text: # Authors: Nicolas Goix <nicolas.goix@telecom-paristech.fr>
  #          Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
  # License: BSD 3 clause
  
  import numpy as np
  import warnings
  
  from .base import NeighborsBase
  from .base import KNeighborsMixin
  from .base import UnsupervisedMixin
  from ..base import OutlierMixin
  
  from ..utils.validation import check_is_fitted
  from ..utils import check_array
  
  __all__ = ["LocalOutlierFactor"]
  
  
  class LocalOutlierFactor(NeighborsBase, KNeighborsMixin, UnsupervisedMixin,
                           OutlierMixin):
      """Unsupervised Outlier Detection using Local Outlier Factor (LOF)
  
      The anomaly score of each sample is called Local Outlier Factor.
      It measures the local deviation of density of a given sample with
      respect to its neighbors.
      It is local in that the anomaly score depends on how isolated the object
      is with respect to the surrounding neighborhood.
      More precisely, locality is given by k-nearest neighbors, whose distance
      is used to estimate the local density.
      By comparing the local density of a sample to the local densities of
      its neighbors, one can identify samples that have a substantially lower
      density than their neighbors. These are considered outliers.
  
      Parameters
      ----------
      n_neighbors : int, optional (default=20)
          Number of neighbors to use by default for :meth:`kneighbors` queries.
          If n_neighbors is larger than the number of samples provided,
          all samples will be used.
  
      algorithm : {'auto', 'ball_tree', 'kd_tree', 'brute'}, optional
          Algorithm used to compute the nearest neighbors:
  
          - 'ball_tree' will use :class:`BallTree`
          - 'kd_tree' will use :class:`KDTree`
          - 'brute' will use a brute-force search.
          - 'auto' will attempt to decide the most appropriate algorithm
            based on the values passed to :meth:`fit` method.
  
          Note: fitting on sparse input will override the setting of
          this parameter, using brute force.
  
      leaf_size : int, optional (default=30)
          Leaf size passed to :class:`BallTree` or :class:`KDTree`. This can
          affect the speed of the construction and query, as well as the memory
          required to store the tree. The optimal value depends on the
          nature of the problem.
  
      metric : string or callable, default 'minkowski'
          metric used for the distance computation. Any metric from scikit-learn
          or scipy.spatial.distance can be used.
  
          If 'precomputed', the training input X is expected to be a distance
          matrix.
  
          If metric is a callable function, it is called on each
          pair of instances (rows) and the resulting value recorded. The callable
          should take two arrays as input and return one value indicating the
          distance between them. This works for Scipy's metrics, but is less
          efficient than passing the metric name as a string.
  
          Valid values for metric are:
  
          - from scikit-learn: ['cityblock', 'cosine', 'euclidean', 'l1', 'l2',
            'manhattan']
  
          - from scipy.spatial.distance: ['braycurtis', 'canberra', 'chebyshev',
            'correlation', 'dice', 'hamming', 'jaccard', 'kulsinski',
            'mahalanobis', 'minkowski', 'rogerstanimoto', 'russellrao',
            'seuclidean', 'sokalmichener', 'sokalsneath', 'sqeuclidean',
            'yule']
  
          See the documentation for scipy.spatial.distance for details on these
          metrics:
          https://docs.scipy.org/doc/scipy/reference/spatial.distance.html
  
      p : integer, optional (default=2)
          Parameter for the Minkowski metric from
          :func:`sklearn.metrics.pairwise.pairwise_distances`. When p = 1, this
          is equivalent to using manhattan_distance (l1), and euclidean_distance
          (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
  
      metric_params : dict, optional (default=None)
          Additional keyword arguments for the metric function.
  
      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. When fitting this is used to define the
          threshold on the decision function. If "auto", the decision function
          threshold is determined as in the original paper.
  
          .. versionchanged:: 0.20
             The default value of ``contamination`` will change from 0.1 in 0.20
             to ``'auto'`` in 0.22.
  
      novelty : boolean, default False
          By default, LocalOutlierFactor is only meant to be used for outlier
          detection (novelty=False). Set novelty to True if you want to use
          LocalOutlierFactor for novelty detection. In this case be aware that
          that you should only use predict, decision_function and score_samples
          on new unseen data and not on the training set.
  
      n_jobs : int or None, optional (default=None)
          The number of parallel jobs to run for neighbors search.
          ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
          ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
          for more details.
          Affects only :meth:`kneighbors` and :meth:`kneighbors_graph` methods.
  
  
      Attributes
      ----------
      negative_outlier_factor_ : numpy array, shape (n_samples,)
          The opposite LOF of the training samples. The higher, the more normal.
          Inliers tend to have a LOF score close to 1 (``negative_outlier_factor_``
          close to -1), while outliers tend to have a larger LOF score.
  
          The local outlier factor (LOF) of a sample captures its
          supposed 'degree of abnormality'.
          It is the average of the ratio of the local reachability density of
          a sample and those of its k-nearest neighbors.
  
      n_neighbors_ : integer
          The actual number of neighbors used for :meth:`kneighbors` queries.
  
      offset_ : float
          Offset used to obtain binary labels from the raw scores.
          Observations having a negative_outlier_factor smaller than `offset_`
          are detected as abnormal.
          The offset is set to -1.5 (inliers score around -1), except when a
          contamination parameter different than "auto" is provided. In that
          case, the offset is defined in such a way we obtain the expected
          number of outliers in training.
  
      References
      ----------
      .. [1] Breunig, M. M., Kriegel, H. P., Ng, R. T., & Sander, J. (2000, May).
             LOF: identifying density-based local outliers. In ACM sigmod record.
      """
      def __init__(self, n_neighbors=20, algorithm='auto', leaf_size=30,
                   metric='minkowski', p=2, metric_params=None,
                   contamination="legacy", novelty=False, n_jobs=None):
          super(LocalOutlierFactor, self).__init__(
              n_neighbors=n_neighbors,
              algorithm=algorithm,
              leaf_size=leaf_size, metric=metric, p=p,
              metric_params=metric_params, n_jobs=n_jobs)
          self.contamination = contamination
          self.novelty = novelty
  
      @property
      def fit_predict(self):
          """"Fits the model to the training set X and returns the labels.
  
          Label is 1 for an inlier and -1 for an outlier according to the LOF
          score and the contamination parameter.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features), default=None
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. to the training samples.
  
          y : Ignored
              not used, present for API consistency by convention.
  
          Returns
          -------
          is_inlier : array, shape (n_samples,)
              Returns -1 for anomalies/outliers and 1 for inliers.
          """
  
          # As fit_predict would be different from fit.predict, fit_predict is
          # only available for outlier detection (novelty=False)
  
          if self.novelty:
              msg = ('fit_predict is not available when novelty=True. Use '
                     'novelty=False if you want to predict on the training set.')
              raise AttributeError(msg)
  
          return self._fit_predict
  
      def _fit_predict(self, X, y=None):
          """"Fits the model to the training set X and returns the labels.
  
          Label is 1 for an inlier and -1 for an outlier according to the LOF
          score and the contamination parameter.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features), default=None
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. to the training samples.
  
          Returns
          -------
          is_inlier : array, shape (n_samples,)
              Returns -1 for anomalies/outliers and 1 for inliers.
          """
  
          # As fit_predict would be different from fit.predict, fit_predict is
          # only available for outlier detection (novelty=False)
  
          return self.fit(X)._predict()
  
      def fit(self, X, y=None):
          """Fit the model using X as training data.
  
          Parameters
          ----------
          X : {array-like, sparse matrix, BallTree, KDTree}
              Training data. If array or matrix, shape [n_samples, n_features],
              or [n_samples, n_samples] if metric='precomputed'.
  
          y : Ignored
              not used, present for API consistency by convention.
  
          Returns
          -------
          self : object
          """
          if self.contamination == "legacy":
              warnings.warn('default contamination parameter 0.1 will change '
                            'in version 0.22 to "auto". This will change the '
                            'predict method behavior.',
                            FutureWarning)
              self._contamination = 0.1
          else:
              self._contamination = self.contamination
  
          if self._contamination != 'auto':
              if not(0. < self._contamination <= .5):
                  raise ValueError("contamination must be in (0, 0.5], "
                                   "got: %f" % self._contamination)
  
          super(LocalOutlierFactor, self).fit(X)
  
          n_samples = self._fit_X.shape[0]
          if self.n_neighbors > n_samples:
              warnings.warn("n_neighbors (%s) is greater than the "
                            "total number of samples (%s). n_neighbors "
                            "will be set to (n_samples - 1) for estimation."
                            % (self.n_neighbors, n_samples))
          self.n_neighbors_ = max(1, min(self.n_neighbors, n_samples - 1))
  
          self._distances_fit_X_, _neighbors_indices_fit_X_ = (
              self.kneighbors(None, n_neighbors=self.n_neighbors_))
  
          self._lrd = self._local_reachability_density(
              self._distances_fit_X_, _neighbors_indices_fit_X_)
  
          # Compute lof score over training samples to define offset_:
          lrd_ratios_array = (self._lrd[_neighbors_indices_fit_X_] /
                              self._lrd[:, np.newaxis])
  
          self.negative_outlier_factor_ = -np.mean(lrd_ratios_array, axis=1)
  
          if self._contamination == "auto":
              # inliers score around -1 (the higher, the less abnormal).
              self.offset_ = -1.5
          else:
              self.offset_ = np.percentile(self.negative_outlier_factor_,
                                           100. * self._contamination)
  
          return self
  
      @property
      def predict(self):
          """Predict the labels (1 inlier, -1 outlier) of X according to LOF.
  
          This method allows to generalize prediction to *new observations* (not
          in the training set). Only available for novelty detection (when
          novelty is set to True).
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. to the training samples.
  
          Returns
          -------
          is_inlier : array, shape (n_samples,)
              Returns -1 for anomalies/outliers and +1 for inliers.
          """
          if not self.novelty:
              msg = ('predict is not available when novelty=False, use '
                     'fit_predict if you want to predict on training data. Use '
                     'novelty=True if you want to use LOF for novelty detection '
                     'and predict on new unseen data.')
              raise AttributeError(msg)
  
          return self._predict
  
      def _predict(self, X=None):
          """Predict the labels (1 inlier, -1 outlier) of X according to LOF.
  
          If X is None, returns the same as fit_predict(X_train).
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features), default=None
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. to the training samples. If None, makes prediction on the
              training data without considering them as their own neighbors.
  
          Returns
          -------
          is_inlier : array, shape (n_samples,)
              Returns -1 for anomalies/outliers and +1 for inliers.
          """
          check_is_fitted(self, ["offset_", "negative_outlier_factor_",
                                 "n_neighbors_", "_distances_fit_X_"])
  
          if X is not None:
              X = check_array(X, accept_sparse='csr')
              is_inlier = np.ones(X.shape[0], dtype=int)
              is_inlier[self.decision_function(X) < 0] = -1
          else:
              is_inlier = np.ones(self._fit_X.shape[0], dtype=int)
              is_inlier[self.negative_outlier_factor_ < self.offset_] = -1
  
          return is_inlier
  
      @property
      def decision_function(self):
          """Shifted opposite of the Local Outlier Factor of X.
  
          Bigger is better, i.e. large values correspond to inliers.
  
          The shift offset allows a zero threshold for being an outlier.
          Only available for novelty detection (when novelty is set to True).
          The argument X is supposed to contain *new data*: if X contains a
          point from training, it considers the later in its own neighborhood.
          Also, the samples in X are not considered in the neighborhood of any
          point.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. the training samples.
  
          Returns
          -------
          shifted_opposite_lof_scores : array, shape (n_samples,)
              The shifted opposite of the Local Outlier Factor of each input
              samples. The lower, the more abnormal. Negative scores represent
              outliers, positive scores represent inliers.
          """
          if not self.novelty:
              msg = ('decision_function is not available when novelty=False. '
                     'Use novelty=True if you want to use LOF for novelty '
                     'detection and compute decision_function for new unseen '
                     'data. Note that the opposite LOF of the training samples '
                     'is always available by considering the '
                     'negative_outlier_factor_ attribute.')
              raise AttributeError(msg)
  
          return self._decision_function
  
      def _decision_function(self, X):
          """Shifted opposite of the Local Outlier Factor of X.
  
          Bigger is better, i.e. large values correspond to inliers.
  
          The shift offset allows a zero threshold for being an outlier.
          Only available for novelty detection (when novelty is set to True).
          The argument X is supposed to contain *new data*: if X contains a
          point from training, it considers the later in its own neighborhood.
          Also, the samples in X are not considered in the neighborhood of any
          point.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. the training samples.
  
          Returns
          -------
          shifted_opposite_lof_scores : array, shape (n_samples,)
              The shifted opposite of the Local Outlier Factor of each input
              samples. The lower, the more abnormal. Negative scores represent
              outliers, positive scores represent inliers.
          """
  
          return self._score_samples(X) - self.offset_
  
      @property
      def score_samples(self):
          """Opposite of the Local Outlier Factor of X.
  
          It is the opposite as as bigger is better, i.e. large values correspond
          to inliers.
  
          Only available for novelty detection (when novelty is set to True).
          The argument X is supposed to contain *new data*: if X contains a
          point from training, it considers the later in its own neighborhood.
          Also, the samples in X are not considered in the neighborhood of any
          point.
          The score_samples on training data is available by considering the
          the ``negative_outlier_factor_`` attribute.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. the training samples.
  
          Returns
          -------
          opposite_lof_scores : array, shape (n_samples,)
              The opposite of the Local Outlier Factor of each input samples.
              The lower, the more abnormal.
          """
          if not self.novelty:
              msg = ('score_samples is not available when novelty=False. The '
                     'scores of the training samples are always available '
                     'through the negative_outlier_factor_ attribute. Use '
                     'novelty=True if you want to use LOF for novelty detection '
                     'and compute score_samples for new unseen data.')
              raise AttributeError(msg)
  
          return self._score_samples
  
      def _score_samples(self, X):
          """Opposite of the Local Outlier Factor of X.
  
          It is the opposite as as bigger is better, i.e. large values correspond
          to inliers.
  
          Only available for novelty detection (when novelty is set to True).
          The argument X is supposed to contain *new data*: if X contains a
          point from training, it considers the later in its own neighborhood.
          Also, the samples in X are not considered in the neighborhood of any
          point.
          The score_samples on training data is available by considering the
          the ``negative_outlier_factor_`` attribute.
  
          Parameters
          ----------
          X : array-like, shape (n_samples, n_features)
              The query sample or samples to compute the Local Outlier Factor
              w.r.t. the training samples.
  
          Returns
          -------
          opposite_lof_scores : array, shape (n_samples,)
              The opposite of the Local Outlier Factor of each input samples.
              The lower, the more abnormal.
          """
          check_is_fitted(self, ["offset_", "negative_outlier_factor_",
                                 "_distances_fit_X_"])
          X = check_array(X, accept_sparse='csr')
  
          distances_X, neighbors_indices_X = (
              self.kneighbors(X, n_neighbors=self.n_neighbors_))
          X_lrd = self._local_reachability_density(distances_X,
                                                   neighbors_indices_X)
  
          lrd_ratios_array = (self._lrd[neighbors_indices_X] /
                              X_lrd[:, np.newaxis])
  
          # as bigger is better:
          return -np.mean(lrd_ratios_array, axis=1)
  
      def _local_reachability_density(self, distances_X, neighbors_indices):
          """The local reachability density (LRD)
  
          The LRD of a sample is the inverse of the average reachability
          distance of its k-nearest neighbors.
  
          Parameters
          ----------
          distances_X : array, shape (n_query, self.n_neighbors)
              Distances to the neighbors (in the training samples `self._fit_X`)
              of each query point to compute the LRD.
  
          neighbors_indices : array, shape (n_query, self.n_neighbors)
              Neighbors indices (of each query point) among training samples
              self._fit_X.
  
          Returns
          -------
          local_reachability_density : array, shape (n_samples,)
              The local reachability density of each sample.
          """
          dist_k = self._distances_fit_X_[neighbors_indices,
                                          self.n_neighbors_ - 1]
          reach_dist_array = np.maximum(distances_X, dist_k)
  
          #  1e-10 to avoid `nan' when nb of duplicates > n_neighbors_:
          return 1. / (np.mean(reach_dist_array, axis=1) + 1e-10)
  