Mahalanobis distance with "R" (Exercice)

May 29, 2012

(This article was first published on NIR-Quimiometría, and kindly contributed to R-bloggers)

I have developed this exercise with Excel in another post for the same calculations , I am going to develop it this time with "R".

    edad long. peso    mg.kg
1    28    31   130.0    68.12
2    24    28   143.0   127.89
3    28    20   136.0   89.03
4    32    34   130.5    78.28
5    22    15   125.0 134.08
6    26    37   147.5   135.31
7    24    19   135.0   130.48
8    28    22   125.0   86.48
9    24    26   127.0   129.47
10   30    21   139.0   82.43
11   22    20   121.5   127.41
12   30    38   150.5    71.21
13   24    17   120.0   132.06
14   26    20   125.0    90.85
We import the data into R.
x<-read.table("C:\\lead_fish.txt",header=TRUE)
We are going to apply the Mahalanobis Distance formula:

D^2 = (x - μ)' Σ^-1 (x - μ)

We calculate μ (mean) with:

mean<-colMeans(x)

edad long. peso mg.kg
26.28571 24.85714 132.50000 105.93571

We calculate Σ (covariance matrix (Sx)) with:

Sx<-cov(x)

> Sx
            edad     long.      peso     mg.kg
edad    9.758242 12.81319 12.07692 -72.15407
long. 12.813187 56.90110 49.11538 -70.62066
peso   12.076923 49.11538 92.80769 -46.06962
mg.kg -72.154066 -70.62066 -46.06962 714.00118

The default value for the Mahalanobis function is inverted=FALSE, so the function will calculate the inverse of Sx. If we calculated appart remember to change to TRUE.

See R help:

http://127.0.0.1:25215/library/stats/html/mahalanobis.html

O.K. Let´s go:

>D2<-mahalanobis(x,mean,Sx)

> D2
[1] 5.571677 2.863499 2.686127 7.766153 2.379621 6.366793 2.135347 1.538248
[9] 2.018812 5.143830 3.082734 5.470313 3.158651 1.818195

These are the values in the Diagonal Matrix we saw with the calculations in Excel.