MATLAB | MATLAB 也可以画 Mantel test 相关性热图了？

绘制效果

代码说明

Mantel test 相关性热图的构造复刻自 R 语言代码:

• Houyun Huang(2021). linkET: Everything is Linkable. R package version 0.0.3.

我为我开发的 MATLAB 绘图工具 SHeatmap 添加了新的辅助函数 SMantelLink 使得 MATLAB 也能具备绘制这样图像的能力。因此想要绘制首先需要下载工具函数包，可在以下仓库获取：

• 【gitee】https://gitee.com/slandarer/matlab-special-heatmap
• 【github】https://github.com/slandarer/MATLAB-special-heatmap
• 【fileexchange】https://www.mathworks.com/matlabcentral/fileexchange/125520-special-heatmap

Mantel test

在给出绘图教程前，先给出 Mantel test 的原理和代码实现，这样大家可以在其他地方使用 Mantel test。

Mantel test 被用来检验两个距离矩阵的相关性，基本实现是：将两个矩阵下三角部分(不含对角线)拉成向量计算相关系数 r, 随机同时交换距离矩阵2的行列，之后将矩阵2下三角部分再次拉成长条，对两个列向量进行相关性检验，记录r p r e m r_{prem}rprem​值，看有多少次因为交换行列导致r p r e m r_{prem}rprem​值对比 r 值上升，计算上升次数/总次数作为 p 值，同时为了和主流计算保持一致(如 R 语言的vegan包)，采用加 1 校正：

r 值越高说明相关性越强，p 值越低说明越显著。以下是 Mantel test 实现代码mantel，工具包还有一个拿存储空间换运行速度的mantelFast函数，运行速度是下面这个函数的10倍，可以工具包里瞅瞅。

function[rho,pval,rperm]=mantel(dist1,dist2,varargin)% MANTEL - Mantel test for matrix correlation% rho = mantel(dist1, dist2) performs Mantel test with 999 permutations% using Pearson correlation.%% rho = mantel(dist1, dist2, nperm) specifies number of permutations.%% rho = mantel(dist1, dist2, method) specifies correlation method% ('Pearson' or 'Spearman', default 'Pearson').%% rho = mantel(dist1, dist2, nperm, method) sets both.%% [rho, pval] = mantel(___) also returns the p-value (one-sided).%% [rho, pval, rperm] = mantel(___) returns the permuted r values.% References% [1] Mantel N. The detection of disease clustering and a generalized regression approach.% Cancer Res. 1967 Feb;27(2):209-20. PMID: 6018555.% [2] Borcard, D. & Legendre, P. (2012) Is the Mantel correlogram powerful enough to be% useful in ecological analysis? A simulation study. Ecology 93: 1473-1481.% [3] Legendre, P. and Legendre, L. (2012) Numerical Ecology. 3rd English Edition. Elsevier.% Parse input argumentsswitchnargincase2nperm=999;method='Pearson';case3ifisnumeric(varargin{1})nperm=varargin{1};method='Pearson';elsenperm=999;method=varargin{1};endcase4nperm=varargin{1};method=varargin{2};end% Extract lower-triangular vectorsN=size(dist1,1);ind=tril(true(N),-1);V1=dist1(ind);V2=dist2(ind);% Observed correlationrho=corr(V1,V2,'Type',method);% Permutation testrperm=zeros(nperm,1);fori=1:nperm perm=randperm(N);dist2_perm=dist2(perm,perm);V2_perm=dist2_perm(ind);rperm(i)=corr(V1,V2_perm,'Type',method);end% p-value (one-sided, positive correlation)pval=(sum(rperm>=rho)+1)/(nperm+1);end

以下说明该代码计算结果与 R 语言相同：

MATLAB 计算

rng(1)X1=rand([100,20]);X2=rand([100,5]);writematrix(X1,'X1.csv');writematrix(X2,'X2.csv');D1=squareform(pdist(X1));D2=squareform(pdist(X2));[rho,pval]=mantel(D1,D2,9999,'Pearson')

计算得到：rho = 0.0438, pval = 0.0827

R 语言计算

dataX1<-read.csv("X1.csv",header=FALSE,row.names=NULL)dataX2<-read.csv("X2.csv",header=FALSE,row.names=NULL)D1<-dist(dataX1)D2<-dist(dataX2)result<-mantel(D1,D2,method="pearson",permutations=9999)print(result)

计算得到：Mantel statistic r: 0.04375, Significance: 0.0828 , 计算结果相似。当然 Mantel test 具有随机性，建议加大随机置换次数并设置随机数种子。

mantelFast 函数就是把循环部分完全换成 MATLAB 矩阵运算：但是在数据量超过 2e8 时容易会内存不足：

% Permutation test[~,perm]=sort(rand(N,nperm),1);[indR,indC]=find(tril(true(N),-1));V2=dist2(sub2ind([N,N],perm(indR,:),perm(indC,:)));rperm=corr(V1,V2,'Type',method);

Mantel test 相关性热图

数据准备

数据来源：

• Väre, H., Ohtonen, R. and Oksanen, J. (1995) Effects of reindeer grazing on understorey vegetation in dry Pinus sylvestris forests. Journal of Vegetation Science 6, 523–530.

%% Load data (加载数据)load('lichenData.mat')% Load pre-saved data package (加载预存的数据包)Data1=varechem.Variables;% Environmental matrix (环境因子矩阵)Data2=varespec.Variables;% Species composition matrix (物种组成矩阵)labels=varechem.Properties.VariableNames;% Environmental variable names (环境变量名称)% Define species groups: 44 columns into 4 groups (将44个物种列分为4组)groupName={'Spec01','Spec02','Spec03','Spec04'};group=zeros(1,size(Data2,2));group(1:7)=1;% Group 1: columns 1-7 (第1组：列1-7)group(8:18)=2;% Group 2: columns 8-18 (第2组：列8-18)group(19:37)=3;% Group 3: columns 19-37 (第3组：列19-37)group(38:44)=4;% Group 4: columns 38-44 (第4组：列38-44)

热图绘制

ax=gca;%% Draw heatmap[rho,pval]=corr(Data1);objHM=SHeatmap(ax,rho,'Format','sq');objHM.draw();% Display significance stars: p < 0.05 *, p < 0.01 **, p < 0.001 ***objHM.setText()objHM.showStars(pval,'Levels',[0.05,0.01,0.001],'CorrLabel','off')objHM.setVarName(labels)% Set row/column labels (设置行列标签)objHM.setType('tril0');% Show only lower triangle without diagonal (仅显示下三角矩阵，不含对角线)% Adjust label positions (调整标签位置)objHM.setRowLabelLocation('left')objHM.setColLabelLocation('bottom')% Show all labels, including those that were previously hidden. (显示所有标签，包括被隐藏的标签)objHM.setRowLabel('Visible','on')objHM.setColLabel('Visible','on')delete(objHM.Colorbar)

Mantel 链接绘制

% Create Mantel link object with env data, species data and groups (创建Mantel链接对象，传入环境数据、物种数据及分组信息)objML=SMantelLink(ax,Data1,Data2,'Group',group);objML.GroupName=groupName;% Set group names (设置组名)objML.LegendLocation='west';% Place legend on the left (图例置于左侧)objML.Layout='triu';% Links placed in upper triangle (链接采用上三角布局)objML.draw()% Render the links (渲染链接图)

在draw()之前很多参数都可以设置，比如为了每次结果一致，建议提前设置随机数种子，且可以设置更大的置换次数：

rng(123456)objML.NumPerm=9999;

再比如计算距离矩阵的方式 (以下是默认计算方式)，更多计算方式参见 MATLAB 官网pdist函数的文档，这里不赘述:

objML.Distance1='euclidean';objML.Distance2=@(ZI,ZJ)sum(abs(ZI-ZJ),2)./sum(ZI+ZJ,2);

同时Curvature可以设置链接线的弯曲程度和方向，比如为负数就是反向弯曲，为0就是直线，LinkBendMode，可以设置为simple，就是所有线弯曲方向一致：

objML.Curvature = 0;

objML.Curvature=-1/3;objML.LinkBendMode='simple';

左下角布局与字体、配色修改

%% Figure and axesfig=figure('Units','normalized','Position',[.05,.15,.72,.72]);ax=axes('Parent',fig,'Position',[.06,.05,.88,.9]);%% Draw heatmap[rho,pval]=corr(Data1);objHM=SHeatmap(ax,rho,'Format','sq');objHM.draw();objHM.setText()objHM.showStars(pval,'Levels',[0.05,0.01,0.001],'CorrLabel','off')objHM.setVarName(labels)objHM.setType('triu0');objHM.setRowLabelLocation('right')objHM.setColLabelLocation('top')objHM.setRowLabel('Visible','on')objHM.setColLabel('Visible','on')delete(objHM.Colorbar)% Apply a custom colormap with 25 colors (应用自定义 25 色 colormap)colormap(slanCM(102,25))% Adjust font properties for labels (调整标签字体)set([objHM.rowLabelHdl,objHM.colLabelHdl],'FontSize',14,'FontName','Helvetica')%% Draw mantel linksobjML=SMantelLink(ax,Data1,Data2,'Group',group);objML.GroupName=groupName;objML.Layout='tril';% Customize colors (自定义颜色)objML.PColor=[0,64,115;79,148,204;224,224,224]./255;objML.NodeColor1=[184,207,248]./255;objML.NodeColor2=[184,207,248]./255;objML.draw()% Adjust legend and group label fonts (调整图例和组标签字体)set(objML.legendTitleHdl,'FontName','Helvetica')set(objML.legendTickLabelHdl,'FontSize',13,'FontName','Helvetica')set(objML.groupLabelHdl,'FontSize',14,'FontName','Helvetica')

结

以上绘图代码需要下载工具函数才能运行：

• 【gitee】https://gitee.com/slandarer/matlab-special-heatmap
• 【github】https://github.com/slandarer/MATLAB-special-heatmap
• 【fileexchange】https://www.mathworks.com/matlabcentral/fileexchange/125520-special-heatmap