# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - initial API and implementation and/or initial
# documentation
# :author: Syver Doving Agdestein
# OTHER AUTHORS - MACROSCOPIC CHANGES
r"""The Gaussian mixture algorithm for clustering.
The Gaussian mixture algorithm groups the data into clusters.
The number of clusters is fixed.
Each cluster :math:`i=1, \\cdots, k` is defined
by a mean :math:`\\mu_i` and a covariance matrix :math:`\\Sigma_i`.
The prediction of the cluster value of a point is simply the cluster
where the probability density of the Gaussian distribution
defined by the given mean and covariance matrix
is the highest:
.. math::
\\operatorname{cluster}(x) =
\\underset{i=1,\\cdots,k}{\\operatorname{argmax}}
\\ \\mathcal{N}(x; \\mu_i, \\Sigma_i)
where :math:`\\mathcal{N}(x; \\mu_i, \\Sigma_i)` is the value
of the probability density function
of a Gaussian random variable :math:`X \\sim \\mathcal{N}(\\mu_i, \\Sigma_i)`
at the point :math:`x`
and :math:`\\|x-\\mu_i\\|_{\\Sigma_i^{-1}} =
\\sqrt{(x-\\mu_i)^T \\Sigma_i^{-1} (x-\\mu_i)}`
is the Mahalanobis distance between :math:`x`
and :math:`\\mu_i` weighted by :math:`\\Sigma_i`.
Likewise,
the probability of belonging to a cluster :math:`i=1, \\cdots, k`
may be determined through
.. math::
\\mathbb{P}(x \\in C_i) = \\frac{\\mathcal{N}(x; \\mu_i, \\Sigma_i)}
{\\sum_{j=1}^k \\mathcal{N}(x; \\mu_j, \\Sigma_j)},
where :math:`C_i = \\{x\\, | \\, \\operatorname{cluster}(x) = i \\}`.
When fitting the algorithm,
the cluster centers :math:`\\mu_i` and the covariance matrices :math:`\\Sigma_i`
are computed using the expectation-maximization algorithm.
This concept is implemented through the :class:`.GaussianMixture` class
which inherits from the :class:`.BaseMLClusteringAlgo` class.
Dependence
----------
This clustering algorithm relies on the GaussianMixture class
of the `scikit-learn library <https://scikit-learn.org/stable/modules/
generated/sklearn.mixture.GaussianMixture.html>`_.
"""
from __future__ import annotations
from typing import TYPE_CHECKING
from typing import ClassVar
from typing import NoReturn
from sklearn.mixture import GaussianMixture as SKLGaussianMixture
from gemseo.mlearning.clustering.clustering import BaseMLPredictiveClusteringAlgo
from gemseo.utils.seeder import SEED
if TYPE_CHECKING:
from collections.abc import Iterable
from numpy import ndarray
from gemseo.datasets.dataset import Dataset
from gemseo.mlearning.core.ml_algo import TransformerType
[docs]
class GaussianMixture(BaseMLPredictiveClusteringAlgo):
"""The Gaussian mixture clustering algorithm."""
SHORT_ALGO_NAME: ClassVar[str] = "GMM"
LIBRARY: ClassVar[str] = "scikit-learn"
def __init__(
self,
data: Dataset,
transformer: TransformerType = BaseMLPredictiveClusteringAlgo.IDENTITY,
var_names: Iterable[str] | None = None,
n_components: int = 5,
random_state: int | None = SEED,
**parameters: int | float | str | bool | None,
) -> None:
"""
Args:
n_components: The number of components of the Gaussian mixture.
random_state: The random state passed to the random number generator.
Use an integer for reproducible results.
""" # noqa: D205 D212
super().__init__(
data,
transformer=transformer,
var_names=var_names,
n_components=n_components,
random_state=random_state,
**parameters,
)
self.algo = SKLGaussianMixture(
n_components, random_state=random_state, **parameters
)
def _fit(
self,
data: ndarray,
) -> NoReturn:
self.algo.fit(data)
self.labels = self.algo.predict(data)
def _predict(
self,
data: ndarray,
) -> ndarray:
return self.algo.predict(data)
def _predict_proba_soft(
self,
data: ndarray,
) -> ndarray:
return self.algo.predict_proba(data)
