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Python Outlier Detection (PyOD)

Deployment & Documentation & Stats & License

PyPI version

Anaconda version

Documentation status

GitHub stars

GitHub forks

Downloads

testing

Coverage Status

Maintainability

License

Benchmark

News: We just released a 45-page, the most comprehensive anomaly detection benchmark paper. The fully open-sourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.

For time-series outlier detection, please use TODS. For graph outlier detection, please use PyGOD.

PyOD is the most comprehensive and scalable Python library for detecting outlying objects in multivariate data. This exciting yet challenging field is commonly referred as Outlier Detection or Anomaly Detection.

PyOD includes more than 40 detection algorithms, from classical LOF (SIGMOD 2000) to the latest ECOD (TKDE 2022). Since 2017, PyOD has been successfully used in numerous academic researches and commercial products with more than 10 million downloads. It is also well acknowledged by the machine learning community with various dedicated posts/tutorials, including Analytics Vidhya, KDnuggets, and Towards Data Science.

PyOD is featured for:

  • Unified APIs, detailed documentation, and interactive examples across various algorithms.
  • Advanced models, including classical distance and density estimation, latest deep learning methods, and emerging algorithms like ECOD.
  • Optimized performance with JIT and parallelization using numba and joblib.
  • Fast training & prediction with SUOD1.

Outlier Detection with 5 Lines of Code:

# train an ECOD detector
from pyod.models.ecod import ECOD
clf = ECOD()
clf.fit(X_train)

# get outlier scores
y_train_scores = clf.decision_scores_  # raw outlier scores on the train data
y_test_scores = clf.decision_function(X_test)  # predict raw outlier scores on test

Personal suggestion on selecting an OD algorithm. If you do not know which algorithm to try, go with:

  • ECOD: Example of using ECOD for outlier detection
  • Isolation Forest: Example of using Isolation Forest for outlier detection

They are both fast and interpretable. Or, you could try more data-driven approach MetaOD.

Citing PyOD:

PyOD paper is published in Journal of Machine Learning Research (JMLR) (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.

If you want more general insights of anomaly detection and/or algorithm performance comparison, please see our NeurIPS 2022 paper ADBench: Anomaly Detection Benchmark Paper:

@inproceedings{han2022adbench,
    title={ADBench: Anomaly Detection Benchmark},
    author={Songqiao Han and Xiyang Hu and Hailiang Huang and Mingqi Jiang and Yue Zhao},
    booktitle={Neural Information Processing Systems (NeurIPS)}
    year={2022},
}

Key Links and Resources:

Table of Contents:

Installation

It is recommended to use pip or conda for installation. Please make sure the latest version is installed, as PyOD is updated frequently:

pip install pyod            # normal install
pip install --upgrade pyod  # or update if needed
conda install -c conda-forge pyod

Alternatively, you could clone and run setup.py file:

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

Required Dependencies:

  • Python 3.6+
  • joblib
  • matplotlib
  • numpy>=1.19
  • numba>=0.51
  • scipy>=1.5.1
  • scikit_learn>=0.20.0
  • six

Optional Dependencies (see details below):

  • combo (optional, required for models/combination.py and FeatureBagging)
  • keras/tensorflow (optional, required for AutoEncoder, and other deep learning models)
  • pandas (optional, required for running benchmark)
  • suod (optional, required for running SUOD model)
  • xgboost (optional, required for XGBOD)
  • pythresh to use thresholding

Warning: PyOD has multiple neural network based models, e.g., AutoEncoders, which are implemented in both Tensorflow and PyTorch. However, PyOD does NOT install these deep learning libraries for you. This reduces the risk of interfering with your local copies. If you want to use neural-net based models, please make sure these deep learning libraries are installed. Instructions are provided: neural-net FAQ. Similarly, models depending on xgboost, e.g., XGBOD, would NOT enforce xgboost installation by default.

API Cheatsheet & Reference

Full API Reference: (https://pyod.readthedocs.io/en/latest/pyod.html). API cheatsheet for all detectors:

  • fit(X): Fit detector. y is ignored in unsupervised methods.
  • decision_function(X): Predict raw anomaly score of X using the fitted detector.
  • predict(X): Predict if a particular sample is an outlier or not using the fitted detector.
  • predict_proba(X): Predict the probability of a sample being outlier using the fitted detector.
  • predict_confidence(X): Predict the model's sample-wise confidence (available in predict and predict_proba)2.

Key Attributes of a fitted model:

  • decision_scores_: The outlier scores of the training data. The higher, the more abnormal. Outliers tend to have higher scores.
  • labels_: The binary labels of the training data. 0 stands for inliers and 1 for outliers/anomalies.

ADBench Benchmark

We just released a 45-page, the most comprehensive ADBench: Anomaly Detection Benchmark3. The fully open-sourced ADBench compares 30 anomaly detection algorithms on 57 benchmark datasets.

The organization of ADBench is provided below:

benchmark-fig

The comparison of selected models is made available below (Figure, compare_all_models.py, Interactive Jupyter Notebooks). For Jupyter Notebooks, please navigate to "/notebooks/Compare All Models.ipynb".

Comparision_of_All

Model Save & Load

PyOD takes a similar approach of sklearn regarding model persistence. See model persistence for clarification.

In short, we recommend to use joblib or pickle for saving and loading PyOD models. See "examples/save_load_model_example.py" for an example. In short, it is simple as below:

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 and #88 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 framework4. See SUOD Paper and SUOD example.

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)

Implemented Algorithms

PyOD toolkit consists of three major functional groups:

(i) Individual Detection Algorithms :

Type Abbr Algorithm Year Ref
Probabilistic ECOD Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions 2022 5
Probabilistic ABOD Angle-Based Outlier Detection 2008 6
Probabilistic FastABOD Fast Angle-Based Outlier Detection using approximation 2008 7
Probabilistic COPOD COPOD: Copula-Based Outlier Detection 2020 8
Probabilistic MAD Median Absolute Deviation (MAD) 1993 9
Probabilistic SOS Stochastic Outlier Selection 2012 10
Probabilistic QMCD Quasi-Monte Carlo Discrepancy outlier detection 2001 11
Probabilistic KDE Outlier Detection with Kernel Density Functions 2007 12

Probabilistic Probabilistic

Sampling GMM

Rapid distance-based outlier detection via sampling Probabilistic Mixture Modeling for Outlier Analysis

2013

13 14 [Ch.2]
Linear Model PCA Principal Component Analysis (the sum of weighted projected distances to the eigenvector hyperplanes) 2003 15
Linear Model KPCA Kernel Principal Component Analysis 2007 16
Linear Model MCD Minimum Covariance Determinant (use the mahalanobis distances as the outlier scores) 1999 1718
Linear Model CD Use Cook's distance for outlier detection 1977 19
Linear Model OCSVM One-Class Support Vector Machines 2001 20
Linear Model LMDD Deviation-based Outlier Detection (LMDD) 1996 21
Proximity-Based LOF Local Outlier Factor 2000 22
Proximity-Based COF Connectivity-Based Outlier Factor 2002 23
Proximity-Based (Incremental) COF Memory Efficient Connectivity-Based Outlier Factor (slower but reduce storage complexity) 2002 24
Proximity-Based CBLOF Clustering-Based Local Outlier Factor 2003 25
Proximity-Based LOCI LOCI: Fast outlier detection using the local correlation integral 2003 26
Proximity-Based HBOS Histogram-based Outlier Score 2012 27
Proximity-Based kNN k Nearest Neighbors (use the distance to the kth nearest neighbor as the outlier score) 2000 28
Proximity-Based AvgKNN Average kNN (use the average distance to k nearest neighbors as the outlier score) 2002 29
Proximity-Based MedKNN Median kNN (use the median distance to k nearest neighbors as the outlier score) 2002 30
Proximity-Based SOD Subspace Outlier Detection 2009 31
Proximity-Based ROD Rotation-based Outlier Detection 2020 32
Outlier Ensembles IForest Isolation Forest 2008 33
Outlier Ensembles INNE Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles 2018 34
Outlier Ensembles FB Feature Bagging 2005 35
Outlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 36
Outlier Ensembles XGBOD Extreme Boosting Based Outlier Detection (Supervised) 2018 37
Outlier Ensembles LODA Lightweight On-line Detector of Anomalies 2016 38

Outlier Ensembles Neural Networks

SUOD AutoEncoder

SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration) Fully connected AutoEncoder (use reconstruction error as the outlier score)

2021

39 40 [Ch.3]
Neural Networks VAE Variational AutoEncoder (use reconstruction error as the outlier score) 2013 41
Neural Networks Beta-VAE Variational AutoEncoder (all customized loss term by varying gamma and capacity) 2018 42
Neural Networks SO_GAAL Single-Objective Generative Adversarial Active Learning 2019 43
Neural Networks MO_GAAL Multiple-Objective Generative Adversarial Active Learning 2019 44
Neural Networks DeepSVDD Deep One-Class Classification 2018 45
Neural Networks AnoGAN Anomaly Detection with Generative Adversarial Networks 2017 46
Neural Networks ALAD Adversarially learned anomaly detection 2018 47
Graph-based R-Graph Outlier detection by R-graph 2017 48
Graph-based LUNAR LUNAR: Unifying Local Outlier Detection Methods via Graph Neural Networks 2022 49

(ii) Outlier Ensembles & Outlier Detector Combination Frameworks:

Type Abbr Algorithm Year Ref
Outlier Ensembles FB Feature Bagging 2005 50
Outlier Ensembles LSCP LSCP: Locally Selective Combination of Parallel Outlier Ensembles 2019 51
Outlier Ensembles XGBOD Extreme Boosting Based Outlier Detection (Supervised) 2018 52
Outlier Ensembles LODA Lightweight On-line Detector of Anomalies 2016 53
Outlier Ensembles SUOD SUOD: Accelerating Large-scale Unsupervised Heterogeneous Outlier Detection (Acceleration) 2021 54
Outlier Ensembles INNE Isolation-based Anomaly Detection Using Nearest-Neighbor Ensembles 2018 55
Combination Average Simple combination by averaging the scores 2015 56
Combination Weighted Average Simple combination by averaging the scores with detector weights 2015 57
Combination Maximization Simple combination by taking the maximum scores 2015 58
Combination AOM Average of Maximum 2015 59
Combination MOA Maximization of Average 2015 60
Combination Median Simple combination by taking the median of the scores 2015 61
Combination majority Vote Simple combination by taking the majority vote of the labels (weights can be used) 2015 62

(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
Data generate_data_clusters Synthesized data generation in clusters; more complex data patterns can be created with multiple clusters generate_data_clusters
Stat wpearsonr Calculate the weighted Pearson correlation of two samples wpearsonr
Utility get_label_n Turn raw outlier scores into binary labels by assign 1 to top n outlier scores get_label_n
Utility precision_n_scores calculate precision @ rank n 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

KDnuggets: Intuitive Visualization of Outlier Detection Methods, An Overview of Outlier Detection Methods from PyOD

Towards Data Science: Anomaly Detection for Dummies

Computer Vision News (March 2019): Python Open Source Toolbox for Outlier Detection

"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.

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

    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]

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

    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)

  3. See a sample output & visualization.

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

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

kNN example figure

How to Contribute

You are welcome to contribute to this exciting project:

  • Please first check Issue lists for "help wanted" tag and comment the one you are interested. We will assign the issue to you.
  • Fork the master branch and add your improvement/modification/fix.
  • Create a pull request to development branch and follow the pull request template PR template
  • Automatic tests will be triggered. Make sure all tests are passed. Please make sure all added modules are accompanied with proper test functions.

To make sure the code has the same style and standard, please refer to abod.py, hbos.py, or feature_bagging.py for example.

You are also welcome to share your ideas by opening an issue or dropping me an email at zhaoy@cmu.edu :)

Inclusion Criteria

Similarly to scikit-learn, We mainly consider well-established algorithms for inclusion. A rule of thumb is at least two years since publication, 50+ citations, and usefulness.

However, we encourage the author(s) of newly proposed models to share and add your implementation into PyOD for boosting ML accessibility and reproducibility. This exception only applies if you could commit to the maintenance of your model for at least two year period.

Reference

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  2. 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.↩

  3. Han, S., Hu, X., Huang, H., Jiang, M. and Zhao, Y., 2022. ADBench: Anomaly Detection Benchmark. arXiv preprint arXiv:2206.09426.↩

  4. 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).↩

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  52. Zhao, Y. and Hryniewicki, M.K. XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning. IEEE International Joint Conference on Neural Networks, 2018.↩

  53. Pevný, T., 2016. Loda: Lightweight on-line detector of anomalies. Machine Learning, 102(2), pp.275-304.↩

  54. 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).↩

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