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 [R429ad44fa1ac-4], and has been applied to the analysis of molecular dynamics data in [R429ad44fa1ac-1], [R429ad44fa1ac-2], and [R429ad44fa1ac-3]. In [R429ad44fa1ac-1] and [R429ad44fa1ac-2], 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 :math:`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)¶: Initialize self. See help(type(self)) for accurate signature.

Methods

`__init__`([n_components, lag_time, …])	Initialize self.
`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, Rayleigh quotient, the sum of the first n_components eigenvalues
`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

[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:	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)