Note
Go to the end to download the full example code.
Clustering Vectors#
This can be used to segment a 4-D STEM dataset into different clusters based on the diffraction pattern at each real space position.
import pyxem as pxm
from scipy.ndimage import gaussian_filter
import matplotlib.pyplot as plt
from sklearn.cluster import DBSCAN
# Getting the vectors for some dataset
s = pxm.data.mgo_nanocrystals()
s.data[s.data < 120] = 1
s.filter(gaussian_filter, sigma=(0.5, 0.5, 0, 0), inplace=True) # only in real space
s.template_match_disk(disk_r=3, subtract_min=False, inplace=True)
vectors = s.get_diffraction_vectors(threshold_abs=0.5, min_distance=3)
# Now we can convert the vectors into a 2D array of rows/columns
flat_vectors = (
vectors.flatten_diffraction_vectors()
) # flatten the vectors into a 2D array
scan = DBSCAN(eps=1.0, min_samples=2)
# It is very important that we first normalize the real and reciprocal space distances
# The column scale factors map the real space and reciprocal space distances to the same scale
# Here this means that the clustering algorithm operates on 10 nm in real space and .1 nm^-1 in
# reciprocal space based on the units for the vectors.
clustered = flat_vectors.cluster(
scan,
column_scale_factors=[10, 10, 0.05, 0.05],
columns=[0, 1, 2, 3],
min_vectors=40,
)
m, p = clustered.to_markers(s, alpha=0.8, get_polygons=True)
s.plot()
s.add_marker(m)
s.add_marker(p, plot_on_signal=False)
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vect = clustered.map_vectors(
pxm.utils.vectors.column_mean,
columns=[0, 1],
label_index=-1,
dtype=float,
shape=(2,),
)
plt.figure()
plt.scatter(vect[:, 1], vect[:, 0])
/home/docs/checkouts/readthedocs.org/user_builds/pyxem/envs/stable/lib/python3.10/site-packages/numpy/core/fromnumeric.py:3504: RuntimeWarning: Mean of empty slice.
return _methods._mean(a, axis=axis, dtype=dtype,
/home/docs/checkouts/readthedocs.org/user_builds/pyxem/envs/stable/lib/python3.10/site-packages/numpy/core/_methods.py:121: RuntimeWarning: invalid value encountered in divide
ret = um.true_divide(
<matplotlib.collections.PathCollection object at 0x7f97fc4d4ac0>
clusterer = DBSCAN(min_samples=2, eps=20)
clustered2 = clustered.cluster_labeled_vectors(method=clusterer)
m, p = clustered2.to_markers(s, alpha=0.8, get_polygons=True)
# This clustering is decent. It shows that there might be some small tilt boundaries in the data
# which segment some of the nano-crystals into different clusters. It also shows the effect of using
# a phosphor screen which has some pretty severe after glow. This results in a smearing of the
# features and elongated clusters along the scan direction.
s.plot()
s.add_marker(m)
s.add_marker(p, plot_on_signal=False)
7 : Clusters Found!
Total running time of the script: (0 minutes 40.975 seconds)