Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Mahalanobis distance

`d = mahal(Y,X)`

`d = mahal(Y,X)`

computes the Mahalanobis distance (in squared units) of each observation
in `Y`

from the reference sample in matrix `X`

.
If `Y`

is *n*-by-*m*,
where *n* is the number of observations and *m* is
the dimension of the data, `d`

is *n*-by-1. `X`

and `Y`

must
have the same number of columns, but can have different numbers of
rows. `X`

must have more rows than columns.

For observation `I`

, the Mahalanobis distance
is defined by `d(I) = (Y(I,:)-mu)*inv(SIGMA)*(Y(I,:)-mu)'`

,
where `mu`

and `SIGMA`

are the sample
mean and covariance of the data in `X`

. `mahal`

performs
an equivalent, but more efficient, computation.

Was this topic helpful?