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Perform Nonmetric Multidimensional Scaling
==========================================
.. sectionauthor:: Justin Kuczynski
An example of how to use nmds.
.. doctest::
>>> 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)
.. doctest::
>>> 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
.. doctest::
>>> distmtx = dist_euclidean(abundance)
>>> nm = NMDS(distmtx, verbosity=0)
The NMDS object provides a list of points, which can be plotted if desired
.. doctest::
>>> pts = nm.getPoints()
>>> stress = nm.getStress()
With matplotlib installed, we could then do ``plt.plot(pts[:,0], pts[:,1])``
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