Source code for pyod.models.kpca

# -*- coding: utf-8 -*-
"""Kernel Principal Component Analysis (KPCA) Outlier Detector
"""
# Author: Akira Tamamori <tamamori5917@gmail.com>
# License: BSD 2 clause

import numpy as np
import sklearn
from sklearn.decomposition import KernelPCA
from sklearn.utils import check_array, check_random_state
from sklearn.utils.validation import check_is_fitted

from .base import BaseDetector
from ..utils.utility import check_parameter


[docs]class PyODKernelPCA(KernelPCA): """A wrapper class for KernelPCA class of scikit-learn.""" def __init__( self, n_components=None, kernel="rbf", gamma=None, degree=3, coef0=1, kernel_params=None, alpha=1.0, fit_inverse_transform=False, eigen_solver="auto", tol=0, max_iter=None, remove_zero_eig=False, copy_X=True, n_jobs=None, random_state=None, ): super().__init__( kernel=kernel, gamma=gamma, degree=degree, coef0=coef0, kernel_params=kernel_params, alpha=alpha, fit_inverse_transform=fit_inverse_transform, eigen_solver=eigen_solver, tol=tol, max_iter=max_iter, remove_zero_eig=remove_zero_eig, n_jobs=n_jobs, copy_X=copy_X, random_state=check_random_state(random_state), ) @property def get_centerer(self): """Return a protected member _centerer.""" return self._centerer @property def get_kernel(self): """Return a protected member _get_kernel.""" return self._get_kernel
[docs]class KPCA(BaseDetector): """KPCA class for outlier detection. PCA is performed on the feature space uniquely determined by the kernel, and the reconstruction error on the feature space is used as the anomaly score. See :cite:`hoffmann2007kernel` Heiko Hoffmann, "Kernel PCA for novelty detection," Pattern Recognition, vol.40, no.3, pp. 863-874, 2007. https://www.sciencedirect.com/science/article/pii/S0031320306003414 for details. Parameters ---------- n_components : int, optional (default=None) Number of components. If None, all non-zero components are kept. n_selected_components : int, optional (default=None) Number of selected principal components for calculating the outlier scores. It is not necessarily equal to the total number of the principal components. If not set, use all principal components. kernel : string {'linear', 'poly', 'rbf', 'sigmoid', 'cosine', 'precomputed'}, optional (default='rbf') Kernel used for PCA. gamma : float, optional (default=None) Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other kernels. If ``gamma`` is ``None``, then it is set to ``1/n_features``. degree : int, optional (default=3) Degree for poly kernels. Ignored by other kernels. coef0 : float, optional (default=1) Independent term in poly and sigmoid kernels. Ignored by other kernels. kernel_params : dict, optional (default=None) Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels. alpha : float, optional (default=1.0) Hyperparameter of the ridge regression that learns the inverse transform (when inverse_transform=True). eigen_solver : string, {'auto', 'dense', 'arpack', 'randomized'}, \ default='auto' Select eigensolver to use. If `n_components` is much less than the number of training samples, randomized (or arpack to a smaller extend) may be more efficient than the dense eigensolver. Randomized SVD is performed according to the method of Halko et al. auto : the solver is selected by a default policy based on n_samples (the number of training samples) and `n_components`: if the number of components to extract is less than 10 (strict) and the number of samples is more than 200 (strict), the 'arpack' method is enabled. Otherwise the exact full eigenvalue decomposition is computed and optionally truncated afterwards ('dense' method). dense : run exact full eigenvalue decomposition calling the standard LAPACK solver via `scipy.linalg.eigh`, and select the components by postprocessing. arpack : run SVD truncated to n_components calling ARPACK solver using `scipy.sparse.linalg.eigsh`. It requires strictly 0 < n_components < n_samples randomized : run randomized SVD. implementation selects eigenvalues based on their module; therefore using this method can lead to unexpected results if the kernel is not positive semi-definite. tol : float, optional (default=0) Convergence tolerance for arpack. If 0, optimal value will be chosen by arpack. max_iter : int, optional (default=None) Maximum number of iterations for arpack. If None, optimal value will be chosen by arpack. remove_zero_eig : bool, optional (default=False) If True, then all components with zero eigenvalues are removed, so that the number of components in the output may be < n_components (and sometimes even zero due to numerical instability). When n_components is None, this parameter is ignored and components with zero eigenvalues are removed regardless. copy_X : bool, optional (default=True) If True, input X is copied and stored by the model in the `X_fit_` attribute. If no further changes will be done to X, setting `copy_X=False` saves memory by storing a reference. n_jobs : int, optional (default=None) The number of parallel jobs to run. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. sampling : bool, optional (default=False) If True, sampling subset from the dataset is performed only once, in order to reduce time complexity while keeping detection performance. subset_size : float in (0., 1.0) or int (0, n_samples), optional (default=20) If sampling is True, the size of subset is specified. random_state : int, RandomState instance or None, optional (default=None) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Attributes ---------- decision_scores_ : numpy array of shape (n_samples,) The outlier scores of the training data. The higher, the more abnormal. Outliers tend to have higher scores. This value is available once the detector is fitted. threshold_ : float The threshold is based on ``contamination``. It is the ``n_samples * contamination`` most abnormal samples in ``decision_scores_``. The threshold is calculated for generating binary outlier labels. labels_ : int, either 0 or 1 The binary labels of the training data. 0 stands for inliers and 1 for outliers/anomalies. It is generated by applying ``threshold_`` on ``decision_scores_``. """ def __init__( self, contamination=0.1, n_components=None, n_selected_components=None, kernel="rbf", gamma=None, degree=3, coef0=1, kernel_params=None, alpha=1.0, eigen_solver="auto", tol=0, max_iter=None, remove_zero_eig=False, copy_X=True, n_jobs=None, sampling=False, subset_size=20, random_state=None, ): super().__init__(contamination=contamination) self.n_components = n_components self.n_selected_components = n_selected_components self.copy_x = copy_X self.sampling = sampling self.subset_size = subset_size self.random_state = check_random_state(random_state) self.decision_scores_ = None self.n_selected_components_ = None self.kpca = PyODKernelPCA( n_components=n_components, kernel=kernel, gamma=gamma, degree=degree, coef0=coef0, kernel_params=kernel_params, alpha=alpha, fit_inverse_transform=False, eigen_solver=eigen_solver, tol=tol, max_iter=max_iter, remove_zero_eig=remove_zero_eig, copy_X=copy_X, n_jobs=n_jobs, ) def _check_subset_size(self, array): """Check subset size.""" n_samples, _ = array.shape if isinstance(self.subset_size, int) is True: if 0 < self.subset_size <= n_samples: subset_size = self.subset_size else: raise ValueError( f"subset_size={self.subset_size} " f"must be between 0 and n_samples={n_samples}." ) if isinstance(self.subset_size, float) is True: if 0.0 < self.subset_size <= 1.0: subset_size = int(self.subset_size * n_samples) else: raise ValueError("subset_size=%r must be between 0.0 and 1.0") return subset_size
[docs] def fit(self, X, y=None): """Fit detector. y is ignored in unsupervised methods. Parameters ---------- X : numpy array of shape (n_samples, n_features) The input samples. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Fitted estimator. """ # validate inputs X and y (optional) X = check_array(X, copy=self.copy_x) self._set_n_classes(y) # perform subsampling to reduce time complexity if self.sampling is True: subset_size = self._check_subset_size(X) random_indices = self.random_state.choice( X.shape[0], size=subset_size, replace=False, ) X = X[random_indices, :] # copy the attributes from the sklearn Kernel PCA object if self.n_components is None: n_components = X.shape[1] # use all dimensions else: if self.n_components < 1: raise ValueError( f"`n_components` should be >= 1, got: {self.n_components}" ) n_components = min(X.shape[0], self.n_components) # validate the number of components to be used for outlier detection if self.n_selected_components is None: self.n_selected_components_ = n_components else: self.n_selected_components_ = self.n_selected_components check_parameter( self.n_selected_components_, 1, n_components, include_left=True, include_right=True, param_name="n_selected_components", ) self.kpca.fit(X) centerer = self.kpca.get_centerer kernel = self.kpca.get_kernel if int(sklearn.__version__[0]) < 1: eigenvalues_ = self.kpca.lambdas_ eigenvectors_ = self.kpca.alphas_ else: eigenvalues_ = self.kpca.eigenvalues_ eigenvectors_ = self.kpca.eigenvectors_ x_transformed = eigenvectors_ * np.sqrt(eigenvalues_) x_transformed = x_transformed[:, : self.n_selected_components_] potential = [] for i in range(X.shape[0]): sample = X[i, :].reshape(1, -1) potential.append(kernel(sample)) potential = np.array(potential).squeeze() potential = potential - 2 * centerer.K_fit_rows_ + centerer.K_fit_all_ # reconstruction error self.decision_scores_ = potential - np.sum(np.square(x_transformed), axis=1) self._process_decision_scores() return self
[docs] def decision_function(self, X): """Predict raw anomaly score of X using the fitted detector. The anomaly score of an input sample is computed based on different detector algorithms. For consistency, outliers are assigned with larger anomaly scores. Parameters ---------- X : numpy array of shape (n_samples, n_features) The training input samples. Sparse matrices are accepted only if they are supported by the base estimator. Returns ------- anomaly_scores : numpy array of shape (n_samples,) The anomaly score of the input samples. """ check_is_fitted(self, ["decision_scores_", "threshold_", "labels_"]) X = check_array(X) # Compute centered gram matrix between X and training data X_fit_ centerer = self.kpca.get_centerer kernel = self.kpca.get_kernel gram_matrix = kernel(X, self.kpca.X_fit_) centered_g = centerer.transform(gram_matrix) if int(sklearn.__version__[0]) < 1: eigenvalues_ = self.kpca.lambdas_ eigenvectors_ = self.kpca.alphas_ else: eigenvalues_ = self.kpca.eigenvalues_ eigenvectors_ = self.kpca.eigenvectors_ # scale eigenvectors (properly account for null-space for dot product) non_zeros = np.flatnonzero(eigenvalues_) scaled_alphas = np.zeros_like(eigenvectors_) scaled_alphas[:, non_zeros] = eigenvectors_[:, non_zeros] / np.sqrt( eigenvalues_[non_zeros] ) # Project with a scalar product between K and the scaled eigenvectors x_transformed = np.dot(centered_g, scaled_alphas) x_transformed = x_transformed[:, : self.n_selected_components_] potential = [] for i in range(X.shape[0]): sample = X[i, :].reshape(1, -1) potential.append(kernel(sample)) potential = np.array(potential).squeeze() gram_fit_rows = np.sum(gram_matrix, axis=1) / gram_matrix.shape[1] potential = potential - 2 * gram_fit_rows + centerer.K_fit_all_ # reconstruction error anomaly_scores = potential - np.sum(np.square(x_transformed), axis=1) return anomaly_scores