# wmahalanobis: Compute weighted Mahalanobis distance In WMDB: Discriminant Analysis Methods by Weight Mahalanobis Distance and bayes

## Description

compute weighted Mahalanobis distance between two samples

## Usage

 `1` ```wmahalanobis(x, center, cov, weight) ```

## Arguments

 `x` vector or matrix of data with, say, p columns. `center` mean vector of the distribution or second data vector of length p `cov` covariance matrix (p x p) of the distribution `weight` the weight of the parameters

## Details

the weight of parameters is defined by users;if you do not define the weight,the corresponding percent contributions of the parameters based on the principal component analysis scheme will be used instead

## Value

weighted Mahalanobis distance will be returned

Bingpei Wu

## References

passage: "APPLICATION OF WEIGHTED MAHALANOBIS DISTANCE DISCRIMINANT ANALYSIS METHOD TO CLASSIFICATION OF ROCK MASS QUALITY",whose author is YAO Yinpei

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. x=iris[1:50,1:4] center=colMeans(x) cov=var(x) weight=diag(rep(0.25,4)) wmahalanobis(x,center,cov,weight) ## The function is currently defined as function (x, center, cov, weight) { if (is.vector(x)) x = matrix(x, ncol = length(x)) else x=as.matrix(x) x <- sweep(x, 2, center) cov <- weight %*% solve(cov) retval <- diag(x %*% cov %*% t(x)) retval } ```

### Example output

```         1          2          3          4          5          6          7
0.11227845 0.52027354 0.32108378 0.42655174 0.19042135 0.92816184 0.85604903
8          9         10         11         12         13         14
0.08585981 0.74911912 0.80002148 0.47273815 0.50371984 0.73683328 1.76005248
15         16         17         18         19         20         21
2.55551925 1.91345081 1.43559218 0.15906369 1.29644367 0.40310318 1.33726468
22         23         24         25         26         27         28
0.68058880 2.76110699 1.80759383 2.43699346 0.94262760 0.63142180 0.20728231
29         30         31         32         33         34         35
0.33075371 0.54359893 0.49862653 1.22227788 1.92481960 1.31200598 0.31674524
36         37         38         39         40         41         42
0.82545609 1.43031746 0.77141225 0.81756152 0.14733683 0.42121179 3.08190967
43         44         45         46         47         48         49
1.05025964 3.07751443 2.15028994 0.54866294 0.68893557 0.37221693 0.31318194
50
0.12368898
function (x, center, cov, weight)
{
if (is.vector(x))
x = matrix(x, ncol = length(x))
else x = as.matrix(x)
x <- sweep(x, 2, center)
cov <- weight %*% solve(cov)
retval <- diag(x %*% cov %*% t(x))
retval
}
```

WMDB documentation built on May 2, 2019, 6:12 a.m.