Source code for gemseo.mlearning.clustering.algos.gaussian_mixture

# 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:`.BaseClusterer` 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 sklearn.mixture import GaussianMixture as SKLGaussianMixture

from gemseo.mlearning.clustering.algos.base_predictive_clusterer import (
    BasePredictiveClusterer,
)
from gemseo.mlearning.clustering.algos.gaussian_mixture_settings import (
    GaussianMixture_Settings,
)

if TYPE_CHECKING:
    from numpy import ndarray

    from gemseo.typing import RealArray




class GaussianMixture(BasePredictiveClusterer):
    """The Gaussian mixture clustering algorithm."""

    SHORT_ALGO_NAME: ClassVar[str] = "GMM"
    LIBRARY: ClassVar[str] = "scikit-learn"

    Settings: ClassVar[type[GaussianMixture_Settings]] = GaussianMixture_Settings

    def _post_init(self):
        super()._post_init()
        self.algo = SKLGaussianMixture(
            n_components=self._settings.n_clusters,
            random_state=self._settings.random_state,
            **self._settings.parameters,
        )

    def _fit(
        self,
        data: RealArray,
    ) -> None:
        self.algo.fit(data)
        self.labels = self.algo.predict(data)

    def _predict(
        self,
        data: RealArray,
    ) -> ndarray:
        return self.algo.predict(data)

    def _predict_proba_soft(
        self,
        data: RealArray,
    ) -> RealArray:
        return self.algo.predict_proba(data)