Eigenvalues associated with the eigenvectors of TICA

[qasimpars]

Hi,

I would calculate the (positional) variance associated with the first eigenvector of TICA but I don't know how to do that. Could you please tell me how I can get/write the eigenvalues associated the eigenvectors of TICA? Is there a command line for that?

Best,

[clonker]

Hi you can access them like this:

import pyemma
import deeptime
sys = deeptime.data.double_well_2d()
traj = sys.trajectory([[0, 0]], 10000)
print(traj.shape)
>> (10000, 2)

tica = pyemma.coordinates.tica(traj)
print(tica.eigenvalues)
>> array([ 0.0257529 , -0.00124387])

print(tica.eigenvectors)
>> array([[ 0.02641758,  0.00022611],
       [ 0.01163282, -0.0034579 ]])

Or using deeptime:

import deeptime
sys = deeptime.data.double_well_2d()
traj = sys.trajectory([[0, 0]], 10000)
print(traj.shape)

tica = deeptime.decomposition.TICA(lagtime=1).fit_fetch(traj)
print(tica.singular_values)
print(tica.singular_vectors_left)

[qasimpars]

Hi,

Thank you very much @clonker. It works. Sorry but I have two more questions about the variance:

1. How can I get the percentages of the variance associated with the first and the second eigenvectors of TICA (e.g. X% for eigenvector 1 and y% for eigenvector 2?
2. How can I get the total variance associated with all eigenvector of a trajectory?

Regards,

[clonker]

Hi,

this is not really how TICA works and I am not sure you even can associate a positional variance to TICs. You are probably thinking in terms of PCA, where you can identify a projection axis with variance captured in the data. Here however we look at covariances and autocovariances, so in particular at timelagged pairs of data and slow processes in the data. What you can do is look at feature correlations though.

[qasimpars]

Hi,

Thanks. How can I look at feature correlations of a trajectory using TICA? Can you recommend me a tutorial or something like that?

Best,

[clonker]

You can just access the feature_TIC_correlation attribute on an estimated TICA object. That will give you the correlation matrix between (mean free) input features and tics.