machine_learning.gaussian_mixture_model

README, Author - Md Ruman Islam (mailto:ruman23.github.io) Requirements:

  • numpy

  • matplotlib

Python:

  • 3.8+

Inputs:

  • data : a 2D numpy array of features.

  • n_components : number of Gaussian distributions (clusters) to fit.

  • max_iter : maximum number of EM iterations.

  • tol : convergence tolerance.

Usage:

  1. define ‘n_components’ value and ‘data’ features array

  2. initialize model:

    gmm = GaussianMixture(n_components=3, max_iter=100)

  3. fit model to data:

    gmm.fit(data)

  4. get cluster predictions:

    labels = gmm.predict(data)

  5. visualize results:

    gmm.plot_results(data)

Attributes

TAG

gmm

Classes

GaussianMixture

Gaussian Mixture Model implemented using the Expectation-Maximization algorithm.

Module Contents

class machine_learning.gaussian_mixture_model.GaussianMixture(n_components: int = 2, max_iter: int = 100, tol: float = 0.0001, seed: int | None = None)

Gaussian Mixture Model implemented using the Expectation-Maximization algorithm.

_compute_log_likelihood(data: numpy.typing.NDArray[numpy.float64]) → float

Compute total log-likelihood of the model.

Note: assumes the model parameters are already initialized.

Examples

>>> sample = np.array(
...     [[0.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 3.5]]
... )
>>> model = GaussianMixture(n_components=2, seed=0)
>>> model._initialize_parameters(sample)
>>> bool(np.isfinite(model._compute_log_likelihood(sample)))
True
_e_step(data: numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.float64]

Compute responsibilities (posterior probabilities).

Examples

>>> sample = np.array(
...     [[0.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 3.5]]
... )
>>> model = GaussianMixture(n_components=2, seed=0)
>>> model._initialize_parameters(sample)
>>> resp = model._e_step(sample)
>>> resp.shape
(4, 2)
>>> bool(np.allclose(resp.sum(axis=1), 1.0))
True
_initialize_parameters(data: numpy.typing.NDArray[numpy.float64]) → None

Randomly initialize means, covariances, and mixture weights.

Examples

>>> sample = np.array(
...     [[0.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 3.5]]
... )
>>> model = GaussianMixture(n_components=2, seed=0)
>>> model._initialize_parameters(sample)
>>> model.means_.shape
(2, 2)
>>> bool(np.isclose(model.weights_.sum(), 1.0))
True
_m_step(data: numpy.typing.NDArray[numpy.float64], responsibilities: numpy.typing.NDArray[numpy.float64]) → None

Update weights, means, and covariances.

Note: assumes the model parameters are already initialized.

Examples

>>> sample = np.array(
...     [[0.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 3.5]]
... )
>>> model = GaussianMixture(n_components=2, seed=0)
>>> model._initialize_parameters(sample)
>>> resp = model._e_step(sample)
>>> model._m_step(sample, resp)
>>> bool(np.isclose(model.weights_.sum(), 1.0))
True
fit(data: numpy.typing.NDArray[numpy.float64]) → None

Fit the Gaussian Mixture Model to data using the EM algorithm.

Examples

>>> sample = np.array(
...     [[0.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 3.5]]
... )
>>> model = GaussianMixture(n_components=2, max_iter=5, tol=1e-3, seed=0)
>>> model.fit(sample)
GAUSSIAN-MIXTURE/ ...
>>> len(model.log_likelihoods_) > 0
True
plot_results(data: numpy.typing.NDArray[numpy.float64]) → None

Visualize GMM clustering results (2D only).

Note: This method assumes self.means_ is initialized.

Examples

>>> sample = np.ones((3, 3))
>>> model = GaussianMixture()
>>> model.plot_results(sample)
GAUSSIAN-MIXTURE/ Plotting only supported for 2D data.
predict(data: numpy.typing.NDArray[numpy.float64]) → numpy.typing.NDArray[numpy.int_]

Predict cluster assignment for each data point.

Note: assumes the model parameters are already initialized.

Examples

>>> sample = np.array(
...     [[0.0, 0.5], [1.0, 1.5], [2.0, 2.5], [3.0, 3.5]]
... )
>>> model = GaussianMixture(n_components=2, max_iter=5, tol=1e-3, seed=0)
>>> model.fit(sample)
GAUSSIAN-MIXTURE/ ...
>>> labels = model.predict(sample)
>>> labels.shape
(4,)
covariances_: numpy.typing.NDArray[numpy.float64] | None = None
log_likelihoods_: list[float] = []
max_iter: int = 100
means_: numpy.typing.NDArray[numpy.float64] | None = None
n_components: int = 2
seed: int | None = None
tol: float = 0.0001
weights_: numpy.typing.NDArray[numpy.float64] | None = None
machine_learning.gaussian_mixture_model.TAG = 'GAUSSIAN-MIXTURE/ '
machine_learning.gaussian_mixture_model.gmm