"""Base class for mixture models."""
# Author: Wei Xue <xuewei4d@gmail.com>
# Modified by Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause
from __future__ import print_function
import warnings
from abc import ABCMeta, abstractmethod
from time import time
import numpy as np
from .. import cluster
from ..base import BaseEstimator
from ..base import DensityMixin
from ..externals import six
from ..exceptions import ConvergenceWarning
from ..utils import check_array, check_random_state
from ..utils.fixes import logsumexp
def _check_shape(param, param_shape, name):
"""Validate the shape of the input parameter 'param'.
Parameters
----------
param : array
param_shape : tuple
name : string
"""
param = np.array(param)
if param.shape != param_shape:
raise ValueError("The parameter '%s' should have the shape of %s, "
"but got %s" % (name, param_shape, param.shape))
def _check_X(X, n_components=None, n_features=None):
"""Check the input data X.
Parameters
----------
X : array-like, shape (n_samples, n_features)
n_components : int
Returns
-------
X : array, shape (n_samples, n_features)
"""
X = check_array(X, dtype=[np.float64, np.float32])
if n_components is not None and X.shape[0] < n_components:
raise ValueError('Expected n_samples >= n_components '
'but got n_components = %d, n_samples = %d'
% (n_components, X.shape[0]))
if n_features is not None and X.shape[1] != n_features:
raise ValueError("Expected the input data X have %d features, "
"but got %d features"
% (n_features, X.shape[1]))
return X
class BaseMixture(six.with_metaclass(ABCMeta, DensityMixin, BaseEstimator)):
"""Base class for mixture models.
This abstract class specifies an interface for all mixture classes and
provides basic common methods for mixture models.
"""
def __init__(self, n_components, tol, reg_covar,
max_iter, n_init, init_params, random_state, warm_start,
verbose, verbose_interval):
self.n_components = n_components
self.tol = tol
self.reg_covar = reg_covar
self.max_iter = max_iter
self.n_init = n_init
self.init_params = init_params
self.random_state = random_state
self.warm_start = warm_start
self.verbose = verbose
self.verbose_interval = verbose_interval
def _check_initial_parameters(self, X):
"""Check values of the basic parameters.
Parameters
----------
X : array-like, shape (n_samples, n_features)
"""
if self.n_components < 1:
raise ValueError("Invalid value for 'n_components': %d "
"Estimation requires at least one component"
% self.n_components)
if self.tol < 0.:
raise ValueError("Invalid value for 'tol': %.5f "
"Tolerance used by the EM must be non-negative"
% self.tol)
if self.n_init < 1:
raise ValueError("Invalid value for 'n_init': %d "
"Estimation requires at least one run"
% self.n_init)
if self.max_iter < 1:
raise ValueError("Invalid value for 'max_iter': %d "
"Estimation requires at least one iteration"
% self.max_iter)
if self.reg_covar < 0.:
raise ValueError("Invalid value for 'reg_covar': %.5f "
"regularization on covariance must be "
"non-negative"
% self.reg_covar)
# Check all the parameters values of the derived class
self._check_parameters(X)
@abstractmethod
def _check_parameters(self, X):
"""Check initial parameters of the derived class.
Parameters
----------
X : array-like, shape (n_samples, n_features)
"""
pass
def _initialize_parameters(self, X, random_state):
"""Initialize the model parameters.
Parameters
----------
X : array-like, shape (n_samples, n_features)
random_state : RandomState
A random number generator instance.
"""
n_samples, _ = X.shape
if self.init_params == 'kmeans':
resp = np.zeros((n_samples, self.n_components))
label = cluster.KMeans(n_clusters=self.n_components, n_init=1,
random_state=random_state).fit(X).labels_
resp[np.arange(n_samples), label] = 1
elif self.init_params == 'random':
resp = random_state.rand(n_samples, self.n_components)
resp /= resp.sum(axis=1)[:, np.newaxis]
else:
raise ValueError("Unimplemented initialization method '%s'"
% self.init_params)
self._initialize(X, resp)
@abstractmethod
def _initialize(self, X, resp):
"""Initialize the model parameters of the derived class.
Parameters
----------
X : array-like, shape (n_samples, n_features)
resp : array-like, shape (n_samples, n_components)
"""
pass
def fit(self, X, y=None):
"""Estimate model parameters with the EM algorithm.
The method fit the model `n_init` times and set the parameters with
which the model has the largest likelihood or lower bound. Within each
trial, the method iterates between E-step and M-step for `max_iter`
times until the change of likelihood or lower bound is less than
`tol`, otherwise, a `ConvergenceWarning` is raised.
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
-------
self
"""
X = _check_X(X, self.n_components)
self._check_initial_parameters(X)
# if we enable warm_start, we will have a unique initialisation
do_init = not(self.warm_start and hasattr(self, 'converged_'))
n_init = self.n_init if do_init else 1
max_lower_bound = -np.infty
self.converged_ = False
random_state = check_random_state(self.random_state)
n_samples, _ = X.shape
for init in range(n_init):
self._print_verbose_msg_init_beg(init)
if do_init:
self._initialize_parameters(X, random_state)
self.lower_bound_ = -np.infty
for n_iter in range(self.max_iter):
prev_lower_bound = self.lower_bound_
log_prob_norm, log_resp = self._e_step(X)
self._m_step(X, log_resp)
self.lower_bound_ = self._compute_lower_bound(
log_resp, log_prob_norm)
change = self.lower_bound_ - prev_lower_bound
self._print_verbose_msg_iter_end(n_iter, change)
if abs(change) < self.tol:
self.converged_ = True
break
self._print_verbose_msg_init_end(self.lower_bound_)
if self.lower_bound_ > max_lower_bound:
max_lower_bound = self.lower_bound_
best_params = self._get_parameters()
best_n_iter = n_iter
if not self.converged_:
warnings.warn('Initialization %d did not converge. '
'Try different init parameters, '
'or increase max_iter, tol '
'or check for degenerate data.'
% (init + 1), ConvergenceWarning)
self._set_parameters(best_params)
self.n_iter_ = best_n_iter
return self
def _e_step(self, X):
"""E step.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
log_prob_norm : float
Mean of the logarithms of the probabilities of each sample in X
log_responsibility : array, shape (n_samples, n_components)
Logarithm of the posterior probabilities (or responsibilities) of
the point of each sample in X.
"""
log_prob_norm, log_resp = self._estimate_log_prob_resp(X)
return np.mean(log_prob_norm), log_resp
@abstractmethod
def _m_step(self, X, log_resp):
"""M step.
Parameters
----------
X : array-like, shape (n_samples, n_features)
log_resp : array-like, shape (n_samples, n_components)
Logarithm of the posterior probabilities (or responsibilities) of
the point of each sample in X.
"""
pass
@abstractmethod
def _check_is_fitted(self):
pass
@abstractmethod
def _get_parameters(self):
pass
@abstractmethod
def _set_parameters(self, params):
pass
def score_samples(self, X):
"""Compute the weighted log probabilities for each sample.
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
-------
log_prob : array, shape (n_samples,)
Log probabilities of each data point in X.
"""
self._check_is_fitted()
X = _check_X(X, None, self.means_.shape[1])
return logsumexp(self._estimate_weighted_log_prob(X), axis=1)
def score(self, X, y=None):
"""Compute the per-sample average log-likelihood of the given data X.
Parameters
----------
X : array-like, shape (n_samples, n_dimensions)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
Returns
-------
log_likelihood : float
Log likelihood of the Gaussian mixture given X.
"""
return self.score_samples(X).mean()
def predict(self, X):
"""Predict the labels for the data samples in X using trained 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
-------
labels : array, shape (n_samples,)
Component labels.
"""
self._check_is_fitted()
X = _check_X(X, None, self.means_.shape[1])
return self._estimate_weighted_log_prob(X).argmax(axis=1)
def predict_proba(self, X):
"""Predict posterior probability of each component given the data.
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
-------
resp : array, shape (n_samples, n_components)
Returns the probability each Gaussian (state) in
the model given each sample.
"""
self._check_is_fitted()
X = _check_X(X, None, self.means_.shape[1])
_, log_resp = self._estimate_log_prob_resp(X)
return np.exp(log_resp)
def sample(self, n_samples=1):
"""Generate random samples from the fitted Gaussian distribution.
Parameters
----------
n_samples : int, optional
Number of samples to generate. Defaults to 1.
Returns
-------
X : array, shape (n_samples, n_features)
Randomly generated sample
y : array, shape (nsamples,)
Component labels
"""
self._check_is_fitted()
if n_samples < 1:
raise ValueError(
"Invalid value for 'n_samples': %d . The sampling requires at "
"least one sample." % (self.n_components))
_, n_features = self.means_.shape
rng = check_random_state(self.random_state)
n_samples_comp = rng.multinomial(n_samples, self.weights_)
if self.covariance_type == 'full':
X = np.vstack([
rng.multivariate_normal(mean, covariance, int(sample))
for (mean, covariance, sample) in zip(
self.means_, self.covariances_, n_samples_comp)])
elif self.covariance_type == "tied":
X = np.vstack([
rng.multivariate_normal(mean, self.covariances_, int(sample))
for (mean, sample) in zip(
self.means_, n_samples_comp)])
else:
X = np.vstack([
mean + rng.randn(sample, n_features) * np.sqrt(covariance)
for (mean, covariance, sample) in zip(
self.means_, self.covariances_, n_samples_comp)])
y = np.concatenate([j * np.ones(sample, dtype=int)
for j, sample in enumerate(n_samples_comp)])
return (X, y)
def _estimate_weighted_log_prob(self, X):
"""Estimate the weighted log-probabilities, log P(X | Z) + log weights.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
weighted_log_prob : array, shape (n_samples, n_component)
"""
return self._estimate_log_prob(X) + self._estimate_log_weights()
@abstractmethod
def _estimate_log_weights(self):
"""Estimate log-weights in EM algorithm, E[ log pi ] in VB algorithm.
Returns
-------
log_weight : array, shape (n_components, )
"""
pass
@abstractmethod
def _estimate_log_prob(self, X):
"""Estimate the log-probabilities log P(X | Z).
Compute the log-probabilities per each component for each sample.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
log_prob : array, shape (n_samples, n_component)
"""
pass
def _estimate_log_prob_resp(self, X):
"""Estimate log probabilities and responsibilities for each sample.
Compute the log probabilities, weighted log probabilities per
component and responsibilities for each sample in X with respect to
the current state of the model.
Parameters
----------
X : array-like, shape (n_samples, n_features)
Returns
-------
log_prob_norm : array, shape (n_samples,)
log p(X)
log_responsibilities : array, shape (n_samples, n_components)
logarithm of the responsibilities
"""
weighted_log_prob = self._estimate_weighted_log_prob(X)
log_prob_norm = logsumexp(weighted_log_prob, axis=1)
with np.errstate(under='ignore'):
# ignore underflow
log_resp = weighted_log_prob - log_prob_norm[:, np.newaxis]
return log_prob_norm, log_resp
def _print_verbose_msg_init_beg(self, n_init):
"""Print verbose message on initialization."""
if self.verbose == 1:
print("Initialization %d" % n_init)
elif self.verbose >= 2:
print("Initialization %d" % n_init)
self._init_prev_time = time()
self._iter_prev_time = self._init_prev_time
def _print_verbose_msg_iter_end(self, n_iter, diff_ll):
"""Print verbose message on initialization."""
if n_iter % self.verbose_interval == 0:
if self.verbose == 1:
print(" Iteration %d" % n_iter)
elif self.verbose >= 2:
cur_time = time()
print(" Iteration %d\t time lapse %.5fs\t ll change %.5f" % (
n_iter, cur_time - self._iter_prev_time, diff_ll))
self._iter_prev_time = cur_time
def _print_verbose_msg_init_end(self, ll):
"""Print verbose message on the end of iteration."""
if self.verbose == 1:
print("Initialization converged: %s" % self.converged_)
elif self.verbose >= 2:
print("Initialization converged: %s\t time lapse %.5fs\t ll %.5f" %
(self.converged_, time() - self._init_prev_time, ll))
