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"""Principle Component Analysis (PCA) with PyTorch."""
# Copyright (C) 2022-2024 Intel Corporation
# SPDX-License-Identifier: Apache-2.0
import torch
from anomalib.models.components.base import DynamicBufferMixin
class PCA(DynamicBufferMixin):
"""Principle Component Analysis (PCA).
Args:
n_components (float): Number of components. Can be either integer number of components
or a ratio between 0-1.
Example:
>>> import torch
>>> from anomalib.models.components import PCA
Create a PCA model with 2 components:
>>> pca = PCA(n_components=2)
Create a random embedding and fit a PCA model.
>>> embedding = torch.rand(1000, 5).cuda()
>>> pca = PCA(n_components=2)
>>> pca.fit(embedding)
Apply transformation:
>>> transformed = pca.transform(embedding)
>>> transformed.shape
torch.Size([1000, 2])
"""
def __init__(self, n_components: int | float) -> None:
super().__init__()
self.n_components = n_components
self.register_buffer("singular_vectors", torch.Tensor())
self.register_buffer("mean", torch.Tensor())
self.register_buffer("num_components", torch.Tensor())
self.singular_vectors: torch.Tensor
self.singular_values: torch.Tensor
self.mean: torch.Tensor
self.num_components: torch.Tensor
def fit(self, dataset: torch.Tensor) -> None:
"""Fits the PCA model to the dataset.
Args:
dataset (torch.Tensor): Input dataset to fit the model.
Example:
>>> pca.fit(embedding)
>>> pca.singular_vectors
tensor([9.6053, 9.2763], device='cuda:0')
>>> pca.mean
tensor([0.4859, 0.4959, 0.4906, 0.5010, 0.5042], device='cuda:0')
"""
mean = dataset.mean(dim=0)
dataset -= mean
_, sig, v_h = torch.linalg.svd(dataset.double(), full_matrices=False)
num_components: int
if self.n_components <= 1:
variance_ratios = torch.cumsum(sig * sig, dim=0) / torch.sum(sig * sig)
num_components = torch.nonzero(variance_ratios >= self.n_components)[0]
else:
num_components = int(self.n_components)
self.num_components = torch.Tensor([num_components])
self.singular_vectors = v_h.transpose(-2, -1)[:, :num_components].float()
self.singular_values = sig[:num_components].float()
self.mean = mean
def fit_transform(self, dataset: torch.Tensor) -> torch.Tensor:
"""Fit and transform PCA to dataset.
Args:
dataset (torch.Tensor): Dataset to which the PCA if fit and transformed
Returns:
Transformed dataset
Example:
>>> pca.fit_transform(embedding)
>>> transformed_embedding = pca.fit_transform(embedding)
>>> transformed_embedding.shape
torch.Size([1000, 2])
"""
mean = dataset.mean(dim=0)
dataset -= mean
num_components = int(self.n_components)
self.num_components = torch.Tensor([num_components])
v_h = torch.linalg.svd(dataset)[-1]
self.singular_vectors = v_h.transpose(-2, -1)[:, :num_components]
self.mean = mean
return torch.matmul(dataset, self.singular_vectors)
def transform(self, features: torch.Tensor) -> torch.Tensor:
"""Transform the features based on singular vectors calculated earlier.
Args:
features (torch.Tensor): Input features
Returns:
Transformed features
Example:
>>> pca.transform(embedding)
>>> transformed_embedding = pca.transform(embedding)
>>> embedding.shape
torch.Size([1000, 5])
#
>>> transformed_embedding.shape
torch.Size([1000, 2])
"""
features -= self.mean
return torch.matmul(features, self.singular_vectors)
def inverse_transform(self, features: torch.Tensor) -> torch.Tensor:
"""Inverses the transformed features.
Args:
features (torch.Tensor): Transformed features
Returns:
Inverse features
Example:
>>> inverse_embedding = pca.inverse_transform(transformed_embedding)
>>> inverse_embedding.shape
torch.Size([1000, 5])
"""
return torch.matmul(features, self.singular_vectors.transpose(-2, -1))
def forward(self, features: torch.Tensor) -> torch.Tensor:
"""Transform the features.
Args:
features (torch.Tensor): Input features
Returns:
Transformed features
Example:
>>> pca(embedding).shape
torch.Size([1000, 2])
"""
return self.transform(features)
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