msmbuilder.decomposition.tICA¶

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

Parameters:

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]. commute_mapping : bool, default=False If True, scale/weigh the projections by the sqrt(ti/2), yielding commute distance as described in [7].

Notes

This method was introduced originally in [R17], and has been applied to the analysis of molecular dynamics data in [R14], [R15], and [R16]. In [R14] and [R15], tICA was used as a dimensionality reduction technique before fitting other kinetic models.

Attributes

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)

Methods

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.

__init__(n_components=None, lag_time=1, shrinkage=None, kinetic_mapping=False, commute_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 : object Returns the instance itself.

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 : 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 : mapping of string to any Parameter names mapped to their values.

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 : object Returns the instance itself.

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 : array-like, shape (n_samples, n_components) TICA-projected features

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 : float 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.

References

[R21]

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:	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 : list of array-like, each of shape (n_samples_i, n_components)