeColor',[0.34 0.47 0.71],'LineWidth',1.2)
ax3.Position=[0.75,0.1,0.15,0.6];
ax3.XColor='none';
ax3.YTickLabel='';
ax3.TickDir='out';
ax3.YLim=ax1.YLim;

4使用方式扩展–与ggplot修饰器联动

ggplot风格修饰器：(点击图片跳转链接)

示例1

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];ax=gca;
ax.XLim=[-1 13];
ax.YLim=[-1 13];
ax=ggplotAxes2D(ax);CData=density2C(PntSet(:,1),PntSet(:,2),0:0.1:15,0:0.1:15);
scatter(PntSet(:,1),PntSet(:,2),'filled','CData',CData);

是不是瞬间有那味了：

示例2

PntSet1=mvnrnd([2 3],[1 0;0 2],800);
PntSet2=mvnrnd([6 7],[1 0;0 2],800);
PntSet3=mvnrnd([8 9],[1 0;0 1],800);PntSet=[PntSet1;PntSet2;PntSet3];ax=gca;
ax.XLim=[-3 13];
ax.YLim=[-3 13];
ax=ggplotAxes2D(ax);[~,~,XMesh,YMesh,ZMesh,colorList]=density2C(PntSet(:,1),PntSet(:,2),-2:0.1:12,-2:0.1:12);
colormap(colorList)
contourf(XMesh,YMesh,ZMesh,10)

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