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.
.. [#Almardeny2020A] Almardeny, Y., Boujnah, N. and Cleary, F., 2020. A Novel Outlier Detection Method for Multivariate Data. *IEEE Transactions on Knowledge and Data Engineering*.
.. [#Angiulli2002Fast] Angiulli, F. and Pizzuti, C., 2002, August. Fast outlier detection in high dimensional spaces. In *European Conference on Principles of Data Mining and Knowledge Discovery* pp. 15-27.
.. [#Arning1996A] Arning, A., Agrawal, R. and Raghavan, P., 1996, August. A Linear Method for Deviation Detection in Large Databases. In *KDD* (Vol. 1141, No. 50, pp. 972-981).
.. [#Bandaragoda2018Isolation] Bandaragoda, T. R., Ting, K. M., Albrecht, D., Liu, F. T., Zhu, Y., and Wells, J. R., 2018, Isolation-based anomaly detection using nearest-neighbor ensembles. *Computational Intelligence*\ , 34(4), pp. 968-998.
.. [#Breunig2000LOF] Breunig, M.M., Kriegel, H.P., Ng, R.T. and Sander, J., 2000, May. LOF: identifying density-based local outliers. *ACM Sigmod Record*\ , 29(2), pp. 93-104.
.. [#Burgess2018Understanding] Burgess, Christopher P., et al. "Understanding disentangling in beta-VAE." arXiv preprint arXiv:1804.03599 (2018).
.. [#Cook1977Detection] Cook, R.D., 1977. Detection of influential observation in linear regression. Technometrics, 19(1), pp.15-18.
.. [#Fang2001Wrap] Fang, K.T. and Ma, C.X., 2001. Wrap-around L2-discrepancy of random sampling, Latin hypercube and uniform designs. Journal of complexity, 17(4), pp.608-624.
.. [#Goldstein2012Histogram] Goldstein, M. and Dengel, A., 2012. Histogram-based outlier score (hbos): A fast unsupervised anomaly detection algorithm. In *KI-2012: Poster and Demo Track*\ , pp.59-63.
.. [#Goodge2022Lunar] Goodge, A., Hooi, B., Ng, S.K. and Ng, W.S., 2022, June. Lunar: Unifying local outlier detection methods via graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence.
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"description": "Python Outlier Detection (PyOD)\r\n===============================\r\n\r\n**Deployment & Documentation & Stats & License**\r\n\r\n|badge_pypi| |badge_anaconda| |badge_docs| |badge_stars| |badge_forks| |badge_downloads| |badge_testing| |badge_coverage| |badge_maintainability| |badge_license| |badge_benchmark|\r\n\r\n.. |badge_pypi| image:: https://img.shields.io/pypi/v/pyod.svg?color=brightgreen\r\n :target: https://pypi.org/project/pyod/\r\n :alt: PyPI version\r\n\r\n.. |badge_anaconda| image:: https://anaconda.org/conda-forge/pyod/badges/version.svg\r\n :target: https://anaconda.org/conda-forge/pyod\r\n :alt: Anaconda version\r\n\r\n.. |badge_docs| image:: https://readthedocs.org/projects/pyod/badge/?version=latest\r\n :target: https://pyod.readthedocs.io/en/latest/?badge=latest\r\n :alt: Documentation status\r\n\r\n.. |badge_stars| image:: https://img.shields.io/github/stars/yzhao062/pyod.svg\r\n :target: https://github.com/yzhao062/pyod/stargazers\r\n :alt: GitHub stars\r\n\r\n.. |badge_forks| image:: https://img.shields.io/github/forks/yzhao062/pyod.svg?color=blue\r\n :target: https://github.com/yzhao062/pyod/network\r\n :alt: GitHub forks\r\n\r\n.. |badge_downloads| image:: https://pepy.tech/badge/pyod\r\n :target: https://pepy.tech/project/pyod\r\n :alt: Downloads\r\n\r\n.. |badge_testing| image:: https://github.com/yzhao062/pyod/actions/workflows/testing.yml/badge.svg\r\n :target: https://github.com/yzhao062/pyod/actions/workflows/testing.yml\r\n :alt: Testing\r\n\r\n\r\n.. |badge_coverage| image:: https://coveralls.io/repos/github/yzhao062/pyod/badge.svg\r\n :target: https://coveralls.io/github/yzhao062/pyod\r\n :alt: Coverage Status\r\n\r\n.. |badge_maintainability| image:: https://api.codeclimate.com/v1/badges/bdc3d8d0454274c753c4/maintainability\r\n :target: https://codeclimate.com/github/yzhao062/Pyod/maintainability\r\n :alt: Maintainability\r\n\r\n.. |badge_license| image:: https://img.shields.io/github/license/yzhao062/pyod.svg\r\n :target: https://github.com/yzhao062/pyod/blob/master/LICENSE\r\n :alt: License\r\n\r\n.. |badge_benchmark| image:: https://img.shields.io/badge/ADBench-benchmark_results-pink\r\n :target: https://github.com/Minqi824/ADBench\r\n :alt: Benchmark\r\n\r\n\r\n-----\r\n\r\n\r\nRead Me First\r\n^^^^^^^^^^^^^\r\n\r\nWelcome 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.\r\n\r\n* **For time-series outlier detection**, please use `TODS <https://github.com/datamllab/tods>`_.\r\n\r\n* **For graph outlier detection**, please use `PyGOD <https://pygod.org/>`_.\r\n\r\n* **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.\r\n\r\n* **Learn more about anomaly detection** at `Anomaly Detection Resources <https://github.com/yzhao062/anomaly-detection-resources>`_\r\n\r\n* **PyOD on Distributed Systems**: you can also run `PyOD on databricks <https://www.databricks.com/blog/2023/03/13/unsupervised-outlier-detection-databricks.html>`_.\r\n\r\n----\r\n\r\nAbout PyOD\r\n^^^^^^^^^^\r\n\r\nPyOD, 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>`_.\r\n\r\nPyOD 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>`_.\r\n\r\n**PyOD is featured for**:\r\n\r\n* **Unified, User-Friendly Interface** across various algorithms.\r\n* **Wide Range of Models**, from classic techniques to the latest deep learning methods in **PyTorch**.\r\n* **High Performance & Efficiency**, leveraging `numba <https://github.com/numba/numba>`_ and `joblib <https://github.com/joblib/joblib>`_ for JIT compilation and parallel processing.\r\n* **Fast Training & Prediction**, achieved through the SUOD framework [#Zhao2021SUOD]_.\r\n\r\n**Outlier Detection with 5 Lines of Code**:\r\n\r\n.. code-block:: python\r\n\r\n # Example: Training an ECOD detector\r\n from pyod.models.ecod import ECOD\r\n clf = ECOD()\r\n clf.fit(X_train)\r\n y_train_scores = clf.decision_scores_ # Outlier scores for training data\r\n y_test_scores = clf.decision_function(X_test) # Outlier scores for test data\r\n\r\n\r\n**Selecting the Right Algorithm:** Unsure where to start? Consider these robust and interpretable options:\r\n\r\n- `ECOD <https://github.com/yzhao062/pyod/blob/master/examples/ecod_example.py>`_: Example of using ECOD for outlier detection\r\n- `Isolation Forest <https://github.com/yzhao062/pyod/blob/master/examples/iforest_example.py>`_: Example of using Isolation Forest for outlier detection\r\n\r\nAlternatively, explore `MetaOD <https://github.com/yzhao062/MetaOD>`_ for a data-driven approach.\r\n\r\n**Citing PyOD**:\r\n\r\n`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::\r\n\r\n @article{zhao2019pyod,\r\n author = {Zhao, Yue and Nasrullah, Zain and Li, Zheng},\r\n title = {PyOD: A Python Toolbox for Scalable Outlier Detection},\r\n journal = {Journal of Machine Learning Research},\r\n year = {2019},\r\n volume = {20},\r\n number = {96},\r\n pages = {1-7},\r\n url = {http://jmlr.org/papers/v20/19-011.html}\r\n }\r\n\r\nor::\r\n\r\n 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.\r\n\r\nFor 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>`_::\r\n\r\n @article{han2022adbench,\r\n title={Adbench: Anomaly detection benchmark},\r\n author={Han, Songqiao and Hu, Xiyang and Huang, Hailiang and Jiang, Minqi and Zhao, Yue},\r\n journal={Advances in Neural Information Processing Systems},\r\n volume={35},\r\n pages={32142--32159},\r\n year={2022}\r\n }\r\n\r\n @article{jiang2023adgym,\r\n title={ADGym: Design Choices for Deep Anomaly Detection},\r\n author={Jiang, Minqi and Hou, Chaochuan and Zheng, Ao and Han, Songqiao and Huang, Hailiang and Wen, Qingsong and Hu, Xiyang and Zhao, Yue},\r\n journal={Advances in Neural Information Processing Systems},\r\n volume={36},\r\n year={2023}\r\n }\r\n\r\n\r\n**Table of Contents**:\r\n\r\n* `Installation <#installation>`_\r\n* `API Cheatsheet & Reference <#api-cheatsheet--reference>`_\r\n* `ADBench Benchmark and Datasets <#adbench-benchmark-and-datasets>`_\r\n* `Model Save & Load <#model-save--load>`_\r\n* `Fast Train with SUOD <#fast-train-with-suod>`_\r\n* `Thresholding Outlier Scores <#thresholding-outlier-scores>`_\r\n* `Implemented Algorithms <#implemented-algorithms>`_\r\n* `Quick Start for Outlier Detection <#quick-start-for-outlier-detection>`_\r\n* `How to Contribute <#how-to-contribute>`_\r\n* `Inclusion Criteria <#inclusion-criteria>`_\r\n\r\n----\r\n\r\nInstallation\r\n^^^^^^^^^^^^\r\n\r\nPyOD is designed for easy installation using either **pip** or **conda**. We recommend using the latest version of PyOD due to frequent updates and enhancements:\r\n\r\n.. code-block:: bash\r\n\r\n pip install pyod # normal install\r\n pip install --upgrade pyod # or update if needed\r\n\r\n.. code-block:: bash\r\n\r\n conda install -c conda-forge pyod\r\n\r\nAlternatively, you can clone and run the setup.py file:\r\n\r\n.. code-block:: bash\r\n\r\n git clone https://github.com/yzhao062/pyod.git\r\n cd pyod\r\n pip install .\r\n\r\n**Required Dependencies**:\r\n\r\n* Python 3.8 or higher\r\n* joblib\r\n* matplotlib\r\n* numpy>=1.19\r\n* numba>=0.51\r\n* scipy>=1.5.1\r\n* scikit_learn>=0.22.0\r\n\r\n**Optional Dependencies (see details below)**:\r\n\r\n* combo (optional, required for models/combination.py and FeatureBagging)\r\n* pytorch (optional, required for AutoEncoder, and other deep learning models)\r\n* suod (optional, required for running SUOD model)\r\n* xgboost (optional, required for XGBOD)\r\n* pythresh (optional, required for thresholding)\r\n\r\n----\r\n\r\n\r\nAPI Cheatsheet & Reference\r\n^^^^^^^^^^^^^^^^^^^^^^^^^^\r\n\r\nThe full API Reference is available at `PyOD Documentation <https://pyod.readthedocs.io/en/latest/pyod.html>`_. Below is a quick cheatsheet for all detectors:\r\n\r\n* **fit(X)**: Fit the detector. The parameter y is ignored in unsupervised methods.\r\n* **decision_function(X)**: Predict raw anomaly scores for X using the fitted detector.\r\n* **predict(X)**: Determine whether a sample is an outlier or not as binary labels using the fitted detector.\r\n* **predict_proba(X)**: Estimate the probability of a sample being an outlier using the fitted detector.\r\n* **predict_confidence(X)**: Assess the model's confidence on a per-sample basis (applicable in predict and predict_proba) [#Perini2020Quantifying]_.\r\n\r\n**Key Attributes of a fitted model**:\r\n\r\n* **decision_scores_**: Outlier scores of the training data. Higher scores typically indicate more abnormal behavior. Outliers usually have higher scores.\r\n* **labels_**: Binary labels of the training data, where 0 indicates inliers and 1 indicates outliers/anomalies.\r\n\r\n\r\n----\r\n\r\n\r\nADBench Benchmark and Datasets\r\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\r\n\r\nWe just released a 45-page, the most comprehensive `ADBench: Anomaly Detection Benchmark <https://arxiv.org/abs/2206.09426>`_ [#Han2022ADBench]_.\r\nThe fully `open-sourced ADBench <https://github.com/Minqi824/ADBench>`_ compares 30 anomaly detection algorithms on 57 benchmark datasets.\r\n\r\nThe organization of **ADBench** is provided below:\r\n\r\n.. image:: https://github.com/Minqi824/ADBench/blob/main/figs/ADBench.png?raw=true\r\n :target: https://github.com/Minqi824/ADBench/blob/main/figs/ADBench.png?raw=true\r\n :alt: benchmark-fig\r\n\r\n\r\nFor a simpler visualization, we make **the comparison of selected models** via\r\n`compare_all_models.py <https://github.com/yzhao062/pyod/blob/master/examples/compare_all_models.py>`_\\.\r\n\r\n.. image:: https://github.com/yzhao062/pyod/blob/development/examples/ALL.png?raw=true\r\n :target: https://github.com/yzhao062/pyod/blob/development/examples/ALL.png?raw=true\r\n :alt: Comparison_of_All\r\n\r\n\r\n\r\n----\r\n\r\nModel Save & Load\r\n^^^^^^^^^^^^^^^^^\r\n\r\nPyOD takes a similar approach of sklearn regarding model persistence.\r\nSee `model persistence <https://scikit-learn.org/stable/modules/model_persistence.html>`_ for clarification.\r\n\r\nIn short, we recommend to use joblib or pickle for saving and loading PyOD models.\r\nSee `\"examples/save_load_model_example.py\" <https://github.com/yzhao062/pyod/blob/master/examples/save_load_model_example.py>`_ for an example.\r\nIn short, it is simple as below:\r\n\r\n.. code-block:: python\r\n\r\n from joblib import dump, load\r\n\r\n # save the model\r\n dump(clf, 'clf.joblib')\r\n # load the model\r\n clf = load('clf.joblib')\r\n\r\nIt is known that there are challenges in saving neural network models.\r\nCheck `#328 <https://github.com/yzhao062/pyod/issues/328#issuecomment-917192704>`_\r\nand `#88 <https://github.com/yzhao062/pyod/issues/88#issuecomment-615343139>`_\r\nfor temporary workaround.\r\n\r\n\r\n----\r\n\r\n\r\nFast Train with SUOD\r\n^^^^^^^^^^^^^^^^^^^^\r\n\r\n**Fast training and prediction**: it is possible to train and predict with\r\na large number of detection models in PyOD by leveraging SUOD framework [#Zhao2021SUOD]_.\r\nSee `SUOD Paper <https://www.andrew.cmu.edu/user/yuezhao2/papers/21-mlsys-suod.pdf>`_\r\nand `SUOD example <https://github.com/yzhao062/pyod/blob/master/examples/suod_example.py>`_.\r\n\r\n\r\n.. code-block:: python\r\n\r\n from pyod.models.suod import SUOD\r\n\r\n # initialized a group of outlier detectors for acceleration\r\n detector_list = [LOF(n_neighbors=15), LOF(n_neighbors=20),\r\n LOF(n_neighbors=25), LOF(n_neighbors=35),\r\n COPOD(), IForest(n_estimators=100),\r\n IForest(n_estimators=200)]\r\n\r\n # decide the number of parallel process, and the combination method\r\n # then clf can be used as any outlier detection model\r\n clf = SUOD(base_estimators=detector_list, n_jobs=2, combination='average',\r\n verbose=False)\r\n\r\n----\r\n\r\nThresholding Outlier Scores\r\n^^^^^^^^^^^^^^^^^^^^^^^^^^^\r\n\r\nA 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.\r\n\r\n.. code-block:: python\r\n\r\n from pyod.models.knn import KNN\r\n from pyod.models.thresholds import FILTER\r\n\r\n # Set the outlier detection and thresholding methods\r\n clf = KNN(contamination=FILTER())\r\n\r\n\r\nSee supported thresholding methods in `thresholding <https://github.com/yzhao062/pyod/blob/master/docs/thresholding.rst>`_.\r\n\r\n----\r\n\r\n\r\n\r\nImplemented Algorithms\r\n^^^^^^^^^^^^^^^^^^^^^^\r\n\r\nPyOD toolkit consists of four major functional groups:\r\n\r\n**(i) Individual Detection Algorithms** :\r\n\r\n=================== ================== ====================================================================================================== ===== ========================================\r\nType Abbr Algorithm Year Ref\r\n=================== ================== ====================================================================================================== ===== ========================================\r\nProbabilistic ECOD Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions 2022 [#Li2021ECOD]_\r\nProbabilistic ABOD Angle-Based Outlier Detection 2008 [#Kriegel2008Angle]_\r\nProbabilistic FastABOD Fast Angle-Based Outlier Detection using approximation 2008 [#Kriegel2008Angle]_\r\nProbabilistic COPOD COPOD: Copula-Based Outlier Detection 2020 [#Li2020COPOD]_\r\nProbabilistic MAD Median Absolute Deviation (MAD) 1993 [#Iglewicz1993How]_\r\nProbabilistic SOS Stochastic Outlier Selection 2012 [#Janssens2012Stochastic]_\r\nProbabilistic QMCD Quasi-Monte Carlo Discrepancy outlier detection 2001 [#Fang2001Wrap]_\r\nProbabilistic KDE Outlier Detection with Kernel Density Functions 2007 [#Latecki2007Outlier]_\r\nProbabilistic Sampling Rapid distance-based outlier detection via sampling 2013 [#Sugiyama2013Rapid]_\r\nProbabilistic GMM Probabilistic Mixture Modeling for Outlier Analysis [#Aggarwal2015Outlier]_ [Ch.2]\r\nLinear Model PCA Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes) 2003 [#Shyu2003A]_\r\nLinear Model KPCA Kernel Principal Component Analysis 2007 [#Hoffmann2007Kernel]_\r\nLinear Model MCD Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 1999 [#Hardin2004Outlier]_ [#Rousseeuw1999A]_\r\nLinear Model CD Use Cook's distance for outlier detection 1977 [#Cook1977Detection]_\r\nLinear Model OCSVM One-Class Support Vector Machines 2001 [#Scholkopf2001Estimating]_\r\nLinear Model LMDD Deviation-based Outlier Detection (LMDD) 1996 [#Arning1996A]_\r\nProximity-Based LOF Local Outlier Factor 2000 [#Breunig2000LOF]_\r\nProximity-Based COF Connectivity-Based Outlier Factor 2002 [#Tang2002Enhancing]_\r\nProximity-Based (Incremental) COF Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity) 2002 [#Tang2002Enhancing]_\r\nProximity-Based CBLOF Clustering-Based Local Outlier Factor 2003 [#He2003Discovering]_\r\nProximity-Based LOCI LOCI: Fast outlier detection using the local correlation integral 2003 [#Papadimitriou2003LOCI]_\r\nProximity-Based HBOS Histogram-based Outlier Score 2012 [#Goldstein2012Histogram]_\r\nProximity-Based kNN k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score) 2000 [#Ramaswamy2000Efficient]_\r\nProximity-Based AvgKNN Average kNN (use the average distance to k nearest neighbors as the outlier score) 2002 [#Angiulli2002Fast]_\r\nProximity-Based MedKNN Median kNN (use the median distance to k nearest neighbors as the outlier score) 2002 [#Angiulli2002Fast]_\r\nProximity-Based SOD Subspace Outlier Detection 2009 [#Kriegel2009Outlier]_\r\nProximity-Based ROD Rotation-based Outlier Detection 2020 [#Almardeny2020A]_\r\nOutlier Ensembles IForest Isolation Forest 2008 [#Liu2008Isolation]_\r\nOutlier Ensembles INNE Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles 2018 [#Bandaragoda2018Isolation]_\r\nOutlier Ensembles DIF Deep Isolation Forest for Anomaly Detection 2023 [#Xu2023Deep]_\r\nOutlier Ensembles FB Feature Bagging 2005 [#Lazarevic2005Feature]_\r\nOutlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 [#Zhao2019LSCP]_\r\nOutlier Ensembles XGBOD Extreme Boosting Based Outlier Detection **(Supervised)** 2018 [#Zhao2018XGBOD]_\r\nOutlier Ensembles LODA Lightweight On-line Detector of Anomalies 2016 [#Pevny2016Loda]_\r\nOutlier Ensembles SUOD SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection **(Acceleration)** 2021 [#Zhao2021SUOD]_\r\nNeural Networks AutoEncoder Fully connected AutoEncoder (use reconstruction error as the outlier score) [#Aggarwal2015Outlier]_ [Ch.3]\r\nNeural Networks VAE Variational AutoEncoder (use reconstruction error as the outlier score) 2013 [#Kingma2013Auto]_\r\nNeural Networks Beta-VAE Variational AutoEncoder (all customized loss term by varying gamma and capacity) 2018 [#Burgess2018Understanding]_\r\nNeural Networks SO_GAAL Single-Objective Generative Adversarial Active Learning 2019 [#Liu2019Generative]_\r\nNeural Networks MO_GAAL Multiple-Objective Generative Adversarial Active Learning 2019 [#Liu2019Generative]_\r\nNeural Networks DeepSVDD Deep One-Class Classification 2018 [#Ruff2018Deep]_\r\nNeural Networks AnoGAN Anomaly Detection with Generative Adversarial Networks 2017 [#Schlegl2017Unsupervised]_\r\nNeural Networks ALAD Adversarially learned anomaly detection 2018 [#Zenati2018Adversarially]_\r\nNeural Networks AE1SVM Autoencoder-based One-class Support Vector Machine 2019 [#Nguyen2019scalable]_\r\nNeural Networks DevNet Deep Anomaly Detection with Deviation Networks 2019 [#Pang2019Deep]_\r\nGraph-based R-Graph Outlier detection by R-graph 2017 [#You2017Provable]_\r\nGraph-based LUNAR LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks 2022 [#Goodge2022Lunar]_\r\n=================== ================== ====================================================================================================== ===== ========================================\r\n\r\n\r\n**(ii) Outlier Ensembles & Outlier Detector Combination Frameworks**:\r\n\r\n=================== ================ ===================================================================================================== ===== ========================================\r\nType Abbr Algorithm Year Ref\r\n=================== ================ ===================================================================================================== ===== ========================================\r\nOutlier Ensembles FB Feature Bagging 2005 [#Lazarevic2005Feature]_\r\nOutlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 [#Zhao2019LSCP]_\r\nOutlier Ensembles XGBOD Extreme Boosting Based Outlier Detection **(Supervised)** 2018 [#Zhao2018XGBOD]_\r\nOutlier Ensembles LODA Lightweight On-line Detector of Anomalies 2016 [#Pevny2016Loda]_\r\nOutlier Ensembles SUOD SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection **(Acceleration)** 2021 [#Zhao2021SUOD]_\r\nOutlier Ensembles INNE Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles 2018 [#Bandaragoda2018Isolation]_\r\nCombination Average Simple combination by averaging the scores 2015 [#Aggarwal2015Theoretical]_\r\nCombination Weighted Average Simple combination by averaging the scores with detector weights 2015 [#Aggarwal2015Theoretical]_\r\nCombination Maximization Simple combination by taking the maximum scores 2015 [#Aggarwal2015Theoretical]_\r\nCombination AOM Average of Maximum 2015 [#Aggarwal2015Theoretical]_\r\nCombination MOA Maximization of Average 2015 [#Aggarwal2015Theoretical]_\r\nCombination Median Simple combination by taking the median of the scores 2015 [#Aggarwal2015Theoretical]_\r\nCombination majority Vote Simple combination by taking the majority vote of the labels (weights can be used) 2015 [#Aggarwal2015Theoretical]_\r\n=================== ================ ===================================================================================================== ===== ========================================\r\n\r\n\r\n**(iii) Utility Functions**:\r\n\r\n=================== ====================== ===================================================================================================================================================== ======================================================================================================================================\r\nType Name Function Documentation\r\n=================== ====================== ===================================================================================================================================================== ======================================================================================================================================\r\nData 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>`_\r\nData 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>`_\r\nStat 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>`_\r\nUtility 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>`_\r\nUtility 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>`_\r\n=================== ====================== ===================================================================================================================================================== ======================================================================================================================================\r\n\r\n----\r\n\r\nQuick Start for Outlier Detection\r\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\r\n\r\nPyOD has been well acknowledged by the machine learning community with a few featured posts and tutorials.\r\n\r\n**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/>`_\r\n\r\n**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>`_\r\n\r\n**Towards Data Science**: `Anomaly Detection for Dummies <https://towardsdatascience.com/anomaly-detection-for-dummies-15f148e559c1>`_\r\n\r\n`\"examples/knn_example.py\" <https://github.com/yzhao062/pyod/blob/master/examples/knn_example.py>`_\r\ndemonstrates the basic API of using kNN detector. **It is noted that the API across all other algorithms are consistent/similar**.\r\n\r\nMore detailed instructions for running examples can be found in `examples directory <https://github.com/yzhao062/pyod/blob/master/examples>`_.\r\n\r\n\r\n#. Initialize a kNN detector, fit the model, and make the prediction.\r\n\r\n .. code-block:: python\r\n\r\n\r\n from pyod.models.knn import KNN # kNN detector\r\n\r\n # train kNN detector\r\n clf_name = 'KNN'\r\n clf = KNN()\r\n clf.fit(X_train)\r\n\r\n # get the prediction label and outlier scores of the training data\r\n y_train_pred = clf.labels_ # binary labels (0: inliers, 1: outliers)\r\n y_train_scores = clf.decision_scores_ # raw outlier scores\r\n\r\n # get the prediction on the test data\r\n y_test_pred = clf.predict(X_test) # outlier labels (0 or 1)\r\n y_test_scores = clf.decision_function(X_test) # outlier scores\r\n\r\n # it is possible to get the prediction confidence as well\r\n 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]\r\n\r\n#. Evaluate the prediction by ROC and Precision @ Rank n (p@n).\r\n\r\n .. code-block:: python\r\n\r\n from pyod.utils.data import evaluate_print\r\n \r\n # evaluate and print the results\r\n print(\"\\nOn Training Data:\")\r\n evaluate_print(clf_name, y_train, y_train_scores)\r\n print(\"\\nOn Test Data:\")\r\n evaluate_print(clf_name, y_test, y_test_scores)\r\n\r\n\r\n#. See a sample output & visualization.\r\n\r\n\r\n .. code-block:: python\r\n\r\n\r\n On Training Data:\r\n KNN ROC:1.0, precision @ rank n:1.0\r\n\r\n On Test Data:\r\n KNN ROC:0.9989, precision @ rank n:0.9\r\n\r\n .. code-block:: python\r\n\r\n\r\n visualize(clf_name, X_train, y_train, X_test, y_test, y_train_pred,\r\n y_test_pred, show_figure=True, save_figure=False)\r\n\r\nVisualization (\\ `knn_figure <https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png>`_\\ ):\r\n\r\n.. image:: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png\r\n :target: https://raw.githubusercontent.com/yzhao062/pyod/master/examples/KNN.png\r\n :alt: kNN example figure\r\n\r\n----\r\n\r\nReference\r\n^^^^^^^^^\r\n\r\n\r\n.. [#Aggarwal2015Outlier] Aggarwal, C.C., 2015. Outlier analysis. In Data mining (pp. 237-263). Springer, Cham.\r\n\r\n.. [#Aggarwal2015Theoretical] Aggarwal, C.C. and Sathe, S., 2015. Theoretical foundations and algorithms for outlier ensembles.\\ *ACM SIGKDD Explorations Newsletter*\\ , 17(1), pp.24-47.\r\n\r\n.. [#Aggarwal2017Outlier] Aggarwal, C.C. and Sathe, S., 2017. Outlier ensembles: An introduction. Springer.\r\n\r\n.. [#Almardeny2020A] Almardeny, Y., Boujnah, N. and Cleary, F., 2020. A Novel Outlier Detection Method for Multivariate Data. *IEEE Transactions on Knowledge and Data Engineering*.\r\n\r\n.. [#Angiulli2002Fast] Angiulli, F. and Pizzuti, C., 2002, August. Fast outlier detection in high dimensional spaces. In *European Conference on Principles of Data Mining and Knowledge Discovery* pp. 15-27.\r\n\r\n.. [#Arning1996A] Arning, A., Agrawal, R. and Raghavan, P., 1996, August. A Linear Method for Deviation Detection in Large Databases. In *KDD* (Vol. 1141, No. 50, pp. 972-981).\r\n\r\n.. [#Bandaragoda2018Isolation] Bandaragoda, T. R., Ting, K. M., Albrecht, D., Liu, F. T., Zhu, Y., and Wells, J. R., 2018, Isolation-based anomaly detection using nearest-neighbor ensembles. *Computational Intelligence*\\ , 34(4), pp. 968-998.\r\n\r\n.. [#Breunig2000LOF] Breunig, M.M., Kriegel, H.P., Ng, R.T. and Sander, J., 2000, May. LOF: identifying density-based local outliers. *ACM Sigmod Record*\\ , 29(2), pp. 93-104.\r\n\r\n.. [#Burgess2018Understanding] Burgess, Christopher P., et al. \"Understanding disentangling in beta-VAE.\" arXiv preprint arXiv:1804.03599 (2018).\r\n\r\n.. [#Cook1977Detection] Cook, R.D., 1977. Detection of influential observation in linear regression. Technometrics, 19(1), pp.15-18.\r\n\r\n.. [#Fang2001Wrap] Fang, K.T. and Ma, C.X., 2001. Wrap-around L2-discrepancy of random sampling, Latin hypercube and uniform designs. Journal of complexity, 17(4), pp.608-624.\r\n\r\n.. [#Goldstein2012Histogram] Goldstein, M. and Dengel, A., 2012. Histogram-based outlier score (hbos): A fast unsupervised anomaly detection algorithm. In *KI-2012: Poster and Demo Track*\\ , pp.59-63.\r\n\r\n.. [#Goodge2022Lunar] Goodge, A., Hooi, B., Ng, S.K. and Ng, W.S., 2022, June. Lunar: Unifying local outlier detection methods via graph neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence.\r\n\r\n.. [#Gopalan2019PIDForest] Gopalan, P., Sharan, V. and Wieder, U., 2019. PIDForest: Anomaly Detection via Partial Identification. In Advances in Neural Information Processing Systems, pp. 15783-15793.\r\n\r\n.. [#Han2022ADBench] Han, S., Hu, X., Huang, H., Jiang, M. and Zhao, Y., 2022. ADBench: Anomaly Detection Benchmark. arXiv preprint arXiv:2206.09426.\r\n\r\n.. [#Hardin2004Outlier] Hardin, J. and Rocke, D.M., 2004. Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator. *Computational Statistics & Data Analysis*\\ , 44(4), pp.625-638.\r\n\r\n.. [#He2003Discovering] He, Z., Xu, X. and Deng, S., 2003. Discovering cluster-based local outliers. *Pattern Recognition Letters*\\ , 24(9-10), pp.1641-1650.\r\n\r\n.. [#Hoffmann2007Kernel] Hoffmann, H., 2007. Kernel PCA for novelty detection. Pattern recognition, 40(3), pp.863-874.\r\n\r\n.. [#Iglewicz1993How] Iglewicz, B. and Hoaglin, D.C., 1993. How to detect and handle outliers (Vol. 16). Asq Press.\r\n\r\n.. [#Janssens2012Stochastic] Janssens, J.H.M., Husz\u00e1r, F., Postma, E.O. and van den Herik, H.J., 2012. Stochastic outlier selection. Technical report TiCC TR 2012-001, Tilburg University, Tilburg Center for Cognition and Communication, Tilburg, The Netherlands.\r\n\r\n.. [#Kingma2013Auto] Kingma, D.P. and Welling, M., 2013. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114.\r\n\r\n.. [#Kriegel2008Angle] Kriegel, H.P. and Zimek, A., 2008, August. Angle-based outlier detection in high-dimensional data. In *KDD '08*\\ , pp. 444-452. ACM.\r\n\r\n.. [#Kriegel2009Outlier] Kriegel, H.P., Kr\u00f6ger, P., Schubert, E. and Zimek, A., 2009, April. Outlier detection in axis-parallel subspaces of high dimensional data. In *Pacific-Asia Conference on Knowledge Discovery and Data Mining*\\ , pp. 831-838. Springer, Berlin, Heidelberg.\r\n\r\n.. [#Latecki2007Outlier] Latecki, L.J., Lazarevic, A. and Pokrajac, D., 2007, July. Outlier detection with kernel density functions. In International Workshop on Machine Learning and Data Mining in Pattern Recognition (pp. 61-75). Springer, Berlin, Heidelberg.\r\n\r\n.. [#Lazarevic2005Feature] Lazarevic, A. and Kumar, V., 2005, August. Feature bagging for outlier detection. In *KDD '05*. 2005.\r\n\r\n.. [#Li2019MADGAN] Li, D., Chen, D., Jin, B., Shi, L., Goh, J. and Ng, S.K., 2019, September. MAD-GAN: Multivariate anomaly detection for time series data with generative adversarial networks. In *International Conference on Artificial Neural Networks* (pp. 703-716). Springer, Cham.\r\n\r\n.. [#Li2020COPOD] Li, Z., Zhao, Y., Botta, N., Ionescu, C. and Hu, X. COPOD: Copula-Based Outlier Detection. *IEEE International Conference on Data Mining (ICDM)*, 2020.\r\n\r\n.. [#Li2021ECOD] Li, Z., Zhao, Y., Hu, X., Botta, N., Ionescu, C. and Chen, H. G. ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions. *IEEE Transactions on Knowledge and Data Engineering (TKDE)*, 2022.\r\n\r\n.. [#Liu2008Isolation] Liu, F.T., Ting, K.M. and Zhou, Z.H., 2008, December. Isolation forest. In *International Conference on Data Mining*\\ , pp. 413-422. IEEE.\r\n\r\n.. [#Liu2019Generative] Liu, Y., Li, Z., Zhou, C., Jiang, Y., Sun, J., Wang, M. and He, X., 2019. Generative adversarial active learning for unsupervised outlier detection. *IEEE Transactions on Knowledge and Data Engineering*.\r\n\r\n.. [#Nguyen2019scalable] Nguyen, M.N. and Vien, N.A., 2019. Scalable and interpretable one-class svms with deep learning and random fourier features. In *Machine Learning and Knowledge Discovery in Databases: European Conference*, ECML PKDD, 2018.\r\n\r\n.. [#Pang2019Deep] Pang, Guansong, Chunhua Shen, and Anton Van Den Hengel. \"Deep anomaly detection with deviation networks.\" In *KDD*, pp. 353-362. 2019.\r\n\r\n.. [#Papadimitriou2003LOCI] Papadimitriou, S., Kitagawa, H., Gibbons, P.B. and Faloutsos, C., 2003, March. LOCI: Fast outlier detection using the local correlation integral. In *ICDE '03*, pp. 315-326. IEEE.\r\n\r\n.. [#Pevny2016Loda] Pevn\u00fd, T., 2016. Loda: Lightweight on-line detector of anomalies. *Machine Learning*, 102(2), pp.275-304.\r\n\r\n.. [#Perini2020Quantifying] Perini, L., Vercruyssen, V., Davis, J. Quantifying the confidence of anomaly detectors in their example-wise predictions. In *Joint European Conference on Machine Learning and Knowledge Discovery in Databases (ECML-PKDD)*, 2020.\r\n\r\n.. [#Ramaswamy2000Efficient] Ramaswamy, S., Rastogi, R. and Shim, K., 2000, May. Efficient algorithms for mining outliers from large data sets. *ACM Sigmod Record*\\ , 29(2), pp. 427-438.\r\n\r\n.. [#Rousseeuw1999A] Rousseeuw, P.J. and Driessen, K.V., 1999. A fast algorithm for the minimum covariance determinant estimator. *Technometrics*\\ , 41(3), pp.212-223.\r\n\r\n.. [#Ruff2018Deep] Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S.A., Binder, A., M\u00fcller, E. and Kloft, M., 2018, July. Deep one-class classification. In *International conference on machine learning* (pp. 4393-4402). PMLR.\r\n\r\n.. [#Schlegl2017Unsupervised] Schlegl, T., Seeb\u00f6ck, P., Waldstein, S.M., Schmidt-Erfurth, U. and Langs, G., 2017, June. Unsupervised anomaly detection with generative adversarial networks to guide marker discovery. In International conference on information processing in medical imaging (pp. 146-157). Springer, Cham.\r\n\r\n.. [#Scholkopf2001Estimating] Scholkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J. and Williamson, R.C., 2001. Estimating the support of a high-dimensional distribution. *Neural Computation*, 13(7), pp.1443-1471.\r\n\r\n.. [#Shyu2003A] Shyu, M.L., Chen, S.C., Sarinnapakorn, K. and Chang, L., 2003. A novel anomaly detection scheme based on principal component classifier. *MIAMI UNIV CORAL GABLES FL DEPT OF ELECTRICAL AND COMPUTER ENGINEERING*.\r\n\r\n.. [#Sugiyama2013Rapid] Sugiyama, M. and Borgwardt, K., 2013. Rapid distance-based outlier detection via sampling. Advances in neural information processing systems, 26.\r\n\r\n.. [#Tang2002Enhancing] Tang, J., Chen, Z., Fu, A.W.C. and Cheung, D.W., 2002, May. Enhancing effectiveness of outlier detections for low density patterns. In *Pacific-Asia Conference on Knowledge Discovery and Data Mining*, pp. 535-548. Springer, Berlin, Heidelberg.\r\n\r\n.. [#Wang2020adVAE] Wang, X., Du, Y., Lin, S., Cui, P., Shen, Y. and Yang, Y., 2019. adVAE: A self-adversarial variational autoencoder with Gaussian anomaly prior knowledge for anomaly detection. *Knowledge-Based Systems*.\r\n\r\n.. [#Xu2023Deep] Xu, H., Pang, G., Wang, Y., Wang, Y., 2023. Deep isolation forest for anomaly detection. *IEEE Transactions on Knowledge and Data Engineering*.\r\n\r\n.. [#You2017Provable] You, C., Robinson, D.P. and Vidal, R., 2017. Provable self-representation based outlier detection in a union of subspaces. In Proceedings of the IEEE conference on computer vision and pattern recognition.\r\n\r\n.. [#Zenati2018Adversarially] Zenati, H., Romain, M., Foo, C.S., Lecouat, B. and Chandrasekhar, V., 2018, November. Adversarially learned anomaly detection. In 2018 IEEE International conference on data mining (ICDM) (pp. 727-736). IEEE.\r\n\r\n.. [#Zhao2018XGBOD] Zhao, Y. and Hryniewicki, M.K. XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning. *IEEE International Joint Conference on Neural Networks*\\ , 2018.\r\n\r\n.. [#Zhao2019LSCP] Zhao, Y., Nasrullah, Z., Hryniewicki, M.K. and Li, Z., 2019, May. LSCP: Locally selective combination in parallel outlier ensembles. In *Proceedings of the 2019 SIAM International Conference on Data Mining (SDM)*, pp. 585-593. Society for Industrial and Applied Mathematics.\r\n\r\n.. [#Zhao2021SUOD] Zhao, Y., Hu, X., Cheng, C., Wang, C., Wan, C., Wang, W., Yang, J., Bai, H., Li, Z., Xiao, C., Wang, Y., Qiao, Z., Sun, J. and Akoglu, L. (2021). SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection. *Conference on Machine Learning and Systems (MLSys)*.\r\n",
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