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How to calculate mahalanobis distance in R?
The Mahalanobis distance is the relative distance between two cases and the centroid, where centroid can be thought of as an overall mean for multivariate data. We can say that the centroid is the multivariate equivalent of mean. If the mahalanobis distance is zero that means both the cases are very same and positive value of mahalanobis distance represents that the distance between the two variables is large. In R, we can use mahalanobis function to find the malanobis distance.
Example1
Consider the below data frame −
set.seed(981) x1<−rnorm(20,5,1) x2<−rnorm(20,5,0.84) x3<−rnorm(20,10,1.5) x4<−rnorm(20,10,3.87) x5<−rnorm(20,1,0.0025) df1<−data.frame(x1,x2,x3,x4,x5) df1
Output
x1 x2 x3 x4 x5 1 4.016851 4.749189 10.166216 9.681625 1.0014171 2 5.208083 4.252389 8.886381 8.407824 0.9973355 3 4.000509 5.680469 10.452573 9.799825 0.9996433 4 4.968047 5.572099 12.813119 10.603569 0.9970847 5 5.253632 4.523665 8.961203 6.135956 0.9974229 6 4.556114 5.963955 7.784837 3.701523 0.9965163 7 4.987874 5.372996 10.104144 12.125932 1.0014389 8 6.164940 4.762497 9.826518 17.002388 0.9998966 9 5.497089 5.006558 11.701747 7.392629 1.0013103 10 4.649598 4.620766 11.955838 7.700963 1.0058710 11 4.947477 4.583403 9.431569 13.005483 0.9963742 12 7.074752 5.093332 9.743409 15.232665 1.0006305 13 4.042776 5.117288 9.603592 12.308203 1.0013562 14 5.364624 3.846084 11.919156 12.546169 1.0034000 15 6.079298 4.270361 10.527513 9.828845 0.9971954 16 4.410121 4.783754 8.844011 15.277243 1.0002428 17 4.213869 5.879465 9.651568 4.334237 1.0018883 18 4.142827 5.619082 9.544201 10.336943 0.9978379 19 3.012995 3.713027 11.487735 13.324214 1.0029497 20 5.481955 3.778913 9.074235 10.391055 0.9982697
Finding the mahalanobis distance for rows in df1 −
mahalanobis(df1,colMeans(df1),cov(df1))
Output
[1] 1.192919 3.207677 2.531851 12.073066 3.664532 6.912468 1.766881 [8] 4.880830 3.652825 6.954114 3.152966 8.433015 2.310850 4.239761 [15] 4.013792 4.358375 5.665279 2.711948 9.063510 4.213342
Example2
y1<−rpois(20,1) y2<−rpois(20,3) y3<−rpois(20,5) y4<−rpois(20,8) y5<−rpois(20,12) y6<−rpois(20,10) df2<−data.frame(y1,y2,y3,y4,y5,y6) df2
Output
y1 y2 y3 y4 y5 y6 1 0 2 4 6 11 10 2 1 6 7 4 9 9 3 1 1 6 13 14 11 4 3 3 9 9 16 9 5 2 3 6 10 9 13 6 0 6 7 13 14 13 7 2 2 7 4 15 7 8 0 2 4 8 14 10 9 2 7 3 7 6 12 10 0 2 6 10 10 9 11 0 5 5 10 8 6 12 2 3 5 7 11 9 13 0 5 3 6 9 7 14 0 2 6 3 13 7 15 1 1 7 10 9 9 16 0 3 3 8 12 11 17 0 3 4 5 13 13 18 1 2 6 14 13 8 19 1 2 4 10 8 7 20 1 5 11 13 12 16
mahalanobis(df2,colMeans(df2),cov(df2))
[1] 2.588021 6.383910 4.101547 8.860628 5.248206 8.669764 6.332766 [8] 3.065049 10.556830 2.882808 6.945220 2.333995 4.171714 5.990775 [15] 5.921976 3.198976 5.971216 5.382210 4.167775 11.226611
Example3
z1<−runif(20,1,2) z2<−runif(20,1,4) z3<−runif(20,1,5) z4<−runif(20,2,5) z5<−runif(20,5,10) df3<−data.frame(z1,z2,z3,z4,z5) df3
Output
z1 z2 z3 z4 z5 1 1.388613 3.591918 4.950430 3.012227 7.646999 2 1.536406 2.346386 4.009326 3.344235 6.804723 3 1.307832 2.156929 1.548907 3.719957 9.647134 4 1.452674 3.659639 4.067904 2.821600 9.042116 5 1.821635 1.581077 1.848880 2.133112 8.606968 6 1.472712 1.853850 2.757099 4.971375 8.195671 7 1.129696 1.007614 3.454963 4.500837 9.512772 8 1.084507 3.509503 3.972340 2.557956 5.070359 9 1.066166 3.487398 3.235659 2.692450 8.566473 10 1.622298 3.285975 3.214168 2.816199 6.811145 11 1.215978 2.695426 4.459403 3.883969 7.015267 12 1.748907 1.855413 1.100227 3.676822 8.668907 13 1.785502 3.365582 1.089094 2.232694 6.207582 14 1.313907 1.010318 2.040431 3.337156 6.281897 15 1.211392 2.821926 3.427129 4.835524 8.469758 16 1.127482 1.589360 4.105524 4.575452 7.425941 17 1.914011 1.015687 1.900738 2.542681 8.710688 18 1.156077 1.237109 1.667345 4.654083 6.764100 19 1.770988 3.685755 4.417545 4.637382 6.155797 20 1.594745 3.750948 1.394754 4.548843 9.902893 mahalanobis(df3,colMeans(df3),cov(df3)) [1] 3.680650 2.011037 3.520353 4.338257 5.095421 2.698317 5.394089 7.190855 [9] 6.030547 1.608436 1.705612 2.770687 7.343208 4.676116 2.461363 3.186534 [17] 6.758622 6.152332 9.599646 8.777917
Updated on: 07-Nov-2020
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