【基础教程】Matlab创建三维箱线图
【基础教程】Matlab创建三维箱线图
TT_Matlab
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1 内容介绍
主要介绍 箱线图 （Box-plot）和利用Matlab绘制箱线图。
1、箱线图介绍
统计指标一般包括：四分位数、均值、中位数、众数、方差、标准差等，箱线图作为一种数据统计的方法，内容包括：
最小值，第一分位，中位数，第三分位数，最大值
。
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箱线图于1977年由美国著名 统计学 家约翰·图基（John Tukey）发明，能够明确的展示离群点的信息，同时能够让我们了解数据是否对称，数据如何分组、数据的峰度。
箱线图（Box- plot ）是一种用于显示一组数据分散情况的统计图，多用于多组数据的比较，相对于直方图，既可以节省空间，还可以展示更多信息（如均值、四分位数等）。
箱线图包含数学统计量，能够分析不同类别数据各层次水平差异，还可以揭示数据间离散程度、异常值、分布差异等。
箱线图内容详细介绍：
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【注】图片来自
你似乎来到了没有知识存在的荒原 - 知乎
四分位数： 一组数据按照从小到大顺序排列后，把该组数据四等分的数，称为四分位数。第一四分位数 (Q1)、第二四分位数 (Q2，也叫“中位数”)和第三四分位数 (Q3)分别等于该样本中所有数值由小到大排列后第25%、第50%和第75%的数字。第三四分位数与第一四分位数的差距又称四分位距（interquartile range, IQR）。
（1）第一个四分位数Q1：也称作25th百分位数，表示最小数（不是“最小值”）和数据集的中位数之间的中间数。
（2）第二四分位数Q2：也称作中位数Median/50th百分位数，表示数据集的中间值。
（3）第三四分位数Q3：也称作75th百分位数，表示数据集的中位数和最大值之间的中间值（不是“最大值”）。
（4）四分位间距IQR：第25至第75个百分点的距离。
（5）离群值：Outliers
（6）最大值max、最小值min
利用正态分布的箱线图，可以帮助理解箱线图：
2 完整代码
function boxPlot3D(xx,g1,g2,quantDistribution) %function boxPlot3D(xx,g1,g2,quantDistribution) %-------------------------------------------------------------------------- % boxPlot3D(x) creates a three dimensional box plot of the data in x. If x % is 3D a matrix, boxPlot3D creates one box for each column. Example, % create a 3D matrix with normal distributions with different means: % % xx=randn(50,2,4)+repmat((permute([0 1 2 -2;1 2 3 4],[3 1 2])),[50,1,1]); % boxPlot3D(xx) % % boxPlot3D(x,g1,g2) groups the data of x, with the grouping variables of % g1, and g2. Example, create a 1D Matrix with different values and the % corresponding grouping parameters: % % xx=randn(500,1)+linspace(0,5,500)’; % g1= [0.1*ones(250,1);0.2*ones(250,1)]; % g2= [3*ones(150,1);4*ones(150,1);5*ones(200,1)]; % boxPlot3D(xx,g1,g2) % % boxPlot3D(x,[],[],quantDistribution) allows the selection of the % quantiles to select, e.g. [0 0.25 0.5 0.75 1] % [0 0.25 0.5 0.75 1] (default) creates a box between 0.25 and 0.75 % with a line in 0.5 and two planes at 0 and 1 % connected with a dashed line. These values can be % changed. % [ 0 1] creates a box within the extremes of the values % selected. These values can be changed, e.g. % [0.25 0.75] % [ 0.25 0.5 0.75] creates a box and a line, same as the option with % 5 values, but will not draw the planes with the % dashed line. % The colours of the boxes can be changed in the code. %-------------------------------------------------------------------------- % %
if nargin <1 else figure hold on; if ~exist(’quantDistribution’,’var’) % Calculate the positions of the edges of the boxplot, and the % quantiles at 25,50 75% quantDistribution = [0 0.25 0.50 0.75 1 ]; end if ~exist(’g1’,’var’) % Only one parameter received, the data is in a 3D Matrix with one % column per group. [rows,columns,levels] = size( xx); for counterCols = 1:columns for counterLevs = 1:levels % Select columns, extract positions, and call display % The column is directly extracted from the matrix currentColumn = xx(:,counterCols,counterLevs); % The positions correspond to the extreme, median and 25%/75% % positions of the distribution, these are obtained with % quantile currentPositions = quantile(currentColumn,quantDistribution); display3Dbox(counterCols,counterLevs,currentPositions); end end else % Three arguments, the data and two grouping parameters % all should be the same size. First, detect the unique cases of % each of the grouping parameters cases_g1=unique(g1); cases_g2=unique(g2); % Count how many cases there are for each dimension num_g1 = numel(cases_g1); num_g2 = numel(cases_g2); % The separation may vary and not necessarily be 0,1,2,3... width_g1 = min(diff(cases_g1)); width_g2 = min(diff(cases_g2)); for counterCols = 1:num_g1 current_g1 = cases_g1(counterCols); address_g1 = (g1==current_g1); for counterLevs = 1:num_g2 current_g2 = cases_g2(counterLevs); address_g2 = (g2==current_g2); % Select columns, extract positions, and call display % The column is directly extracted from the matrix currentColumn = xx((address_g1)&(address_g2)); % The positions correspond to the extreme, median and 25%/75% % positions of the distribution, these are obtained with % quantile currentPositions = quantile(currentColumn,quantDistribution); % Call the display with the extra parameters for width display3Dbox(current_g1,current_g2,currentPositions,width_g1,width_g2); end end end view(3) rotate3d on axis tight grid on end
end
function display3Dbox(counterCols,counterLevs,currentPositions,width_g1,width_g2)
if ~exist(’width_g1’,’var’) width_g1 = 1; end if ~exist(’width_g2’,’var’) width_g2 = 1; end if ~exist(’colourFace’,’var’) colourFace=’red’; end if ~exist(’colourFace2’,’var’) colourFace2=’cyan’; end lenZStats=length(currentPositions);
% to avoid overlap between boxes, use only 35% to each dimension x=width_g1 * 0.35*[-1 1 1 -1 -1 1 1 -1]’; y=width_g2 * 0.35*[-1 -1 1 1 -1 -1 1 1]’; % This are the parameters to create the boxes and faces z=[1 1 1 1]’; face_Mat=[1 2 6 5;2 3 7 6;3 4 8 7;4 1 5 8;4 1 5 8;1 2 3 4; 5 6 7 8];
switch lenZStats case 2 %----- a single box with extremes (.25 .75 / 0 1) to be plotted vert_Mat=[counterCols+x counterLevs+y [currentPositions(1)*z;currentPositions(2)*z]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace,’edgecolor’,’black’,’linewidth’,1); case 3 %----- a central box with median (0.25 0.5 0.75) delta=0.05*(currentPositions(3)-currentPositions(1)); vert_Mat=[counterCols+x counterLevs+y [currentPositions(1)*z;currentPositions(2)*z-delta/2]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace,’edgecolor’,’black’,’linewidth’,1); vert_Mat=[counterCols+x counterLevs+y [currentPositions(2)*z-delta/2;currentPositions(2)*z+delta/2]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace2,’edgecolor’,’black’,’linewidth’,1); vert_Mat=[counterCols+x counterLevs+y [currentPositions(2)*z+delta/2;currentPositions(3)*z-delta/2]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace,’edgecolor’,’black’,’linewidth’,1); case 5 %----- central box with extemes (0 0.25 0.5 0.75 1) delta=0.05*(currentPositions(3)-currentPositions(1)); colourFace3=0.5*[1 1 1]; vert_Mat=[counterCols+x counterLevs+y [currentPositions(2)*z;currentPositions(3)*z-delta/2]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace,’edgecolor’,’black’,’linewidth’,1); vert_Mat=[counterCols+x counterLevs+y [currentPositions(3)*z-delta/2;currentPositions(3)*z+delta/2]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace2,’edgecolor’,’black’,’linewidth’,1); vert_Mat=[counterCols+x counterLevs+y [currentPositions(3)*z+delta/2;currentPositions(4)*z-delta/2]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace,’edgecolor’,’black’,’linewidth’,1); vert_Mat=[counterCols+x*(0.5) counterLevs+y*(0.5) [currentPositions(1)*z;currentPositions(1)*z]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace3,’edgecolor’,’black’,’linewidth’,0.5); vert_Mat=[counterCols+x*(0.5) counterLevs+y*(0.5) [currentPositions(5)*z;currentPositions(5)*z]]; patch(’Vertices’,vert_Mat,’Faces’,face_Mat,’facecolor’,colourFace3,’edgecolor’,’black’,’linewidth’,0.5); line([counterCols counterCols],[counterLevs counterLevs],[currentPositions(1) currentPositions(2)],’linewidth’,0.5,’color’,’k’,’marker’,’.’,’linestyle’,’--’) line([counterCols counterCols],[counterLevs counterLevs],[currentPositions(4) currentPositions(5)],’linewidth’,0.5,’color’,’k’,’marker’,’.’,’linestyle’,’--’) end
end %delta=0.04;
%alpha(0.5);
%grid on;axis tight;rotate3d on;view(3)
3 运行结果
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