"""Base class for mixture models."""
# Author: Wei Xue <xuewei4d@gmail.com>
# Modified by Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause
import warnings
from abc import ABCMeta, abstractmethod
from time import time
from numbers import Integral, Real
import numpy as np
from scipy.special import logsumexp
from .. import cluster
from ..cluster import kmeans_plusplus
from ..base import BaseEstimator
from ..base import DensityMixin
from ..exceptions import ConvergenceWarning
from ..utils import check_random_state
from ..utils.validation import check_is_fitted
from ..utils._param_validation import Interval, StrOptions
def _check_shape(param, param_shape, name):
"""Validate the shape of the input parameter 'param'.
Parameters
----------
param : array
param_shape : tuple
name : str
"""
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)
)
class BaseMixture(DensityMixin, BaseEstimator, metaclass=ABCMeta):
"""Base class for mixture models.
This abstract class specifies an interface for all mixture classes and
provides basic common methods for mixture models.
"""
_parameter_constraints: dict = {
"n_components": [Interval(Integral, 1, None, closed="left")],
"tol": [Interval(Real, 0.0, None, closed="left")],
"reg_covar": [Interval(Real, 0.0, None, closed="left")],
"max_iter": [Interval(Integral, 0, None, closed="left")],
"n_init": [Interval(Integral, 1, None, closed="left")],
"init_params": [
StrOptions({"kmeans", "random", "random_from_data", "k-means++"})
],
"random_state": ["random_state"],
"warm_start": ["boolean"],
"verbose": ["verbose"],
"verbose_interval": [Interval(Integral, 1, None, closed="left")],
}
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
@abstractmethod
def _check_parameters(self, X):
"""Check initial parameters of the derived class.
Parameters
----------
X : array-like of shape (n_samples, n_features)
"""
pass
def _initialize_parameters(self, X, random_state):
"""Initialize the model parameters.
Parameters
----------
X : array-like of shape (n_samples, n_features)
random_state : RandomState
A random number generator instance that controls the random seed
used for the method chosen to initialize the parameters.
"""
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.uniform(size=(n_samples, self.n_components))
resp /= resp.sum(axis=1)[:, np.newaxis]
elif self.init_params == "random_from_data":
resp = np.zeros((n_samples, self.n_components))
indices = random_state.choice(
n_samples, size=self.n_components, replace=False
)
resp[indices, np.arange(self.n_components)] = 1
elif self.init_params == "k-means++":
resp = np.zeros((n_samples, self.n_components))
_, indices = kmeans_plusplus(
X,
self.n_components,
random_state=random_state,
)
resp[indices, np.arange(self.n_components)] = 1
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 of shape (n_samples, n_features)
resp : array-like of shape (n_samples, n_components)
"""
pass
def fit(self, X, y=None):
"""Estimate model parameters with the EM algorithm.
The method fits the model ``n_init`` times and sets 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.
If ``warm_start`` is ``True``, then ``n_init`` is ignored and a single
initialization is performed upon the first call. Upon consecutive
calls, training starts where it left off.
Parameters
----------
X : array-like of shape (n_samples, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
The fitted mixture.
"""
# parameters are validated in fit_predict
self.fit_predict(X, y)
return self
def fit_predict(self, X, y=None):
"""Estimate model parameters using X and predict the labels for X.
The method fits the model n_init times and sets 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 :class:`~sklearn.exceptions.ConvergenceWarning` is
raised. After fitting, it predicts the most probable label for the
input data points.
.. versionadded:: 0.20
Parameters
----------
X : array-like of shape (n_samples, n_features)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
labels : array, shape (n_samples,)
Component labels.
"""
self._validate_params()
X = self._validate_data(X, dtype=[np.float64, np.float32], ensure_min_samples=2)
if X.shape[0] < self.n_components:
raise ValueError(
"Expected n_samples >= n_components "
f"but got n_components = {self.n_components}, "
f"n_samples = {X.shape[0]}"
)
self._check_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.inf
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)
lower_bound = -np.inf if do_init else self.lower_bound_
if self.max_iter == 0:
best_params = self._get_parameters()
best_n_iter = 0
else:
for n_iter in range(1, self.max_iter + 1):
prev_lower_bound = lower_bound
log_prob_norm, log_resp = self._e_step(X)
self._m_step(X, log_resp)
lower_bound = self._compute_lower_bound(log_resp, log_prob_norm)
change = 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(lower_bound)
if lower_bound > max_lower_bound or max_lower_bound == -np.inf:
max_lower_bound = lower_bound
best_params = self._get_parameters()
best_n_iter = n_iter
# Should only warn about convergence if max_iter > 0, otherwise
# the user is assumed to have used 0-iters initialization
# to get the initial means.
if not self.converged_ and self.max_iter > 0:
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
self.lower_bound_ = max_lower_bound
# Always do a final e-step to guarantee that the labels returned by
# fit_predict(X) are always consistent with fit(X).predict(X)
# for any value of max_iter and tol (and any random_state).
_, log_resp = self._e_step(X)
return log_resp.argmax(axis=1)
def _e_step(self, X):
"""E step.
Parameters
----------
X : array-like of 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 of shape (n_samples, n_features)
log_resp : array-like of shape (n_samples, n_components)
Logarithm of the posterior probabilities (or responsibilities) of
the point of each sample in X.
"""
pass
@abstractmethod
def _get_parameters(self):
pass
@abstractmethod
def _set_parameters(self, params):
pass
def score_samples(self, X):
"""Compute the log-likelihood of each sample.
Parameters
----------
X : array-like of 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-likelihood of each sample in `X` under the current model.
"""
check_is_fitted(self)
X = self._validate_data(X, reset=False)
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 of shape (n_samples, n_dimensions)
List of n_features-dimensional data points. Each row
corresponds to a single data point.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
log_likelihood : float
Log-likelihood of `X` under the Gaussian mixture model.
"""
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 of 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.
"""
check_is_fitted(self)
X = self._validate_data(X, reset=False)
return self._estimate_weighted_log_prob(X).argmax(axis=1)
def predict_proba(self, X):
"""Evaluate the components' density for each sample.
Parameters
----------
X : array-like of 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)
Density of each Gaussian component for each sample in X.
"""
check_is_fitted(self)
X = self._validate_data(X, reset=False)
_, 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, default=1
Number of samples to generate.
Returns
-------
X : array, shape (n_samples, n_features)
Randomly generated sample.
y : array, shape (nsamples,)
Component labels.
"""
check_is_fitted(self)
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.standard_normal(size=(sample, n_features))
* np.sqrt(covariance)
for (mean, covariance, sample) in zip(
self.means_, self.covariances_, n_samples_comp
)
]
)
y = np.concatenate(
[np.full(sample, j, 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 of 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 of 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 of 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)
)