def my_kernelPCA(kernel):
pca_traj.superpose(
pca_traj, 0, atom_indices=sele_grp
) # Superpose each conformation in the trajectory upon first frame
sele_trj = pca_traj.xyz[:,
sele_grp, :] # select coordinates of selected atom groups
sele_traj_reshaped = sele_trj.reshape(pca_traj.n_frames, len(sele_grp) * 3)
sele_traj_reshaped = sele_traj_reshaped.astype(
float) ## to avoid numpy Conversion Error during scaling
sele_traj_reshaped_scaled = preprocessing.scale(
sele_traj_reshaped, axis=0, with_std=False) # center to the mean
kpca = KernelPCA(kernel=kernel, fit_inverse_transform=True, gamma=10)
kpca.fit(sele_traj_reshaped_scaled)
#print "Trace of the covariance matrix is: ", np.trace(kpca.get_covariance())
kpca_reduced = kpca.transform(sele_traj_reshaped_scaled)
#write plots
write_plots('kpca_projection', kpca_reduced, out_dir)
title = 'kPCA Projection'
write_fig('kpca_projection', kpca_reduced, out_dir, title)
#write variance
kpca_variance_fname = out_dir + '/kpca_variance'
np.savetxt(kpca_variance_fname, kpca.lambdas_)
pc1_cos = get_cosine(kpca_reduced, 0)
print 'cosine content of first PC=', pc1_cos
pc2_cos = get_cosine(kpca_reduced, 1)
print 'cosine content of second PC=', pc2_cos
pc3_cos = get_cosine(kpca_reduced, 2)
print 'cosine content of 3rd PC=', pc3_cos
pc4_cos = get_cosine(kpca_reduced, 3)
print 'cosine content of 4th PC=', pc4_cos
return
def mds(input, type):
'metric and nonmetric Multidimensional scaling'
seed = np.random.RandomState(seed=1)
#np.savetxt('mds_input.txt', input) ## testing value error
if type == 'nm':
nmds = MDS(n_components=100,
max_iter=3000,
metric=False,
random_state=seed,
dissimilarity="precomputed")
print("Performing non-metric MDS..")
npos = nmds.fit_transform(input)
# write PC plots
write_plots('nmds_projection', npos, out_dir)
title = 'nMDS Projection'
write_fig('nmds_projection', npos, out_dir, title)
# cosine content
pc1_cos = get_cosine(npos, 0)
print('cosine content of first PC=', pc1_cos)
pc2_cos = get_cosine(npos, 1)
print('cosine content of second PC=', pc2_cos)
pc3_cos = get_cosine(npos, 2)
print('cosine content of 3rd PC=', pc3_cos)
pc4_cos = get_cosine(npos, 3)
print('cosine content of 4th PC=', pc4_cos)
elif type == 'metric':
mmds = MDS(n_components=100,
max_iter=3000,
random_state=seed,
dissimilarity="precomputed")
print("Performing metric MDS..")
mpos = mmds.fit_transform(input)
# write PC plots
write_plots('mmds_projection', mpos, out_dir)
title = 'mMDS Projection'
write_fig('mmds_projection', mpos, out_dir, title)
# cosine content
pc1_cos = get_cosine(mpos, 0)
print('cosine content of first PC=', pc1_cos)
pc2_cos = get_cosine(mpos, 1)
print('cosine content of second PC=', pc2_cos)
pc3_cos = get_cosine(mpos, 2)
print('cosine content of 3rd PC=', pc3_cos)
pc4_cos = get_cosine(mpos, 3)
print('cosine content of 4th PC=', pc4_cos)
else:
print('ERROR: Please check -mt flag options by running mds.py -h')
return
def distance_pca(int_cord1):
'Internal Coordinate Based PCA'
pca = PCA(n_components=comp)
dpca = pca.fit(int_cord1)
dpca_reduced=dpca.transform(int_cord1)
write_plots('dpca_projection', dpca_reduced, out_dir)
write_pcs('dpca_pcs', dpca, out_dir)
title='internal coordinate PCA Projection'
write_fig('dpca_projection', dpca_reduced, out_dir, title)
pc1_cos=get_cosine(dpca_reduced, 0)
print 'cosine content of first PC=',pc1_cos
pc2_cos=get_cosine(dpca_reduced, 1)
print 'cosine content of second PC=', pc2_cos
pc3_cos=get_cosine(dpca_reduced, 2)
print 'cosine content of 3rd PC=',pc3_cos
pc4_cos=get_cosine(dpca_reduced, 3)
print 'cosine content of 4th PC=', pc4_cos
return;
def svd_pca(svd):
'single value decomposition based PCA'
pca_traj.superpose(
pca_traj, 0, atom_indices=sele_grp
) # Superpose each conformation in the trajectory upon first frame
sele_trj = pca_traj.xyz[:,
sele_grp, :] # select coordinates of selected atom groups
sele_traj_reshaped = sele_trj.reshape(pca_traj.n_frames, len(sele_grp) * 3)
sele_traj_reshaped = sele_traj_reshaped.astype(
float) ## to avoid numpy Conversion Error during scaling
sele_traj_reshaped_scaled = preprocessing.scale(
sele_traj_reshaped, axis=0, with_std=False) # center to the mean
pca_sele_traj = PCA(n_components=comp)
pca_sele_traj.fit(sele_traj_reshaped_scaled)
pca_sele_traj_reduced = pca_sele_traj.transform(sele_traj_reshaped_scaled)
print "Trace of the covariance matrix is: ", np.trace(
pca_sele_traj.get_covariance())
# write the plots
write_plots('pca_projection', pca_sele_traj_reduced, out_dir)
title = 'PCA Projection'
write_fig('pca_projection', pca_sele_traj_reduced, out_dir, title)
#write the pcs variance
write_pcs('pca_variance', pca_sele_traj, out_dir)
pc1_cos = get_cosine(pca_sele_traj_reduced, 0)
print 'cosine content of first PC=', pc1_cos
pc2_cos = get_cosine(pca_sele_traj_reduced, 1)
print 'cosine content of second PC=', pc2_cos
pc3_cos = get_cosine(pca_sele_traj_reduced, 2)
print 'cosine content of 3rd PC=', pc3_cos
pc4_cos = get_cosine(pca_sele_traj_reduced, 3)
print 'cosine content of 4th PC=', pc4_cos
return
def incremental_pca():
' normal PCA is very memory intesive. It can be problemetic for large dataset, \
since dataset is stored in memory. Incremental principal component analysis (IPCA) is \
typically used for such cases. '
pca_traj.superpose(
pca_traj, 0, atom_indices=sele_grp
) # Superpose each conformation in the trajectory upon first frame
sele_trj = pca_traj.xyz[:,
sele_grp, :] # select coordinates of selected atom groups
sele_traj_reshaped = sele_trj.reshape(pca_traj.n_frames, len(sele_grp) * 3)
sele_traj_reshaped = sele_traj_reshaped.astype(
float) ## to avoid numpy Conversion Error during scaling
sele_traj_reshaped_scaled = preprocessing.scale(
sele_traj_reshaped, axis=0, with_std=False) # center to the mean
ipca = IncrementalPCA()
ipca = ipca.fit(sele_traj_reshaped_scaled)
ipca_reduced = ipca.transform(sele_traj_reshaped_scaled)
#write plots
write_plots('ipca_projection', ipca_reduced, out_dir)
title = 'iPCA Projection'
write_fig('ipca_projection', ipca_reduced, out_dir, title)
#write variance
#np.savetxt('ipca_variance', kpca.lambdas_)
pc1_cos = get_cosine(ipca_reduced, 0)
print 'cosine content of first PC=', pc1_cos
pc2_cos = get_cosine(ipca_reduced, 1)
print 'cosine content of second PC=', pc2_cos
pc3_cos = get_cosine(ipca_reduced, 2)
print 'cosine content of 3rd PC=', pc3_cos
pc4_cos = get_cosine(ipca_reduced, 3)
print 'cosine content of 4th PC=', pc4_cos
return
def my_pca():
'eigenvales decomposition PCA'
pca_traj.superpose(
pca_traj, 0, atom_indices=sele_grp
) # Superpose each conformation in the trajectory upon first frame
sele_trj = pca_traj.xyz[:,
sele_grp, :] # select coordinates of selected atom groups
sele_traj_reshaped = sele_trj.reshape(pca_traj.n_frames, len(sele_grp) * 3)
#arr1=sele_traj_reshaped
sele_traj_reshaped = sele_traj_reshaped.astype(
float) ## to avoid numpy Conversion Error during scaling
sele_traj_reshaped_scaled = preprocessing.scale(
sele_traj_reshaped, axis=0, with_std=False) # center to the mean
arr = sele_traj_reshaped_scaled
#===============================================
# covariance matrix
cov_mat = np.corrcoef(arr, rowvar=False)
trj_eval, trj_evec = np.linalg.eig(cov_mat)
print "Trace of cov matrix is ", np.trace(cov_mat)
#=============================
# sanity check of calculated eigenvector and eigen values
# it must be cov matrix * eigen vector = eigen vector * eigen value
for i in range(len(trj_eval)):
eigv = trj_evec.real[:, i].reshape(
1,
len(trj_evec[:, 0]),
).T
np.testing.assert_array_almost_equal(cov_mat.dot(eigv),
trj_eval[i] * eigv,
decimal=3,
err_msg='',
verbose=True)
#=============================================
# sort the eigenvalues and eigenvector
sort_idx = trj_eval.argsort()[::-1]
trj_eval = trj_eval[sort_idx]
trj_evec = trj_evec[sort_idx]
tot_var = np.sum(trj_eval.real)
variation = []
cum = []
j = 0
eigv = []
n_comp = 100
pca = trj_evec.real[:, 0:n_comp] ## keep first 100 eigenvectors
for i in trj_eval.real[0:n_comp]:
eigv.append(i)
variation.append((i / tot_var) * 100)
j += 1
# write PC plot
pca_variance_fname = out_dir + '/pca_variance.agr'
np.savetxt(pca_variance_fname, variation)
ef = open(pca_variance_fname, 'r')
ef_cont = ef.read()
ef.close()
title = '\tcreated by pca.py\t'
my_time = strftime("%Y-%m-%d %a %H:%M:%S", gmtime())
legends = '@ title "explained_variance of PCs"\n\
@ xaxis label "PCs"\n\
@ yaxis label "% Variance"\n\
@ TYPE xy\n\
@ s0 symbol 1\n\
@ s0 symbol size 0.250000\n\
@ s0 symbol color 1\n\
@ s0 symbol pattern 1\n\
@ s0 symbol fill color 1\n\
@ s0 symbol fill pattern 1\n\
@ s0 symbol linewidth 1.0\n\
@ s0 symbol linestyle 1\n\
@ s0 symbol char 25\n\
@ s0 symbol fill color 2\n\
@ s0 symbol color 2\n\
@ s0 symbol char font 0\n\
@ s0 symbol skip 0\n'
ef = open(pca_variance_fname, 'w')
ef.write('#' + title + '\ton\t' + my_time + '\n' + legends + '\n' +
ef_cont + '\n')
ef.close()
#========================================================
# transform the input data into choosen pc
arr_transformed = arr.dot(pca)
#arr_transformed = pca.T.dot(arr.T)
print arr_transformed.shape
write_plots('pca_projection', arr_transformed, out_dir)
title = 'PCA Projection'
write_fig('pca_projection', arr_transformed, out_dir, title)
## RMSF
get_rmsf(pca_traj, sele_grp, trj_eval, out_dir)
pc1_cos = get_cosine(arr_transformed, 0)
print 'cosine content of first PC=', pc1_cos
pc2_cos = get_cosine(arr_transformed, 1)
print 'cosine content of second PC=', pc2_cos
pc3_cos = get_cosine(arr_transformed, 2)
print 'cosine content of 3rd PC=', pc3_cos
pc4_cos = get_cosine(arr_transformed, 3)
print 'cosine content of 4th PC=', pc4_cos
return
