# Authors: Nicolas Goix # Alexandre Gramfort # License: BSD 3 clause import numbers from numbers import Integral, Real from warnings import warn import numpy as np from scipy.sparse import issparse from ..base import OutlierMixin, _fit_context from ..tree import ExtraTreeRegressor from ..tree._tree import DTYPE as tree_dtype from ..utils import ( check_array, check_random_state, gen_batches, ) from ..utils._chunking import get_chunk_n_rows from ..utils._param_validation import Interval, RealNotInt, StrOptions from ..utils.validation import _num_samples, check_is_fitted from ._bagging import BaseBagging __all__ = ["IsolationForest"] class IsolationForest(OutlierMixin, BaseBagging): """ Isolation Forest Algorithm. Return the anomaly score of each sample using the IsolationForest algorithm The IsolationForest 'isolates' observations by randomly selecting a feature and then randomly selecting a split value between the maximum and minimum values of the selected feature. Since recursive partitioning can be represented by a tree structure, the number of splittings required to isolate a sample is equivalent to the path length from the root node to the terminating node. This path length, averaged over a forest of such random trees, is a measure of normality and our decision function. Random partitioning produces noticeably shorter paths for anomalies. Hence, when a forest of random trees collectively produce shorter path lengths for particular samples, they are highly likely to be anomalies. Read more in the :ref:`User Guide `. .. versionadded:: 0.18 Parameters ---------- n_estimators : int, default=100 The number of base estimators in the ensemble. max_samples : "auto", int or float, default="auto" The number of samples to draw from X to train each base estimator. - If int, then draw `max_samples` samples. - If float, then draw `max_samples * X.shape[0]` samples. - If "auto", then `max_samples=min(256, n_samples)`. If max_samples is larger than the number of samples provided, all samples will be used for all trees (no sampling). contamination : 'auto' or float, default='auto' 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 scores of the samples. - If 'auto', the threshold is determined as in the original paper. - If float, the contamination should be in the range (0, 0.5]. .. versionchanged:: 0.22 The default value of ``contamination`` changed from 0.1 to ``'auto'``. max_features : int or float, default=1.0 The number of features to draw from X to train each base estimator. - If int, then draw `max_features` features. - If float, then draw `max(1, int(max_features * n_features_in_))` features. Note: using a float number less than 1.0 or integer less than number of features will enable feature subsampling and leads to a longer runtime. bootstrap : bool, default=False If True, individual trees are fit on random subsets of the training data sampled with replacement. If False, sampling without replacement is performed. n_jobs : int, default=None The number of jobs to run in parallel for both :meth:`fit` and :meth:`predict`. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. random_state : int, RandomState instance or None, default=None Controls the pseudo-randomness of the selection of the feature and split values for each branching step and each tree in the forest. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. verbose : int, default=0 Controls the verbosity of the tree building process. warm_start : bool, default=False When set to ``True``, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See :term:`the Glossary `. .. versionadded:: 0.21 Attributes ---------- estimator_ : :class:`~sklearn.tree.ExtraTreeRegressor` instance The child estimator template used to create the collection of fitted sub-estimators. .. versionadded:: 1.2 `base_estimator_` was renamed to `estimator_`. estimators_ : list of ExtraTreeRegressor instances The collection of fitted sub-estimators. estimators_features_ : list of ndarray The subset of drawn features for each base estimator. estimators_samples_ : list of ndarray The subset of drawn samples (i.e., the in-bag samples) for each base estimator. max_samples_ : int The actual number of samples. offset_ : float Offset used to define the decision function from the raw scores. We have the relation: ``decision_function = score_samples - offset_``. ``offset_`` is defined as follows. When the contamination parameter is set to "auto", the offset is equal to -0.5 as the scores of inliers are close to 0 and the scores of outliers are close to -1. When a contamination parameter different than "auto" is provided, the offset is defined in such a way we obtain the expected number of outliers (samples with decision function < 0) in training. .. versionadded:: 0.20 n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- sklearn.covariance.EllipticEnvelope : An object for detecting outliers in a Gaussian distributed dataset. sklearn.svm.OneClassSVM : Unsupervised Outlier Detection. Estimate the support of a high-dimensional distribution. The implementation is based on libsvm. sklearn.neighbors.LocalOutlierFactor : Unsupervised Outlier Detection using Local Outlier Factor (LOF). Notes ----- The implementation is based on an ensemble of ExtraTreeRegressor. The maximum depth of each tree is set to ``ceil(log_2(n))`` where :math:`n` is the number of samples used to build the tree (see (Liu et al., 2008) for more details). References ---------- .. [1] Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. "Isolation forest." Data Mining, 2008. ICDM'08. Eighth IEEE International Conference on. .. [2] Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. "Isolation-based anomaly detection." ACM Transactions on Knowledge Discovery from Data (TKDD) 6.1 (2012): 3. Examples -------- >>> from sklearn.ensemble import IsolationForest >>> X = [[-1.1], [0.3], [0.5], [100]] >>> clf = IsolationForest(random_state=0).fit(X) >>> clf.predict([[0.1], [0], [90]]) array([ 1, 1, -1]) For an example of using isolation forest for anomaly detection see :ref:`sphx_glr_auto_examples_ensemble_plot_isolation_forest.py`. """ _parameter_constraints: dict = { "n_estimators": [Interval(Integral, 1, None, closed="left")], "max_samples": [ StrOptions({"auto"}), Interval(Integral, 1, None, closed="left"), Interval(RealNotInt, 0, 1, closed="right"), ], "contamination": [ StrOptions({"auto"}), Interval(Real, 0, 0.5, closed="right"), ], "max_features": [ Integral, Interval(Real, 0, 1, closed="right"), ], "bootstrap": ["boolean"], "n_jobs": [Integral, None], "random_state": ["random_state"], "verbose": ["verbose"], "warm_start": ["boolean"], } def __init__( self, *, n_estimators=100, max_samples="auto", contamination="auto", max_features=1.0, bootstrap=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, ): super().__init__( estimator=None, # here above max_features has no links with self.max_features bootstrap=bootstrap, bootstrap_features=False, n_estimators=n_estimators, max_samples=max_samples, max_features=max_features, warm_start=warm_start, n_jobs=n_jobs, random_state=random_state, verbose=verbose, ) self.contamination = contamination def _get_estimator(self): return ExtraTreeRegressor( # here max_features has no links with self.max_features max_features=1, splitter="random", random_state=self.random_state, ) def _set_oob_score(self, X, y): raise NotImplementedError("OOB score not supported by iforest") def _parallel_args(self): # ExtraTreeRegressor releases the GIL, so it's more efficient to use # a thread-based backend rather than a process-based backend so as # to avoid suffering from communication overhead and extra memory # copies. return {"prefer": "threads"} @_fit_context(prefer_skip_nested_validation=True) def fit(self, X, y=None, sample_weight=None): """ Fit estimator. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) The input samples. Use ``dtype=np.float32`` for maximum efficiency. Sparse matrices are also supported, use sparse ``csc_matrix`` for maximum efficiency. y : Ignored Not used, present for API consistency by convention. sample_weight : array-like of shape (n_samples,), default=None Sample weights. If None, then samples are equally weighted. Returns ------- self : object Fitted estimator. """ X = self._validate_data(X, accept_sparse=["csc"], dtype=tree_dtype) if issparse(X): # Pre-sort indices to avoid that each individual tree of the # ensemble sorts the indices. X.sort_indices() rnd = check_random_state(self.random_state) y = rnd.uniform(size=X.shape[0]) # ensure that max_sample is in [1, n_samples]: n_samples = X.shape[0] if isinstance(self.max_samples, str) and self.max_samples == "auto": max_samples = min(256, n_samples) elif isinstance(self.max_samples, numbers.Integral): if self.max_samples > n_samples: warn( "max_samples (%s) is greater than the " "total number of samples (%s). max_samples " "will be set to n_samples for estimation." % (self.max_samples, n_samples) ) max_samples = n_samples else: max_samples = self.max_samples else: # max_samples is float max_samples = int(self.max_samples * X.shape[0]) self.max_samples_ = max_samples max_depth = int(np.ceil(np.log2(max(max_samples, 2)))) super()._fit( X, y, max_samples, max_depth=max_depth, sample_weight=sample_weight, check_input=False, ) self._average_path_length_per_tree, self._decision_path_lengths = zip( *[ ( _average_path_length(tree.tree_.n_node_samples), tree.tree_.compute_node_depths(), ) for tree in self.estimators_ ] ) if self.contamination == "auto": # 0.5 plays a special role as described in the original paper. # we take the opposite as we consider the opposite of their score. self.offset_ = -0.5 return self # Else, define offset_ wrt contamination parameter # To avoid performing input validation a second time we call # _score_samples rather than score_samples. # _score_samples expects a CSR matrix, so we convert if necessary. if issparse(X): X = X.tocsr() self.offset_ = np.percentile(self._score_samples(X), 100.0 * self.contamination) return self def predict(self, X): """ Predict if a particular sample is an outlier or not. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``. Returns ------- is_inlier : ndarray of shape (n_samples,) For each observation, tells whether or not (+1 or -1) it should be considered as an inlier according to the fitted model. """ check_is_fitted(self) decision_func = self.decision_function(X) is_inlier = np.ones_like(decision_func, dtype=int) is_inlier[decision_func < 0] = -1 return is_inlier def decision_function(self, X): """ Average anomaly score of X of the base classifiers. The anomaly score of an input sample is computed as the mean anomaly score of the trees in the forest. The measure of normality of an observation given a tree is the depth of the leaf containing this observation, which is equivalent to the number of splittings required to isolate this point. In case of several observations n_left in the leaf, the average path length of a n_left samples isolation tree is added. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``. Returns ------- scores : ndarray of shape (n_samples,) The anomaly score of the input samples. The lower, the more abnormal. Negative scores represent outliers, positive scores represent inliers. """ # We subtract self.offset_ to make 0 be the threshold value for being # an outlier: return self.score_samples(X) - self.offset_ def score_samples(self, X): """ Opposite of the anomaly score defined in the original paper. The anomaly score of an input sample is computed as the mean anomaly score of the trees in the forest. The measure of normality of an observation given a tree is the depth of the leaf containing this observation, which is equivalent to the number of splittings required to isolate this point. In case of several observations n_left in the leaf, the average path length of a n_left samples isolation tree is added. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) The input samples. Returns ------- scores : ndarray of shape (n_samples,) The anomaly score of the input samples. The lower, the more abnormal. """ # Check data X = self._validate_data(X, accept_sparse="csr", dtype=tree_dtype, reset=False) return self._score_samples(X) def _score_samples(self, X): """Private version of score_samples without input validation. Input validation would remove feature names, so we disable it. """ # Code structure from ForestClassifier/predict_proba check_is_fitted(self) # Take the opposite of the scores as bigger is better (here less abnormal) return -self._compute_chunked_score_samples(X) def _compute_chunked_score_samples(self, X): n_samples = _num_samples(X) if self._max_features == X.shape[1]: subsample_features = False else: subsample_features = True # We get as many rows as possible within our working_memory budget # (defined by sklearn.get_config()['working_memory']) to store # self._max_features in each row during computation. # # Note: # - this will get at least 1 row, even if 1 row of score will # exceed working_memory. # - this does only account for temporary memory usage while loading # the data needed to compute the scores -- the returned scores # themselves are 1D. chunk_n_rows = get_chunk_n_rows( row_bytes=16 * self._max_features, max_n_rows=n_samples ) slices = gen_batches(n_samples, chunk_n_rows) scores = np.zeros(n_samples, order="f") for sl in slices: # compute score on the slices of test samples: scores[sl] = self._compute_score_samples(X[sl], subsample_features) return scores def _compute_score_samples(self, X, subsample_features): """ Compute the score of each samples in X going through the extra trees. Parameters ---------- X : array-like or sparse matrix Data matrix. subsample_features : bool Whether features should be subsampled. """ n_samples = X.shape[0] depths = np.zeros(n_samples, order="f") average_path_length_max_samples = _average_path_length([self._max_samples]) for tree_idx, (tree, features) in enumerate( zip(self.estimators_, self.estimators_features_) ): X_subset = X[:, features] if subsample_features else X leaves_index = tree.apply(X_subset, check_input=False) depths += ( self._decision_path_lengths[tree_idx][leaves_index] + self._average_path_length_per_tree[tree_idx][leaves_index] - 1.0 ) denominator = len(self.estimators_) * average_path_length_max_samples scores = 2 ** ( # For a single training sample, denominator and depth are 0. # Therefore, we set the score manually to 1. -np.divide( depths, denominator, out=np.ones_like(depths), where=denominator != 0 ) ) return scores def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } } def _average_path_length(n_samples_leaf): """ The average path length in a n_samples iTree, which is equal to the average path length of an unsuccessful BST search since the latter has the same structure as an isolation tree. Parameters ---------- n_samples_leaf : array-like of shape (n_samples,) The number of training samples in each test sample leaf, for each estimators. Returns ------- average_path_length : ndarray of shape (n_samples,) """ n_samples_leaf = check_array(n_samples_leaf, ensure_2d=False) n_samples_leaf_shape = n_samples_leaf.shape n_samples_leaf = n_samples_leaf.reshape((1, -1)) average_path_length = np.zeros(n_samples_leaf.shape) mask_1 = n_samples_leaf <= 1 mask_2 = n_samples_leaf == 2 not_mask = ~np.logical_or(mask_1, mask_2) average_path_length[mask_1] = 0.0 average_path_length[mask_2] = 1.0 average_path_length[not_mask] = ( 2.0 * (np.log(n_samples_leaf[not_mask] - 1.0) + np.euler_gamma) - 2.0 * (n_samples_leaf[not_mask] - 1.0) / n_samples_leaf[not_mask] ) return average_path_length.reshape(n_samples_leaf_shape)