Perform Nonmetric Multidimensional Scaling

Section author: Justin Kuczynski

An example of how to use nmds.

>>> from cogent.cluster.nmds import NMDS
>>> from cogent.maths.distance_transform import dist_euclidean
>>> from numpy import array

We start with an abundance matrix, samples (rows) by sequences/species (cols)

>>> abundance = array(
...        [[7,1,0,0,0,0,0,0,0],
...        [4,2,0,0,0,1,0,0,0],
...        [2,4,0,0,0,1,0,0,0],
...        [1,7,0,0,0,0,0,0,0],
...        [0,8,0,0,0,0,0,0,0],
...        [0,7,1,0,0,0,0,0,0],#idx 5
...        [0,4,2,0,0,0,2,0,0],
...        [0,2,4,0,0,0,1,0,0],
...        [0,1,7,0,0,0,0,0,0],
...        [0,0,8,0,0,0,0,0,0],
...        [0,0,7,1,0,0,0,0,0],#idx 10
...        [0,0,4,2,0,0,0,3,0],
...        [0,0,2,4,0,0,0,1,0],
...        [0,0,1,7,0,0,0,0,0],
...        [0,0,0,8,0,0,0,0,0],
...        [0,0,0,7,1,0,0,0,0],#idx 15
...        [0,0,0,4,2,0,0,0,4],
...        [0,0,0,2,4,0,0,0,1],
...        [0,0,0,1,7,0,0,0,0]], 'float')

Then compute a distance matrix of your choosing, and perform nmds on that matrix

>>> distmtx = dist_euclidean(abundance)
>>> nm = NMDS(distmtx, verbosity=0)

The NMDS object provides a list of points, which can be plotted if desired

>>> pts = nm.getPoints()
>>> stress = nm.getStress()

With matplotlib installed, we could then do plt.plot(pts[:,0], pts[:,1])