msmbuilder.cluster.GMM

class msmbuilder.cluster.GMM(n_components=1, covariance_type='diag', random_state=None, thresh=None, tol=0.001, min_covar=0.001, n_iter=100, n_init=1, params='wmc', init_params='wmc', verbose=0)

Gaussian Mixture Model

Representation of a Gaussian mixture model probability distribution. This class allows for easy evaluation of, sampling from, and maximum-likelihood estimation of the parameters of a GMM distribution.

Initializes parameters such that every mixture component has zero mean and identity covariance.

Read more in the User Guide.

Parameters:

n_components : int, optional

Number of mixture components. Defaults to 1.

covariance_type : string, optional

String describing the type of covariance parameters to use. Must be one of ‘spherical’, ‘tied’, ‘diag’, ‘full’. Defaults to ‘diag’.

random_state: RandomState or an int seed (None by default)

A random number generator instance

min_covar : float, optional

Floor on the diagonal of the covariance matrix to prevent overfitting. Defaults to 1e-3.

tol : float, optional

Convergence threshold. EM iterations will stop when average gain in log-likelihood is below this threshold. Defaults to 1e-3.

n_iter : int, optional

Number of EM iterations to perform.

n_init : int, optional

Number of initializations to perform. the best results is kept

params : string, optional

Controls which parameters are updated in the training process. Can contain any combination of ‘w’ for weights, ‘m’ for means, and ‘c’ for covars. Defaults to ‘wmc’.

init_params : string, optional

Controls which parameters are updated in the initialization process. Can contain any combination of ‘w’ for weights, ‘m’ for means, and ‘c’ for covars. Defaults to ‘wmc’.

verbose : int, default: 0

Enable verbose output. If 1 then it always prints the current initialization and iteration step. If greater than 1 then it prints additionally the change and time needed for each step.

See also

DPGMM
Infinite gaussian mixture model, using the dirichlet process, fit with a variational algorithm
VBGMM
Finite gaussian mixture model fit with a variational algorithm, better for situations where there might be too little data to get a good estimate of the covariance matrix.

Examples

>>> import numpy as np
>>> from sklearn import mixture
>>> np.random.seed(1)
>>> g = mixture.GMM(n_components=2)
>>> # Generate random observations with two modes centered on 0
>>> # and 10 to use for training.
>>> obs = np.concatenate((np.random.randn(100, 1),
...                       10 + np.random.randn(300, 1)))
>>> g.fit(obs) 
GMM(covariance_type='diag', init_params='wmc', min_covar=0.001,
        n_components=2, n_init=1, n_iter=100, params='wmc',
        random_state=None, thresh=None, tol=0.001, verbose=0)
>>> np.round(g.weights_, 2)
array([ 0.75,  0.25])
>>> np.round(g.means_, 2)
array([[ 10.05],
       [  0.06]])
>>> np.round(g.covars_, 2) 
array([[[ 1.02]],
       [[ 0.96]]])
>>> g.predict([[0], [2], [9], [10]]) 
array([1, 1, 0, 0]...)
>>> np.round(g.score([[0], [2], [9], [10]]), 2)
array([-2.19, -4.58, -1.75, -1.21])
>>> # Refit the model on new data (initial parameters remain the
>>> # same), this time with an even split between the two modes.
>>> g.fit(20 * [[0]] +  20 * [[10]]) 
GMM(covariance_type='diag', init_params='wmc', min_covar=0.001,
        n_components=2, n_init=1, n_iter=100, params='wmc',
        random_state=None, thresh=None, tol=0.001, verbose=0)
>>> np.round(g.weights_, 2)
array([ 0.5,  0.5])

Attributes

weights_ (array, shape (n_components,)) This attribute stores the mixing weights for each mixture component.
means_ (array, shape (n_components, n_features)) Mean parameters for each mixture component.
covars_ (array) Covariance parameters for each mixture component. The shape depends on covariance_type:: (n_components, n_features) if ‘spherical’, (n_features, n_features) if ‘tied’, (n_components, n_features) if ‘diag’, (n_components, n_features, n_features) if ‘full’
converged_ (bool) True when convergence was reached in fit(), False otherwise.

Methods

aic(X) Akaike information criterion for the current model fit
bic(X) Bayesian information criterion for the current model fit
fit(sequences[, y]) Fit the clustering on the data
fit_predict(sequences[, y]) Performs clustering on X and returns cluster labels.
fit_transform(sequences[, y]) Alias for fit_predict
get_params([deep]) Get parameters for this estimator.
partial_predict(X[, y]) Predict the closest cluster each sample in X belongs to.
partial_transform(X) Alias for partial_predict
predict(sequences[, y]) Predict the closest cluster each sample in each sequence in sequences belongs to.
predict_proba(X) Predict posterior probability of data under each Gaussian in the model.
sample([n_samples, random_state]) Generate random samples from the model.
score(X[, y]) Compute the log probability under the model.
score_samples(X) Return the per-sample likelihood of the data under the model.
set_params(**params) Set the parameters of this estimator.
summarize() Return some diagnostic summary statistics about this Markov model
transform(sequences) Alias for predict
__init__(n_components=1, covariance_type='diag', random_state=None, thresh=None, tol=0.001, min_covar=0.001, n_iter=100, n_init=1, params='wmc', init_params='wmc', verbose=0)

Methods

__init__([n_components, covariance_type, ...])
aic(X) Akaike information criterion for the current model fit
bic(X) Bayesian information criterion for the current model fit
fit(sequences[, y]) Fit the clustering on the data
fit_predict(sequences[, y]) Performs clustering on X and returns cluster labels.
fit_transform(sequences[, y]) Alias for fit_predict
get_params([deep]) Get parameters for this estimator.
partial_predict(X[, y]) Predict the closest cluster each sample in X belongs to.
partial_transform(X) Alias for partial_predict
predict(sequences[, y]) Predict the closest cluster each sample in each sequence in sequences belongs to.
predict_proba(X) Predict posterior probability of data under each Gaussian in the model.
sample([n_samples, random_state]) Generate random samples from the model.
score(X[, y]) Compute the log probability under the model.
score_samples(X) Return the per-sample likelihood of the data under the model.
set_params(**params) Set the parameters of this estimator.
summarize() Return some diagnostic summary statistics about this Markov model
transform(sequences) Alias for predict
aic(X)

Akaike information criterion for the current model fit and the proposed data

Parameters:X : array of shape(n_samples, n_dimensions)
Returns:aic: float (the lower the better)
bic(X)

Bayesian information criterion for the current model fit and the proposed data

Parameters:X : array of shape(n_samples, n_dimensions)
Returns:bic: float (the lower the better)
fit(sequences, y=None)

Fit the clustering on the data

Parameters:

sequences : list of array-like, each of shape [sequence_length, n_features]

A list of multivariate timeseries. Each sequence may have a different length, but they all must have the same number of features.
Returns:

self
fit_predict(sequences, y=None)

Performs clustering on X and returns cluster labels.

Parameters:

sequences : list of array-like, each of shape [sequence_length, n_features]

A list of multivariate timeseries. Each sequence may have a different length, but they all must have the same number of features.
Returns:

Y : list of ndarray, each of shape [sequence_length, ]

Cluster labels
fit_transform(sequences, y=None)

Alias for fit_predict

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_predict(X, y=None)

Predict the closest cluster each sample in X belongs to.

In the vector quantization literature, cluster_centers_ is called the code book and each value returned by predict is the index of the closest code in the code book.

Parameters:

X : array-like shape=(n_samples, n_features)

A single timeseries.
Returns:

Y : array, shape=(n_samples,)

Index of the cluster that each sample belongs to
partial_transform(X)

Alias for partial_predict

predict(sequences, y=None)

Predict the closest cluster each sample in each sequence in sequences belongs to.

In the vector quantization literature, cluster_centers_ is called the code book and each value returned by predict is the index of the closest code in the code book.

Parameters:

sequences : list of array-like, each of shape [sequence_length, n_features]

A list of multivariate timeseries. Each sequence may have a different length, but they all must have the same number of features.
Returns:

Y : list of arrays, each of shape [sequence_length,]

Index of the closest center each sample belongs to.
predict_proba(X)

Predict posterior probability of data under each Gaussian in the model.

Parameters:

X : array-like, shape = [n_samples, n_features]
Returns:

responsibilities : array-like, shape = (n_samples, n_components)

Returns the probability of the sample for each Gaussian (state) in the model.
sample(n_samples=1, random_state=None)

Generate random samples from the model.

Parameters:

n_samples : int, optional

Number of samples to generate. Defaults to 1.
Returns:

X : array_like, shape (n_samples, n_features)

List of samples
score(X, y=None)

Compute the log probability under the model.

Parameters:

X : array_like, shape (n_samples, n_features)

List of n_features-dimensional data points. Each row corresponds to a single data point.
Returns:

logprob : array_like, shape (n_samples,)

Log probabilities of each data point in X
score_samples(X)

Return the per-sample likelihood of the data under the model.

Compute the log probability of X under the model and return the posterior distribution (responsibilities) of each mixture component for each element of X.

Parameters:

X: array_like, shape (n_samples, n_features)

List of n_features-dimensional data points. Each row corresponds to a single data point.
Returns:

logprob : array_like, shape (n_samples,)

Log probabilities of each data point in X.

responsibilities : array_like, shape (n_samples, n_components)

Posterior probabilities of each mixture component for each observation
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 former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:self
summarize()

Return some diagnostic summary statistics about this Markov model

transform(sequences)

Alias for predict