text: import numpy as np
  from sklearn.neighbors import LocalOutlierFactor
  from pyodds.algo.base import Base
  
  class LOF(LocalOutlierFactor,Base):
  
      """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 anomaly_likelihood(self, X):
          """A normalization function to clip and scale the outlier_scores returned
          by self.decision_function(). Normalization is done separately for data
          points falling above and below the threshold
          Parameters
          ----------
          X : dataframe of shape (n_samples, n_features)
              The training input samples. Sparse matrices are accepted only
              if they are supported by the base estimator.
          Returns
          -------
          normalized_anomaly_scores : numpy array of shape (n_samples,)
              Normalized anomaly scores where 0.5 is the default threshold separating
              inliers with low scores from outliers with high score
          """
          outlier_score = self.decision_function(X)
          # The default threshold in sklearn implementation is 0
          mask = outlier_score < 0
          sc_pos = outlier_score.clip(max=0)
          sc_neg = outlier_score.clip(min=0)
  
          lmn = np.copy(outlier_score)
          sc_pos = np.interp(sc_pos, (sc_pos.min(), sc_pos.max()), (1, 0.5))
          sc_neg = np.interp(sc_neg, (sc_neg.min(), sc_neg.max()), (0.5, 0.0))
  
          lmn[mask] = sc_pos[mask]
          lmn[np.logical_not(mask)] = sc_neg[np.logical_not(mask)]
          del outlier_score, sc_pos, sc_neg
          return lmn
  