如何从矩阵中只保留一个高度相关的值？答案

【问题标题】：How to keep only one of higly correlated values from a matrix?如何从矩阵中只保留一个高度相关的值？
【发布时间】：2019-11-15 18:44:24
【问题描述】：

我在这个网站上创建了我的相关矩阵（在标签 LDmatrix 下），下面粘贴了 246 个 SNP https://ldlink.nci.nih.gov/?tab=ldmatrix 并加载它：

calc.rho=read.table("ro246_matrix.txt")
calc.rho=data.matrix(calc.rho)

我想要做的是从这个矩阵中只提取相关性低于 0.8 的对。

我可以通过：

keeprows<-apply(calc.rho,1,function(x) return(sum(x>0.8)<3))
ro246.lt.8<-calc.rho[keeprows,keeprows]
ro246.lt.8[ro246.lt.8 == 1] <- NA
(mmax <- max(abs(ro246.lt.8), na.rm=TRUE))
[1] 0.566

这里的问题是我只得到了 246 个 SNP 中的 17 个，这意味着我删除了每一对高度相关的 SNP，实际上我应该保留其中一个。在这个例子中： rs3764410 和 rs56192520 的相关性为 0.976，所以我只会随机保留其中一个，比如 rs56192520。

怎么做，请指教。

> calc.rho[30:40,30:40]
           rs4313843 rs8069610 rs883504 rs8072394 rs4280293 rs4465638
rs4313843      1.000     0.642    0.975     0.642     0.642     0.925
rs8069610      0.642     1.000    0.659     1.000     1.000     0.589
rs883504       0.975     0.659    1.000     0.659     0.659     0.901
rs8072394      0.642     1.000    0.659     1.000     1.000     0.589
rs4280293      0.642     1.000    0.659     1.000     1.000     0.589
rs4465638      0.925     0.589    0.901     0.589     0.589     1.000
rs12602378     0.326     0.519    0.335     0.519     0.519     0.344
rs9899059      0.326     0.519    0.335     0.519     0.519     0.344
rs6502530      0.333     0.530    0.342     0.530     0.530     0.351
rs4380085      0.950     0.605    0.926     0.605     0.605     0.975
rs6502532      0.276     0.439    0.283     0.439     0.439     0.292
           rs12602378 rs9899059 rs6502530 rs4380085 rs6502532
rs4313843       0.326     0.326     0.333     0.950     0.276
rs8069610       0.519     0.519     0.530     0.605     0.439
rs883504        0.335     0.335     0.342     0.926     0.283
rs8072394       0.519     0.519     0.530     0.605     0.439
rs4280293       0.519     0.519     0.530     0.605     0.439
rs4465638       0.344     0.344     0.351     0.975     0.292
rs12602378      1.000     1.000     0.980     0.353     0.813
rs9899059       1.000     1.000     0.980     0.353     0.813
rs6502530       0.980     0.980     1.000     0.360     0.833
rs4380085       0.353     0.353     0.360     1.000     0.300
rs6502532       0.813     0.813     0.833     0.300     1.000

或者这是一个更直接的可重现示例：

calc.rho<-matrix(c(0.903,0.268,0.327,0.327,0.327,0.582,
0.928,0.276,0.336,0.336,0.336,0.598,
0.975,0.309,0.371,0.371,0.371,0.638,
0.975,0.309,0.371,0.371,0.371,0.638,
0.975,0.309,0.371,0.371,0.371,0.638,
0.975,0.309,0.371,0.371,0.371,0.638),ncol=6,byrow=TRUE)
rnames<-c("rs56192520","rs3764410","rs145984817","rs1807401",
"rs1807402","rs35350506")
rownames(calc.rho)<-rnames
cnames<-c("rs9900318","rs8069906","rs9908521","rs9908336",
"rs9908870","rs9895995")
colnames(calc.rho)<-cnames

所有 246 个 SNP：

rs56192520 rs3764410 rs145984817 rs1807401 rs1807402 rs35350506 rs2089177 rs12325677 rs62064624 rs62064631 rs2349295 rs2174369 rs7218554 rs62064634 rs4360974 rs4527060 rs6502526 rs6502527 rs9900318 rs8069906 rs9908521 rs9908336 rs9908870 rs9895995 rs7211086 rs9905280 rs8073305 rs8072086 rs4312350 rs4313843 rs8069610 rs883504 rs8072394 rs4280293 rs4465638 rs12602378 rs9899059 rs6502530 rs4380085 rs6502532 rs4792798 rs4792799 rs4316813 rs148563931 rs74751226 rs8068857 rs8069441 rs77397878 rs75339756 rs4608391 rs79569548 rs4275914 rs11870422 rs8075751 rs11658904 rs138437542 rs80344434 rs7222311 rs7221842 rs7223686 rs78013597 rs74965036 rs78063986 rs118106233 rs117345712 rs113004656 rs9898995 rs4985718 rs9893911 rs79110942 rs7208929 rs12601453 rs4078062 rs75129280 rs76664572 rs78961289 rs146364798 rs76715413 rs4078534 rs79457460 rs74369938 rs76423171 rs74668400 rs75146120 rs1135237 rs9914671 rs117759512 rs4985696 rs16961340 rs17794159 rs4247118 rs78572469 rs12601193 rs2349646 rs2090018 rs12601424 rs4985701 rs8064550 rs2271521 rs2271520 rs11078374 rs4985702 rs1124961 rs11652674 rs3924340 rs112450164 rs7208973 rs9910857 rs78574480 rs8072184 rs12602196 rs6502563 rs3744135 rs148779543 rs77689691 rs41319048 rs117340532 rs78647096 rs77712968 rs16961396 rs80054920 rs7206981 rs4985740 rs3803762 rs77103270 rs7207485 rs77342773 rs3826304 rs3744126 rs7210879 rs7211576 rs117967362 rs75978745 rs6502564 rs9894565 rs36079048 rs8076621 rs7218795 rs3803761 rs12602675 rs7208065 rs4985705 rs8080386 rs8065832 rs2018781 rs1736221 rs1736220 rs1736217 rs1708620 rs1708619 rs1736216 rs76319098 rs1736215 rs1736214 rs1708617 rs12602831 rs12602871 rs1736213 rs1736212 rs76045368 rs34518797 rs11078378 rs8079562 rs8065774 rs8066090 rs41337846 rs1736209 rs1736208 rs12949822 rs76246042 rs12600635 rs55689224 rs1736207 rs1708626 rs1736206 rs9896078 rs16961474 rs1708627 rs1736205 rs1708628 rs7220577 rs2294155 rs1736204 rs1736203 rs1736202 rs12937908 rs1736200 rs1708623 rs1708624 rs9894884 rs9901894 rs9903294 rs2472689 rs1630656 rs111478970 rs3182911 rs7219012 rs9890657 rs12453455 rs12947291 rs150267386 rs16961493 rs11652745 rs9907107 rs8070574 rs4985759 rs3866959 rs7219248 rs6502568 rs7220275 rs12450037 rs7225876 rs9892352 rs4985760 rs6502569 rs1029830 rs2012954 rs1029832 rs2270180 rs8072402 rs7221553 rs145597919 rs150772017 rs2041393 rs6502578 rs11078382 rs9912109 rs12601631 rs11869054 rs11869079 rs9912599 rs7220057 rs9896970 rs34121330 rs34668117 rs67773570 rs242252 rs955893 rs28583584 rs9944423 rs7217764 rs11651957 rs73978990 rs8071007 rs56044345 rs17804843

【问题讨论】：

请创建一个最小可重现的例子。分享一个 10x0 或 15x15 的相关矩阵，大到足以说明问题，您会更快地获得帮助。
谢谢！我粘贴了我的矩阵。有其他方法可以做到这一点吗？
我又加了一个例子
此过程可能会使您的结果偏向于它们不可靠的程度，但有了该警告，您可以一次处理一个变量，例如（colSums(calc.rho) 表明 rs9900318 与其他变量的平均相关性最高。删除它并重新计算相关矩阵。在你的相关矩阵中，不再有任何超过 0.8 的相关性。

标签： r matrix correlation

【解决方案1】：

您的可重现示例不是真正的相关矩阵，因此我更喜欢使用 R amd 中可用的数据集mtcars 从那里创建相关矩阵。但是您应该能够将其应用于您的数据集

data(mtcars)
my_data <- mtcars[,c(1,3:7)]

res <- cor(my_data)
res <-data.frame(res)
# Adding rownames as new column to be able to change their format later
res$rnames = rownames(res)

这是res的输出：

> res
            mpg       disp         hp        drat         wt        qsec rnames
mpg   1.0000000 -0.8475514 -0.7761684  0.68117191 -0.8676594  0.41868403    mpg
disp -0.8475514  1.0000000  0.7909486 -0.71021393  0.8879799 -0.43369788   disp
hp   -0.7761684  0.7909486  1.0000000 -0.44875912  0.6587479 -0.70822339     hp
drat  0.6811719 -0.7102139 -0.4487591  1.00000000 -0.7124406  0.09120476   drat
wt   -0.8676594  0.8879799  0.6587479 -0.71244065  1.0000000 -0.17471588     wt
qsec  0.4186840 -0.4336979 -0.7082234  0.09120476 -0.1747159  1.00000000   qsec

现在，使用tidyverse，我们可以重塑data.frame：

library(tidyverse)
res2 = res %>%
  pivot_longer(-rnames,names_to = "col",values_to = "Corr")

现在，它看起来像：

> head(res2)
# A tibble: 6 x 3
  rnames col     Corr
  <chr>  <chr>  <dbl>
1 mpg    mpg    1    
2 mpg    disp  -0.848
3 mpg    hp    -0.776
4 mpg    drat   0.681
5 mpg    wt    -0.868
6 mpg    qsec   0.419

然后，您可以创建一个新的 list 对象，该对象将同时包含 rnames 和 col 排序。

res4 <- unlist(res2 %>% rowwise() %>% do(i = sort(c(.$rnames,.$col))))
# Here is the output of res4
> head(res4)
    i1     i2     i3     i4     i5     i6 
 "mpg"  "mpg" "disp"  "mpg"   "hp"  "mpg

我们使用res4 在res2 中创建了一个名为Comparaison 的新列，这将是rnames 和col 有序的融合。我们将使用这个新列来过滤具有相同名称并因此进行相同比较的行（使用distinct）。最后，我们应用filter 来仅保留高于 0.5 的值（但如果您愿意，可以使用 0.8）并删除等于 1 的值（自我比较）

res2 %>%
  mutate(Comparaison = paste0(res4[seq(1,length(res4),by = 2)],res4[seq(2,length(res4),by = 2)])) %>%
  distinct(Comparaison, .keep_all = T) %>%
  filter(Corr >0.5 & Corr !=1)

这是最终输出

# A tibble: 4 x 4
  rnames col    Corr Comparaison
  <chr>  <chr> <dbl> <chr>      
1 mpg    drat  0.681 dratmpg    
2 disp   hp    0.791 disphp     
3 disp   wt    0.888 dispwt     
4 hp     wt    0.659 hpwt

也许有更简单的方法来获得相同的输出，但至少这个应该适用于您的数据。

【讨论】：