# Principal components analysis (PCA) with scikit-learn¶

scikit-learn is a machine learning library for python, with a very easy to use API and great documentation.

In [1]:
%matplotlib inline
from __future__ import print_function
import mdtraj as md
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA


Lets load up our trajectory. This is the trajectory that we generated in the "Running a simulation in OpenMM and analyzing the results with mdtraj" example.

In [2]:
traj = md.load('ala2.h5')
traj

Out[2]:
<mdtraj.Trajectory with 100 frames, 22 atoms, 3 residues, without unitcells at 0x2b46b6cefed0>

Create a two component PCA model, and project our data down into this reduced dimensional space. Using just the cartesian coordinates as input to PCA, it's important to start with some kind of alignment.

In [3]:
pca1 = PCA(n_components=2)
traj.superpose(traj, 0)

Out[3]:
<mdtraj.Trajectory with 100 frames, 22 atoms, 3 residues, without unitcells at 0x2b46b6cefed0>
In [4]:
reduced_cartesian = pca1.fit_transform(traj.xyz.reshape(traj.n_frames, traj.n_atoms * 3))
print(reduced_cartesian.shape)

(100, 2)


Now we can plot the data on this projection.

In [5]:
plt.figure()
plt.scatter(reduced_cartesian[:, 0], reduced_cartesian[:,1], marker='x', c=traj.time)
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.title('Cartesian coordinate PCA: alanine dipeptide')
cbar = plt.colorbar()
cbar.set_label('Time [ps]')


Lets try cross-checking our result by using a different feature space that isn't sensitive to alignment, and instead to "featurize" our trajectory by computing the pairwise distance between every atom in each frame, and using that as our high dimensional input space for PCA.

In [6]:
pca2 = PCA(n_components=2)

from itertools import combinations
# this python function gives you all unique pairs of elements from a list

atom_pairs = list(combinations(range(traj.n_atoms), 2))
pairwise_distances = md.geometry.compute_distances(traj, atom_pairs)
print(pairwise_distances.shape)
reduced_distances = pca2.fit_transform(pairwise_distances)

(100, 231)

In [7]:
plt.figure()
plt.scatter(reduced_distances[:, 0], reduced_distances[:,1], marker='x', c=traj.time)
plt.xlabel('PC1')
plt.ylabel('PC2')
plt.title('Pairwise distance PCA: alanine dipeptide')
cbar = plt.colorbar()
cbar.set_label('Time [ps]')

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