Python Outlier Detection (PyOD)
===============================

**Deployment & Documentation & Stats & License**

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-----


Read Me First
^^^^^^^^^^^^^

Welcome to PyOD, a comprehensive but easy-to-use Python library for detecting anomalies in multivariate data. Whether you're tackling a small-scale project or large datasets, PyOD offers a range of algorithms to suit your needs.

* **For time-series outlier detection**, please use `TODS <https://github.com/datamllab/tods>`_.

* **For graph outlier detection**, please use `PyGOD <https://pygod.org/>`_.

* **Performance Comparison & Datasets**: We have a 45-page, comprehensive `anomaly detection benchmark paper <https://openreview.net/forum?id=foA_SFQ9zo0>`_. The fully `open-sourced ADBench <https://github.com/Minqi824/ADBench>`_ compares 30 anomaly detection algorithms on 57 benchmark datasets.

* **Learn more about anomaly detection** at `Anomaly Detection Resources <https://github.com/yzhao062/anomaly-detection-resources>`_

* **PyOD on Distributed Systems**: you can also run `PyOD on databricks <https://www.databricks.com/blog/2023/03/13/unsupervised-outlier-detection-databricks.html>`_.

----

About PyOD
^^^^^^^^^^

PyOD, established in 2017, has become a go-to **Python library** for **detecting anomalous/outlying objects** in multivariate data. This exciting yet challenging field is commonly referred to as `Outlier Detection <https://en.wikipedia.org/wiki/Anomaly_detection>`_ or `Anomaly Detection <https://en.wikipedia.org/wiki/Anomaly_detection>`_.

PyOD includes more than 50 detection algorithms, from classical LOF (SIGMOD 2000) to the cutting-edge ECOD and DIF (TKDE 2022 and 2023). Since 2017, PyOD has been successfully used in numerous academic research projects and commercial products with more than `22 million downloads <https://pepy.tech/project/pyod>`_. It is also well acknowledged by the machine learning community with various dedicated posts/tutorials, including `Analytics Vidhya <https://www.analyticsvidhya.com/blog/2019/02/outlier-detection-python-pyod/>`_, `KDnuggets <https://www.kdnuggets.com/2019/02/outlier-detection-methods-cheat-sheet.html>`_, and `Towards Data Science <https://towardsdatascience.com/anomaly-detection-for-dummies-15f148e559c1>`_.

**PyOD is featured for**:

* **Unified, User-Friendly Interface** across various algorithms.
* **Wide Range of Models**, from classic techniques to the latest deep learning methods in **PyTorch**.
* **High Performance & Efficiency**, leveraging `numba <https://github.com/numba/numba>`_ and `joblib <https://github.com/joblib/joblib>`_ for JIT compilation and parallel processing.
* **Fast Training & Prediction**, achieved through the SUOD framework [#Zhao2021SUOD]_.

**Outlier Detection with 5 Lines of Code**:

.. code-block:: python

    # Example: Training an ECOD detector
    from pyod.models.ecod import ECOD
    clf = ECOD()
    clf.fit(X_train)
    y_train_scores = clf.decision_scores_  # Outlier scores for training data
    y_test_scores = clf.decision_function(X_test)  # Outlier scores for test data


**Selecting the Right Algorithm:** Unsure where to start? Consider these robust and interpretable options:

- `ECOD <https://github.com/yzhao062/pyod/blob/master/examples/ecod_example.py>`_: Example of using ECOD for outlier detection
- `Isolation Forest <https://github.com/yzhao062/pyod/blob/master/examples/iforest_example.py>`_: Example of using Isolation Forest for outlier detection

Alternatively, explore `MetaOD <https://github.com/yzhao062/MetaOD>`_ for a data-driven approach.

**Citing PyOD**:

`PyOD paper <http://www.jmlr.org/papers/volume20/19-011/19-011.pdf>`_ is published in `Journal of Machine Learning Research (JMLR) <http://www.jmlr.org/>`_ (MLOSS track). If you use PyOD in a scientific publication, we would appreciate citations to the following paper::

    @article{zhao2019pyod,
        author  = {Zhao, Yue and Nasrullah, Zain and Li, Zheng},
        title   = {PyOD: A Python Toolbox for Scalable Outlier Detection},
        journal = {Journal of Machine Learning Research},
        year    = {2019},
        volume  = {20},
        number  = {96},
        pages   = {1-7},
        url     = {http://jmlr.org/papers/v20/19-011.html}
    }

or::

    Zhao, Y., Nasrullah, Z. and Li, Z., 2019. PyOD: A Python Toolbox for Scalable Outlier Detection. Journal of machine learning research (JMLR), 20(96), pp.1-7.

For a broader perspective on anomaly detection, see our NeurIPS papers `ADBench: Anomaly Detection Benchmark Paper <https://arxiv.org/abs/2206.09426>`_ and `ADGym: Design Choices for Deep Anomaly Detection <https://arxiv.org/abs/2309.15376>`_::

    @article{han2022adbench,
        title={Adbench: Anomaly detection benchmark},
        author={Han, Songqiao and Hu, Xiyang and Huang, Hailiang and Jiang, Minqi and Zhao, Yue},
        journal={Advances in Neural Information Processing Systems},
        volume={35},
        pages={32142--32159},
        year={2022}
    }

    @article{jiang2023adgym,
        title={ADGym: Design Choices for Deep Anomaly Detection},
        author={Jiang, Minqi and Hou, Chaochuan and Zheng, Ao and Han, Songqiao and Huang, Hailiang and Wen, Qingsong and Hu, Xiyang and Zhao, Yue},
        journal={Advances in Neural Information Processing Systems},
        volume={36},
        year={2023}
    }


**Table of Contents**:

* `Installation <#installation>`_
* `API Cheatsheet & Reference <#api-cheatsheet--reference>`_
* `ADBench Benchmark and Datasets <#adbench-benchmark-and-datasets>`_
* `Model Save & Load <#model-save--load>`_
* `Fast Train with SUOD <#fast-train-with-suod>`_
* `Thresholding Outlier Scores <#thresholding-outlier-scores>`_
* `Implemented Algorithms <#implemented-algorithms>`_
* `Quick Start for Outlier Detection <#quick-start-for-outlier-detection>`_
* `How to Contribute <#how-to-contribute>`_
* `Inclusion Criteria <#inclusion-criteria>`_

----

Installation
^^^^^^^^^^^^

PyOD is designed for easy installation using either **pip** or **conda**. We recommend using the latest version of PyOD due to frequent updates and enhancements:

.. code-block:: bash

   pip install pyod            # normal install
   pip install --upgrade pyod  # or update if needed

.. code-block:: bash

   conda install -c conda-forge pyod

Alternatively, you can clone and run the setup.py file:

.. code-block:: bash

   git clone https://github.com/yzhao062/pyod.git
   cd pyod
   pip install .

**Required Dependencies**:

* Python 3.8 or higher
* joblib
* matplotlib
* numpy>=1.19
* numba>=0.51
* scipy>=1.5.1
* scikit_learn>=0.22.0

**Optional Dependencies (see details below)**:

* combo (optional, required for models/combination.py and FeatureBagging)
* pytorch (optional, required for AutoEncoder, and other deep learning models)
* suod (optional, required for running SUOD model)
* xgboost (optional, required for XGBOD)
* pythresh (optional, required for thresholding)

----


API Cheatsheet & Reference
^^^^^^^^^^^^^^^^^^^^^^^^^^

The full API Reference is available at `PyOD Documentation <https://pyod.readthedocs.io/en/latest/pyod.html>`_. Below is a quick cheatsheet for all detectors:

* **fit(X)**: Fit the detector. The parameter y is ignored in unsupervised methods.
* **decision_function(X)**: Predict raw anomaly scores for X using the fitted detector.
* **predict(X)**: Determine whether a sample is an outlier or not as binary labels using the fitted detector.
* **predict_proba(X)**: Estimate the probability of a sample being an outlier using the fitted detector.
* **predict_confidence(X)**: Assess the model's confidence on a per-sample basis (applicable in predict and predict_proba) [#Perini2020Quantifying]_.

**Key Attributes of a fitted model**:

* **decision_scores_**: Outlier scores of the training data. Higher scores typically indicate more abnormal behavior. Outliers usually have higher scores.
* **labels_**: Binary labels of the training data, where 0 indicates inliers and 1 indicates outliers/anomalies.


----


ADBench Benchmark and Datasets
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

We just released a 45-page, the most comprehensive `ADBench: Anomaly Detection Benchmark <https://arxiv.org/abs/2206.09426>`_ [#Han2022ADBench]_.
The fully `open-sourced ADBench <https://github.com/Minqi824/ADBench>`_ compares 30 anomaly detection algorithms on 57 benchmark datasets.

The organization of **ADBench** is provided below:

.. image:: https://github.com/Minqi824/ADBench/blob/main/figs/ADBench.png?raw=true
   :target: https://github.com/Minqi824/ADBench/blob/main/figs/ADBench.png?raw=true
   :alt: benchmark-fig


For a simpler visualization, we make **the comparison of selected models** via
`compare_all_models.py <https://github.com/yzhao062/pyod/blob/master/examples/compare_all_models.py>`_\.

.. image:: https://github.com/yzhao062/pyod/blob/development/examples/ALL.png?raw=true
   :target: https://github.com/yzhao062/pyod/blob/development/examples/ALL.png?raw=true
   :alt: Comparison_of_All



----

Model Save & Load
^^^^^^^^^^^^^^^^^

PyOD takes a similar approach of sklearn regarding model persistence.
See `model persistence <https://scikit-learn.org/stable/modules/model_persistence.html>`_ for clarification.

In short, we recommend to use joblib or pickle for saving and loading PyOD models.
See `"examples/save_load_model_example.py" <https://github.com/yzhao062/pyod/blob/master/examples/save_load_model_example.py>`_ for an example.
In short, it is simple as below:

.. code-block:: python

    from joblib import dump, load

    # save the model
    dump(clf, 'clf.joblib')
    # load the model
    clf = load('clf.joblib')

It is known that there are challenges in saving neural network models.
Check `#328 <https://github.com/yzhao062/pyod/issues/328#issuecomment-917192704>`_
and `#88 <https://github.com/yzhao062/pyod/issues/88#issuecomment-615343139>`_
for temporary workaround.


----


Fast Train with SUOD
^^^^^^^^^^^^^^^^^^^^

**Fast training and prediction**: it is possible to train and predict with
a large number of detection models in PyOD by leveraging SUOD framework [#Zhao2021SUOD]_.
See  `SUOD Paper <https://www.andrew.cmu.edu/user/yuezhao2/papers/21-mlsys-suod.pdf>`_
and  `SUOD example <https://github.com/yzhao062/pyod/blob/master/examples/suod_example.py>`_.


.. code-block:: python

    from pyod.models.suod import SUOD

    # initialized a group of outlier detectors for acceleration
    detector_list = [LOF(n_neighbors=15), LOF(n_neighbors=20),
                     LOF(n_neighbors=25), LOF(n_neighbors=35),
                     COPOD(), IForest(n_estimators=100),
                     IForest(n_estimators=200)]

    # decide the number of parallel process, and the combination method
    # then clf can be used as any outlier detection model
    clf = SUOD(base_estimators=detector_list, n_jobs=2, combination='average',
               verbose=False)

----

Thresholding Outlier Scores
^^^^^^^^^^^^^^^^^^^^^^^^^^^

A more data-based approach can be taken when setting the contamination level. By using a thresholding method, guessing an arbitrary value can be replaced with tested techniques for separating inliers and outliers. Refer to `PyThresh <https://github.com/KulikDM/pythresh>`_ for a more in-depth look at thresholding.

.. code-block:: python

    from pyod.models.knn import KNN
    from pyod.models.thresholds import FILTER

    # Set the outlier detection and thresholding methods
    clf = KNN(contamination=FILTER())


See supported thresholding methods in `thresholding <https://github.com/yzhao062/pyod/blob/master/docs/thresholding.rst>`_.

----



Implemented Algorithms
^^^^^^^^^^^^^^^^^^^^^^

PyOD toolkit consists of four major functional groups:

**(i) Individual Detection Algorithms** :

===================  ==================  ======================================================================================================  =====  ========================================
Type                 Abbr                Algorithm                                                                                               Year   Ref
===================  ==================  ======================================================================================================  =====  ========================================
Probabilistic        ECOD                Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions                        2022   [#Li2021ECOD]_
Probabilistic        ABOD                Angle-Based Outlier Detection                                                                           2008   [#Kriegel2008Angle]_
Probabilistic        FastABOD            Fast Angle-Based Outlier Detection using approximation                                                  2008   [#Kriegel2008Angle]_
Probabilistic        COPOD               COPOD: Copula-Based Outlier Detection                                                                   2020   [#Li2020COPOD]_
Probabilistic        MAD                 Median Absolute Deviation (MAD)                                                                         1993   [#Iglewicz1993How]_
Probabilistic        SOS                 Stochastic Outlier Selection                                                                            2012   [#Janssens2012Stochastic]_
Probabilistic        QMCD                Quasi-Monte Carlo Discrepancy outlier detection                                                         2001   [#Fang2001Wrap]_
Probabilistic        KDE                 Outlier Detection with Kernel Density Functions                                                         2007   [#Latecki2007Outlier]_
Probabilistic        Sampling            Rapid distance-based outlier detection via sampling                                                     2013   [#Sugiyama2013Rapid]_
Probabilistic        GMM                 Probabilistic Mixture Modeling for Outlier Analysis                                                            [#Aggarwal2015Outlier]_ [Ch.2]
Linear Model         PCA                 Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes)   2003   [#Shyu2003A]_
Linear Model         KPCA                Kernel Principal Component Analysis                                                                     2007   [#Hoffmann2007Kernel]_
Linear Model         MCD                 Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores)                    1999   [#Hardin2004Outlier]_ [#Rousseeuw1999A]_
Linear Model         CD                  Use Cook's distance for outlier detection                                                               1977   [#Cook1977Detection]_
Linear Model         OCSVM               One-Class Support Vector Machines                                                                       2001   [#Scholkopf2001Estimating]_
Linear Model         LMDD                Deviation-based Outlier Detection (LMDD)                                                                1996   [#Arning1996A]_
Proximity-Based      LOF                 Local Outlier Factor                                                                                    2000   [#Breunig2000LOF]_
Proximity-Based      COF                 Connectivity-Based Outlier Factor                                                                       2002   [#Tang2002Enhancing]_
Proximity-Based      (Incremental) COF   Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity)               2002   [#Tang2002Enhancing]_
Proximity-Based      CBLOF               Clustering-Based Local Outlier Factor                                                                   2003   [#He2003Discovering]_
Proximity-Based      LOCI                LOCI: Fast outlier detection using the local correlation integral                                       2003   [#Papadimitriou2003LOCI]_
Proximity-Based      HBOS                Histogram-based Outlier Score                                                                           2012   [#Goldstein2012Histogram]_
Proximity-Based      kNN                 k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score)                 2000   [#Ramaswamy2000Efficient]_
Proximity-Based      AvgKNN              Average kNN (use the average distance to k nearest neighbors as the outlier score)                      2002   [#Angiulli2002Fast]_
Proximity-Based      MedKNN              Median kNN (use the median distance to k nearest neighbors as the outlier score)                        2002   [#Angiulli2002Fast]_
Proximity-Based      SOD                 Subspace Outlier Detection                                                                              2009   [#Kriegel2009Outlier]_
Proximity-Based      ROD                 Rotation-based Outlier Detection                                                                        2020   [#Almardeny2020A]_
Outlier Ensembles    IForest             Isolation Forest                                                                                        2008   [#Liu2008Isolation]_
Outlier Ensembles    INNE                Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles                                      2018   [#Bandaragoda2018Isolation]_
Outlier Ensembles    DIF                 Deep Isolation Forest for Anomaly Detection                                                             2023   [#Xu2023Deep]_
Outlier Ensembles    FB                  Feature Bagging                                                                                         2005   [#Lazarevic2005Feature]_
Outlier Ensembles    LSCP                LSCP: Locally Selective Combination of Parallel Outlier Ensembles                                       2019   [#Zhao2019LSCP]_
Outlier Ensembles    XGBOD               Extreme Boosting Based Outlier Detection **(Supervised)**                                               2018   [#Zhao2018XGBOD]_
Outlier Ensembles    LODA                Lightweight On-line Detector of Anomalies                                                               2016   [#Pevny2016Loda]_
Outlier Ensembles    SUOD                SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection **(Acceleration)**          2021   [#Zhao2021SUOD]_
Neural Networks      AutoEncoder         Fully connected AutoEncoder (use reconstruction error as the outlier score)                                    [#Aggarwal2015Outlier]_ [Ch.3]
Neural Networks      VAE                 Variational AutoEncoder (use reconstruction error as the outlier score)                                 2013   [#Kingma2013Auto]_
Neural Networks      Beta-VAE            Variational AutoEncoder (all customized loss term by varying gamma and capacity)                        2018   [#Burgess2018Understanding]_
Neural Networks      SO_GAAL             Single-Objective Generative Adversarial Active Learning                                                 2019   [#Liu2019Generative]_
Neural Networks      MO_GAAL             Multiple-Objective Generative Adversarial Active Learning                                               2019   [#Liu2019Generative]_
Neural Networks      DeepSVDD            Deep One-Class Classification                                                                           2018   [#Ruff2018Deep]_
Neural Networks      AnoGAN              Anomaly Detection with Generative Adversarial Networks                                                  2017   [#Schlegl2017Unsupervised]_
Neural Networks      ALAD                Adversarially learned anomaly detection                                                                 2018   [#Zenati2018Adversarially]_
Neural Networks      AE1SVM              Autoencoder-based One-class Support Vector Machine                                                      2019   [#Nguyen2019scalable]_
Neural Networks      DevNet              Deep Anomaly Detection with Deviation Networks                                                          2019   [#Pang2019Deep]_
Graph-based          R-Graph             Outlier detection by R-graph                                                                            2017   [#You2017Provable]_
Graph-based          LUNAR               LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks                               2022   [#Goodge2022Lunar]_
===================  ==================  ======================================================================================================  =====  ========================================


**(ii) Outlier Ensembles & Outlier Detector Combination Frameworks**:

===================  ================  =====================================================================================================  =====  ========================================
Type                 Abbr              Algorithm                                                                                              Year   Ref
===================  ================  =====================================================================================================  =====  ========================================
Outlier Ensembles    FB                Feature Bagging                                                                                        2005   [#Lazarevic2005Feature]_
Outlier Ensembles    LSCP              LSCP: Locally Selective Combination of Parallel Outlier Ensembles                                      2019   [#Zhao2019LSCP]_
Outlier Ensembles    XGBOD             Extreme Boosting Based Outlier Detection **(Supervised)**                                              2018   [#Zhao2018XGBOD]_
Outlier Ensembles    LODA              Lightweight On-line Detector of Anomalies                                                              2016   [#Pevny2016Loda]_
Outlier Ensembles    SUOD              SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection **(Acceleration)**         2021   [#Zhao2021SUOD]_
Outlier Ensembles    INNE              Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles                                     2018   [#Bandaragoda2018Isolation]_
Combination          Average           Simple combination by averaging the scores                                                             2015   [#Aggarwal2015Theoretical]_
Combination          Weighted Average  Simple combination by averaging the scores with detector weights                                       2015   [#Aggarwal2015Theoretical]_
Combination          Maximization      Simple combination by taking the maximum scores                                                        2015   [#Aggarwal2015Theoretical]_
Combination          AOM               Average of Maximum                                                                                     2015   [#Aggarwal2015Theoretical]_
Combination          MOA               Maximization of Average                                                                                2015   [#Aggarwal2015Theoretical]_
Combination          Median            Simple combination by taking the median of the scores                                                  2015   [#Aggarwal2015Theoretical]_
Combination          majority Vote     Simple combination by taking the majority vote of the labels (weights can be used)                     2015   [#Aggarwal2015Theoretical]_
===================  ================  =====================================================================================================  =====  ========================================


**(iii) Utility Functions**:

===================  ======================  =====================================================================================================================================================  ======================================================================================================================================
Type                 Name                    Function                                                                                                                                               Documentation
===================  ======================  =====================================================================================================================================================  ======================================================================================================================================
Data                 generate_data           Synthesized data generation; normal data is generated by a multivariate Gaussian and outliers are generated by a uniform distribution                  `generate_data <https://pyod.readthedocs.io/en/latest/pyod.utils.html#module-pyod.utils.data.generate_data>`_
Data                 generate_data_clusters  Synthesized data generation in clusters; more complex data patterns can be created with multiple clusters                                              `generate_data_clusters <https://pyod.readthedocs.io/en/latest/pyod.utils.html#pyod.utils.data.generate_data_clusters>`_
Stat                 wpearsonr               Calculate the weighted Pearson correlation of two samples                                                                                              `wpearsonr <https://pyod.readthedocs.io/en/latest/pyod.utils.html#module-pyod.utils.stat_models.wpearsonr>`_
Utility              get_label_n             Turn raw outlier scores into binary labels by assign 1 to top n outlier scores                                                                         `get_label_n <https://pyod.readthedocs.io/en/latest/pyod.utils.html#module-pyod.utils.utility.get_label_n>`_
Utility              precision_n_scores      calculate precision @ rank n                                                                                                                           `precision_n_scores <https://pyod.readthedocs.io/en/latest/pyod.utils.html#module-pyod.utils.utility.precision_n_scores>`_
===================  ======================  =====================================================================================================================================================  ======================================================================================================================================

----

Quick Start for Outlier Detection
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

PyOD has been well acknowledged by the machine learning community with a few featured posts and tutorials.

**Analytics Vidhya**: `An Awesome Tutorial to Learn Outlier Detection in Python using PyOD Library <https://www.analyticsvidhya.com/blog/2019/02/outlier-detection-python-pyod/>`_

**KDnuggets**: `Intuitive Visualization of Outlier Detection Methods <https://www.kdnuggets.com/2019/02/outlier-detection-methods-cheat-sheet.html>`_, `An Overview of Outlier Detection Methods from PyOD <https://www.kdnuggets.com/2019/06/overview-outlier-detection-methods-pyod.html>`_

**Towards Data Science**: `Anomaly Detection for Dummies <https://towardsdatascience.com/anomaly-detection-for-dummies-15f148e559c1>`_

`"examples/knn_example.py" <https://github.com/yzhao062/pyod/blob/master/examples/knn_example.py>`_
demonstrates the basic API of using kNN detector. **It is noted that the API across all other algorithms are consistent/similar**.

More detailed instructions for running examples can be found in `examples directory <https://github.com/yzhao062/pyod/blob/master/examples>`_.


#. Initialize a kNN detector, fit the model, and make the prediction.

   .. code-block:: python


       from pyod.models.knn import KNN   # kNN detector

       # train kNN detector
       clf_name = 'KNN'
       clf = KNN()
       clf.fit(X_train)

       # get the prediction label and outlier scores of the training data
       y_train_pred = clf.labels_  # binary labels (0: inliers, 1: outliers)
       y_train_scores = clf.decision_scores_  # raw outlier scores

       # get the prediction on the test data
       y_test_pred = clf.predict(X_test)  # outlier labels (0 or 1)
       y_test_scores = clf.decision_function(X_test)  # outlier scores

       # it is possible to get the prediction confidence as well
       y_test_pred, y_test_pred_confidence = clf.predict(X_test, return_confidence=True)  # outlier labels (0 or 1) and confidence in the range of [0,1]

#. Evaluate the prediction by ROC and Precision @ Rank n (p@n).

   .. code-block:: python

       from pyod.utils.data import evaluate_print
       
       # evaluate and print the results
       print("\nOn Training Data:")
       evaluate_print(clf_name, y_train, y_train_scores)
       print("\nOn Test Data:")
       evaluate_print(clf_name, y_test, y_test_scores)


#. See a sample output & visualization.


   .. code-block:: python


       On Training Data:
       KNN ROC:1.0, precision @ rank n:1.0

       On Test Data:
       KNN ROC:0.9989, precision @ rank n:0.9

   .. code-block:: python


       visualize(clf_name, X_train, y_train, X_test, y_test, y_train_pred,
           y_test_pred, show_figure=True, save_figure=False)

Visualization (\ `knn_figure <https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png>`_\ ):

.. image:: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png
   :target: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png
   :alt: kNN example figure

----

Reference
^^^^^^^^^


.. [#Aggarwal2015Outlier] Aggarwal, C.C., 2015. Outlier analysis. In Data mining (pp. 237-263). Springer, Cham.

.. [#Aggarwal2015Theoretical] Aggarwal, C.C. and Sathe, S., 2015. Theoretical foundations and algorithms for outlier ensembles.\ *ACM SIGKDD Explorations Newsletter*\ , 17(1), pp.24-47.

.. [#Aggarwal2017Outlier] Aggarwal, C.C. and Sathe, S., 2017. Outlier ensembles: An introduction. Springer.

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