# -*- coding: utf-8 -*- """Autoregressive model for multivariate time series outlier detection. """ import numpy as np from sklearn.utils import check_array from sklearn.utils.validation import check_is_fitted from detection_algorithm.core.CollectiveBase import CollectiveBaseDetector from pyod.models.pca import PCA as PCA_PYOD from detection_algorithm.core.utility import get_sub_matrices class PCA(CollectiveBaseDetector): """PCA-based outlier detection with both univariate and multivariate time series data. TS data will be first transformed to tabular format. For univariate data, it will be in shape of [valid_length, window_size]. for multivariate data with d sequences, it will be in the shape of [valid_length, window_size]. Parameters ---------- window_size : int The moving window size. step_size : int, optional (default=1) The displacement for moving window. contamination : float in (0., 0.5), optional (default=0.1) The amount of contamination of the data set, i.e. the proportion of outliers in the data set. Used when fitting to define the threshold on the decision function. n_components : int, float, None or string Number of components to keep. It should be smaller than the window_size. if n_components is not set all components are kept:: n_components == min(n_samples, n_features) if n_components == 'mle' and svd_solver == 'full', Minka\'s MLE is used to guess the dimension if ``0 < n_components < 1`` and svd_solver == 'full', select the number of components such that the amount of variance that needs to be explained is greater than the percentage specified by n_components n_components cannot be equal to n_features for svd_solver == 'arpack'. 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. copy : bool (default True) If False, data passed to fit are overwritten and running fit(X).transform(X) will not yield the expected results, use fit_transform(X) instead. whiten : bool, optional (default False) When True (False by default) the `components_` vectors are multiplied by the square root of n_samples and then divided by the singular values to ensure uncorrelated outputs with unit component-wise variances. Whitening will remove some information from the transformed signal (the relative variance scales of the components) but can sometime improve the predictive accuracy of the downstream estimators by making their data respect some hard-wired assumptions. svd_solver : string {'auto', 'full', 'arpack', 'randomized'} auto : the solver is selected by a default policy based on `X.shape` and `n_components`: if the input data is larger than 500x500 and the number of components to extract is lower than 80% of the smallest dimension of the data, then the more efficient 'randomized' method is enabled. Otherwise the exact full SVD is computed and optionally truncated afterwards. full : run exact full SVD calling the standard LAPACK solver via `scipy.linalg.svd` and select the components by postprocessing arpack : run SVD truncated to n_components calling ARPACK solver via `scipy.sparse.linalg.svds`. It requires strictly 0 < n_components < X.shape[1] randomized : run randomized SVD by the method of Halko et al. tol : float >= 0, optional (default .0) Tolerance for singular values computed by svd_solver == 'arpack'. iterated_power : int >= 0, or 'auto', (default 'auto') Number of iterations for the power method computed by svd_solver == 'randomized'. 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`. Used when ``svd_solver`` == 'arpack' or 'randomized'. weighted : bool, optional (default=True) If True, the eigenvalues are used in score computation. The eigenvectors with small eigenvalues comes with more importance in outlier score calculation. standardization : bool, optional (default=True) If True, perform standardization first to convert data to zero mean and unit variance. See http://scikit-learn.org/stable/auto_examples/preprocessing/plot_scaling_importance.html 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, window_size, step_size=1, contamination=0.1, n_components=None, n_selected_components=None, copy=True, whiten=False, svd_solver='auto', tol=0.0, iterated_power='auto', random_state=None, weighted=True, standardization=True): super(PCA, self).__init__(contamination=contamination) self.window_size = window_size self.step_size = step_size # parameters for PCA self.n_components = n_components self.n_selected_components = n_selected_components self.copy = copy self.whiten = whiten self.svd_solver = svd_solver self.tol = tol self.iterated_power = iterated_power self.random_state = random_state self.weighted = weighted self.standardization = standardization # initialize a kNN model self.model_ = PCA_PYOD(n_components=self.n_components, n_selected_components=self.n_selected_components, contamination=self.contamination, copy=self.copy, whiten=self.whiten, svd_solver=self.svd_solver, tol=self.tol, iterated_power=self.iterated_power, random_state=self.random_state, weighted=self.weighted, standardization=self.standardization) def fit(self, X: np.array) -> object: """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. """ X = check_array(X).astype(np.float) # first convert it into submatrices, and flatten it sub_matrices, self.left_inds_, self.right_inds_ = get_sub_matrices( X, self.window_size, self.step_size, return_numpy=True, flatten=True, flatten_order='F') # if self.n_components > sub_matrices.shape[1]: # raise ValueError('n_components exceeds window_size times the number of sequences.') # fit the PCA model self.model_.fit(sub_matrices) self.decision_scores_ = self.model_.decision_scores_ self._process_decision_scores() return self def decision_function(self, X: np.array): """Predict raw anomaly scores of X using the fitted detector. The anomaly score of an input sample is computed based on the fitted detector. For consistency, outliers are assigned with higher anomaly scores. Parameters ---------- X : numpy array of shape (n_samples, n_features) The 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, ['model_']) X = check_array(X).astype(np.float) # first convert it into submatrices, and flatten it sub_matrices, X_left_inds, X_right_inds = get_sub_matrices( X, self.window_size, self.step_size, return_numpy=True, flatten=True, flatten_order='F') # return the prediction result by PCA return self.model_.decision_function( sub_matrices), X_left_inds.ravel(), X_right_inds.ravel() if __name__ == "__main__": # X_train = np.asarray( # [3., 4., 8., 16, 18, 13., 22., 36., 59., 128, 62, 67, 78, 100]).reshape(-1, 1) # X_test = np.asarray( # [3., 4., 8.6, 13.4, 22.5, 17, 19.2, 36.1, 127, -23, 59.2]).reshape(-1, # 1) X_train = np.asarray( [[3., 5], [5., 9], [7., 2], [42., 20], [8., 12], [10., 12], [12., 12], [18., 16], [20., 7], [18., 10], [23., 12], [22., 15]]) w = get_sub_matrices(X_train, window_size=3, step=2, flatten=False) X_test = np.asarray( [[12., 10], [8., 12], [80., 80], [92., 983], [18., 16], [20., 7], [18., 10], [3., 5], [5., 9], [23., 12], [22., 15]]) clf = PCA(window_size=3, step_size=2, contamination=0.2) clf.fit(X_train) decision_scores, left_inds_, right_inds = clf.decision_scores_, \ clf.left_inds_, clf.right_inds_ print(clf.left_inds_, clf.right_inds_) pred_scores, X_left_inds, X_right_inds = clf.decision_function(X_test) pred_labels, X_left_inds, X_right_inds = clf.predict(X_test) pred_probs, X_left_inds, X_right_inds = clf.predict_proba(X_test) print(pred_scores) print(pred_labels) print(pred_probs)