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"""Pytorch implementation of Gaussian Mixture Model."""
# Copyright (C) 2023-2024 Intel Corporation
# SPDX-License-Identifier: Apache-2.0
import logging
import torch
from torch.distributions.multivariate_normal import MultivariateNormal
from torch.nn.functional import one_hot
from anomalib.models.components.base import DynamicBufferMixin
from anomalib.models.components.cluster.kmeans import KMeans
logger = logging.getLogger(__name__)
class GaussianMixture(DynamicBufferMixin):
"""Gaussian Mixture Model.
Args:
n_components (int): Number of components.
n_iter (int): Maximum number of iterations to perform.
Defaults to ``100``.
tol (float): Convergence threshold.
Defaults to ``1e-3``.
Example:
The following examples shows how to fit a Gaussian Mixture Model to some data and get the cluster means and
predicted labels and log-likelihood scores of the data.
.. code-block:: python
>>> import torch
>>> from anomalib.models.components.cluster import GaussianMixture
>>> model = GaussianMixture(n_components=2)
>>> data = torch.tensor(
... [
... [2, 1], [2, 2], [2, 3],
... [7, 5], [8, 5], [9, 5],
... ]
... ).float()
>>> model.fit(data)
>>> model.means # get the means of the gaussians
tensor([[8., 5.],
[2., 2.]])
>>> model.predict(data) # get the predicted cluster label of each sample
tensor([1, 1, 1, 0, 0, 0])
>>> model.score_samples(data) # get the log-likelihood score of each sample
tensor([3.8295, 4.5795, 3.8295, 3.8295, 4.5795, 3.8295])
"""
def __init__(self, n_components: int, n_iter: int = 100, tol: float = 1e-3) -> None:
super().__init__()
self.n_components = n_components
self.tol = tol
self.n_iter = n_iter
self.register_buffer("means", torch.Tensor())
self.register_buffer("covariances", torch.Tensor())
self.register_buffer("weights", torch.Tensor())
self.means: torch.Tensor
self.covariances: torch.Tensor
self.weights: torch.Tensor
def fit(self, data: torch.Tensor) -> None:
"""Fit the model to the data.
Args:
data (Tensor): Data to fit the model to. Tensor of shape (n_samples, n_features).
"""
self._initialize_parameters_kmeans(data)
log_likelihood_old = 0
converged = False
for _ in range(self.n_iter):
# E-step
log_likelihood_new, resp = self._e_step(data)
# M-step
self._m_step(data, resp)
# Check for convergence
if torch.abs(log_likelihood_new - log_likelihood_old) < self.tol:
converged = True
break
log_likelihood_old = log_likelihood_new
if not converged:
logger.warning(
f"GMM did not converge after {self.n_iter} iterations. \
Consider increasing the number of iterations.",
)
def _initialize_parameters_kmeans(self, data: torch.Tensor) -> None:
"""Initialize parameters with K-means.
Args:
data (Tensor): Data to fit the model to. Tensor of shape (n_samples, n_features).
"""
labels, _ = KMeans(n_clusters=self.n_components).fit(data)
resp = one_hot(labels, num_classes=self.n_components).float()
self._m_step(data, resp)
def _e_step(self, data: torch.Tensor) -> torch.Tensor:
"""Perform the E-step to estimate the responsibilities of the gaussians.
Args:
data (Tensor): Data to fit the model to. Tensor of shape (n_samples, n_features).
Returns:
Tensor: log probability of the data given the gaussians.
Tensor: Tensor of shape (n_samples, n_components) containing the responsibilities.
"""
weighted_log_prob = self._estimate_weighted_log_prob(data)
log_prob_norm = torch.logsumexp(weighted_log_prob, axis=1)
log_resp = weighted_log_prob - torch.logsumexp(weighted_log_prob, dim=1, keepdim=True)
return torch.mean(log_prob_norm), torch.exp(log_resp)
def _m_step(self, data: torch.Tensor, resp: torch.Tensor) -> None:
"""Perform the M-step to update the parameters of the gaussians.
Args:
data (Tensor): Data to fit the model to. Tensor of shape (n_samples, n_features).
resp (Tensor): Tensor of shape (n_samples, n_components) containing the responsibilities.
"""
cluster_counts = resp.sum(axis=0) # number of points in each cluster
self.weights = resp.mean(axis=0) # new weights
self.means = (resp.T @ data) / cluster_counts[:, None] # new means
diff = data.unsqueeze(0) - self.means.unsqueeze(1)
weighted_diff = diff * resp.T.unsqueeze(-1)
covariances = torch.bmm(weighted_diff.transpose(-2, -1), diff) / cluster_counts.view(-1, 1, 1)
# Add a small constant for numerical stability
self.covariances = covariances + torch.eye(data.shape[1], device=data.device) * 1e-6 # new covariances
def _estimate_weighted_log_prob(self, data: torch.Tensor) -> torch.Tensor:
"""Estimate the log probability of the data given the gaussian parameters.
Args:
data (Tensor): Data to fit the model to. Tensor of shape (n_samples, n_features).
Returns:
Tensor: Tensor of shape (n_samples, n_components) containing the log-probabilities of each sample.
"""
log_prob = torch.stack(
[
MultivariateNormal(self.means[comp], self.covariances[comp]).log_prob(data)
for comp in range(self.n_components)
],
dim=1,
)
return log_prob + torch.log(self.weights)
def score_samples(self, data: torch.Tensor) -> torch.Tensor:
"""Assign a likelihood score to each sample in the data.
Args:
data (Tensor): Samples to assign scores to. Tensor of shape (n_samples, n_features).
Returns:
Tensor: Tensor of shape (n_samples,) containing the log-likelihood score of each sample.
"""
return torch.logsumexp(self._estimate_weighted_log_prob(data), dim=1)
def predict(self, data: torch.Tensor) -> torch.Tensor:
"""Predict the cluster labels of the data.
Args:
data (Tensor): Samples to assign to clusters. Tensor of shape (n_samples, n_features).
Returns:
Tensor: Tensor of shape (n_samples,) containing the predicted cluster label of each sample.
"""
_, resp = self._e_step(data)
return torch.argmax(resp, axis=1)
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