[GRASS-dev] Compute mahalanobis distance using Scipy

[Paulo van Breugel]

Thanks! I am traveling right now so will look at this as soon as I am back,
but this looks promising. Much appreciated.

On Fri, 30 Jan 2015 15:40 Glynn Clements <glynn at gclements.plus.com> wrote:

>
> Paulo van Breugel wrote:
>
> > I would like to compute a raster layer with for each raster cell the
> > mahalanobis distance to the centre of the environmental space formed by
> all
> > reference data points (raster cells). In R this can be done as explained
> > here [1].
> >
> > . I would like to do this using python only (no dependency on R). I came
> up
> > with the following, which works, but is very slow. I guess this is
> because
> > it loops over every raster cell to compute the mahalanobis distance? Any
> > idea how this can be done faster (I am very new to python, so bear with
> me
> > if I am making stupid mistakes)
>
> The main speed-up will come from "inlining" distance.mahalanobis(),
> which is essentially:
>
>     delta = u - v
>     m = np.dot(np.dot(delta, VI), delta)
>     return np.sqrt(m)
>
> np.dot(v, m) is equivalent to np.sum(v * m,axis=0), and np.dot(u,v) is
> equivalent to np.sum(u * v), so the second line above is equivalent to
>
>     m = np.sum(np.sum(delta[:,None] * VI * delta[None,:], axis=-1),
> axis=-1)
>
> Thus, delta can be extended from a 1-D array to 3-D, changing the
> result from a scalar to a 2-D array. The calculation of stat_mah then
> becomes:
>
>     VI = np.linalg.inv(covar)
>     delta = dat_ref - stat_mean[:,None,None]
>     m = np.sum(np.sum(delta[:,:,:,None] * delta[:,:,None,:] *
> VI[None,None,:,:],axis=-1),axis=-1)
>     stat_mah = np.sqrt(m)
>
> This moves the loops from Python into C, which usually results in a
> significant speed increase.
>
> --
> Glynn Clements <glynn at gclements.plus.com>
>
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