msmbuilder.decomposition.tICA

class msmbuilder.decomposition.tICA(n_components=None, lag_time=1, shrinkage=None, kinetic_mapping=False)

Time-structure Independent Component Analysis (tICA)

Linear dimensionality reduction using an eigendecomposition of the time-lag correlation matrix and covariance matrix of the data and keeping only the vectors which decorrelate slowest to project the data into a lower dimensional space.

n_components
: int, None
Number of components to keep.
lag_time
: int
Delay time forward or backward in the input data. The time-lagged correlations is computed between datas X[t] and X[t+lag_time].
shrinkage
: float, default=None
The covariance shrinkage intensity (range 0-1). If shrinkage is not specified (the default) it is estimated using an analytic formula (the Rao-Blackwellized Ledoit-Wolf estimator) introduced in [5].
kinetic_mapping
: bool, default=False
If True, weigh the projections by the tICA eigenvalues, yielding
kinetic distances as described in [6].
components_
: array-like, shape (n_components, n_features)
Components with maximum autocorrelation.
offset_correlation_
: array-like, shape (n_features, n_features)
Symmetric time-lagged correlation matrix, \(C=E[(x_t)^T x_{t+lag}]\).
eigenvalues_
: array-like, shape (n_features,)
Eigenvalues of the tICA generalized eigenproblem, in decreasing order.
eigenvectors_
: array-like, shape (n_components, n_features)
Eigenvectors of the tICA generalized eigenproblem. The vectors give a set of “directions” through configuration space along which the system relaxes towards equilibrium. Each eigenvector is associated with characteritic timescale :math:`-
rac{lag_time}{ln lambda_i}, where \(lambda_i\) is
the corresponding eigenvector. See [2] for more information.
means_
: array, shape (n_features,)
The mean of the data along each feature
n_observations_
: int
Total number of data points fit by the model. Note that the model is “reset” by calling fit() with new sequences, whereas partial_fit() updates the fit with new data, and is suitable for online learning.
n_sequences_
: int

Total number of sequences fit by the model. Note that the model is “reset” by calling fit() with new sequences, whereas partial_fit() updates the fit with new data, and is suitable for

online learning.
timescales_
: array-like, shape (n_features,)
The implied timescales of the tICA model, given by -offset / log(eigenvalues)

This method was introduced originally in [4], and has been applied to the analysis of molecular dynamics data in [1]_, [2], and [3]. In [1]_ and [2], tICA was used as a dimensionality reduction technique before fitting other kinetic models.

[1]Schwantes, Christian R., and Vijay S. Pande. J. Chem Theory Comput. 9.4 (2013): 2000-2009.
[2](1, 2) Perez-Hernandez, Guillermo, et al. J Chem. Phys (2013): 015102.
[3]Naritomi, Yusuke, and Sotaro Fuchigami. J. Chem. Phys. 134.6 (2011): 065101.
[4]Molgedey, Lutz, and Heinz Georg Schuster. Phys. Rev. Lett. 72.23 (1994): 3634.
[5]Chen, Yilun, Ami Wiesel, and Alfred O. Hero III. ICASSP (2009)
[6]Noe, F. and Clementi, C. arXiv arXiv:1506.06259 [physics.comp-ph] (2015)
__init__(n_components=None, lag_time=1, shrinkage=None, kinetic_mapping=False)

Methods

__init__([n_components, lag_time, ...])
fit(sequences[, y]) Fit the model with a collection of sequences.
fit_transform(sequences[, y]) Fit the model with X and apply the dimensionality reduction on X.
get_params([deep]) Get parameters for this estimator.
partial_fit(X) Fit the model with X.
partial_transform(features) Apply the dimensionality reduction on X.
score(sequences[, y]) Score the model on new data using the generalized matrix Rayleigh quotient
set_params(\*\*params) Set the parameters of this estimator.
summarize() Some summary information.
transform(sequences) Apply the dimensionality reduction on X.

Attributes

components_
covariance_
eigenvalues_
eigenvectors_
means_
offset_correlation_
score_ Training score of the model, computed as the generalized matrix,
timescales_
fit(sequences, y=None)

Fit the model with a collection of sequences.

This method is not online. Any state accumulated from previous calls to fit() or partial_fit() will be cleared. For online learning, use partial_fit.

Parameters:
  • sequences (list of array-like, each of shape (n_samples_i, n_features)) – Training data, where n_samples_i in the number of samples in sequence i and n_features is the number of features.
  • y (None) – Ignored
Returns:

self – Returns the instance itself.
Return type:

object
fit_transform(sequences, y=None)

Fit the model with X and apply the dimensionality reduction on X.

This method is not online. Any state accumulated from previous calls to fit() or partial_fit() will be cleared. For online learning, use partial_fit.

Parameters:
  • sequences (list of array-like, each of shape (n_samples_i, n_features)) – Training data, where n_samples_i in the number of samples in sequence i and n_features is the number of features.
  • y (None) – Ignored
Returns:

sequence_new
Return type:

list of array-like, each of shape (n_samples_i, n_components)
get_params(deep=True)

Get parameters for this estimator.

Parameters:deep (boolean, optional) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:params – Parameter names mapped to their values.
Return type:mapping of string to any
partial_fit(X)

Fit the model with X.

This method is suitable for online learning. The state of the model will be updated with the new data X.

Parameters:X (array-like, shape (n_samples, n_features)) – Training data, where n_samples in the number of samples and n_features is the number of features.
Returns:self – Returns the instance itself.
Return type:object
partial_transform(features)

Apply the dimensionality reduction on X.

Parameters:features (array-like, shape (n_samples, n_features)) – Training data, where n_samples in the number of samples and n_features is the number of features. This function acts on a single featurized trajectory.
Returns:sequence_new – TICA-projected features
Return type:array-like, shape (n_samples, n_components)

Notes

This function acts on a single featurized trajectory.

score(sequences, y=None)

Score the model on new data using the generalized matrix Rayleigh quotient

Parameters:sequences (list of array, each of shape (n_samples_i, n_features)) – Test data. A list of sequences in afeature space, each of which is a 2D array of possibily different lengths, but the same number of features.
Returns:gmrq – Generalized matrix Rayleigh quotient. This number indicates how well the top n_timescales+1 eigenvectors of this tICA model perform as slowly decorrelating collective variables for the new data in sequences.
Return type:float

References

[1]McGibbon, R. T. and V. S. Pande, “Variational cross-validation of slow dynamical modes in molecular kinetics” J. Chem. Phys. 142, 124105 (2015)
score_

Training score of the model, computed as the generalized matrix, Rayleigh quotient, the sum of the first n_components eigenvalues

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:
Return type:self
summarize()

Some summary information.

transform(sequences)

Apply the dimensionality reduction on X.

Parameters:sequences (list of array-like, each of shape (n_samples_i, n_features)) – Training data, where n_samples_i in the number of samples in sequence i and n_features is the number of features.
Returns:sequence_new
Return type:list of array-like, each of shape (n_samples_i, n_components)