Python Outlier Detection (PyOD) V2

Deployment & Documentation & Stats & License

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---

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

Welcome to PyOD, a well-developed and easy-to-use Python library for detecting anomalies in multivariate data. Whether you are working with a small-scale project or large datasets, PyOD provides a range of algorithms to fit your needs.

PyOD Version 2 is now available (Paper <https://www.arxiv.org/abs/2412.12154>) [#Chen2024PyOD], featuring:

• Expanded Deep Learning Support: Integrates 12 modern neural models into a single PyTorch-based framework, bringing the total number of outlier detection methods to 45.
• Enhanced Performance and Ease of Use: Models are optimized for efficiency and consistent performance across different datasets.
• LLM-based Model Selection: Automated model selection guided by a large language model reduces manual tuning and assists users who may have limited experience with outlier detection.
• Multi-Modal Detection via EmbeddingOD: Chain foundation model encoders (sentence-transformers, OpenAI, HuggingFace) with any PyOD detector for text and image anomaly detection. See EmbeddingOD example <https://github.com/yzhao062/pyod/blob/master/examples/embedding_od_example.py>_.

PyOD Ecosystem & Resources: NLP-ADBench <https://github.com/USC-FORTIS/NLP-ADBench>_ (NLP anomaly detection) | TODS <https://github.com/datamllab/tods>_ (time-series) | PyGOD <https://pygod.org/>_ (graph) | ADBench <https://github.com/Minqi824/ADBench>_ (benchmark) | AD-LLM <https://arxiv.org/abs/2412.11142>_ (LLM-based AD) [#Yang2024ad]_ | Resources <https://github.com/yzhao062/anomaly-detection-resources>_

---

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 26 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

Text Anomaly Detection with EmbeddingOD (pip install pyod sentence-transformers):

.. code-block:: python

from pyod.models.embedding import EmbeddingOD
clf = EmbeddingOD(encoder='all-MiniLM-L6-v2', detector='KNN')
clf.fit(train_texts)                          # list of strings
scores = clf.decision_function(test_texts)    # anomaly scores
labels = clf.predict(test_texts)              # binary labels

# Or use a preset:
clf = EmbeddingOD.for_text(quality='fast')    # MiniLM + KNN

Image detection requires additional packages (pip install transformers torch). See EmbeddingOD example <https://github.com/yzhao062/pyod/blob/master/examples/embedding_od_example.py>_ for details.

Selecting the Right Algorithm: Start with ECOD <https://github.com/yzhao062/pyod/blob/master/examples/ecod_example.py>_ or Isolation Forest <https://github.com/yzhao062/pyod/blob/master/examples/iforest_example.py>_ for tabular data, EmbeddingOD <https://github.com/yzhao062/pyod/blob/master/examples/embedding_od_example.py>_ for text/image, or MetaOD <https://github.com/yzhao062/MetaOD>_ for data-driven selection.

Citing PyOD:

If you use PyOD in a scientific publication, we would appreciate citations to the following paper(s):

PyOD 2: A Python Library for Outlier Detection with LLM-powered Model Selection <https://arxiv.org/abs/2412.12154>_ is available as a preprint. If you use PyOD in a scientific publication, we would appreciate citations to the following paper::

@inproceedings{chen2025pyod,
  title={Pyod 2: A python library for outlier detection with llm-powered model selection},
  author={Chen, Sihan and Qian, Zhuangzhuang and Siu, Wingchun and Hu, Xingcan and Li, Jiaqi and Li, Shawn and Qin, Yuehan and Yang, Tiankai and Xiao, Zhuo and Ye, Wanghao and others},
  booktitle={Companion Proceedings of the ACM on Web Conference 2025},
  pages={2807--2810},
  year={2025}
}

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).::

@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 on ADBench <https://arxiv.org/abs/2206.09426>_ [#Han2022ADBench]_ and ADGym <https://arxiv.org/abs/2309.15376>_.

Table of Contents:

• Installation <#installation>_
• API Cheatsheet & Reference <#api-cheatsheet--reference>_
• ADBench Benchmark and Datasets <#adbench-benchmark-and-datasets>_
• Additional Topics <#additional-topics>_ (Model Save/Load, SUOD, Thresholding)
• 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)
• sentence-transformers (optional, required for EmbeddingOD text detection)
• openai (optional, required for EmbeddingOD with OpenAI embeddings)
• transformers and torch (optional, required for EmbeddingOD image detection and HuggingFace encoder)

---

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]_.
• predict_with_rejection(X)\ : Allow the detector to reject (i.e., abstain from making) highly uncertain predictions (output = -2) [#Perini2023Rejection]_.

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

---

Additional Topics ^^^^^^^^^^^^^^^^^

• Model Save & Load <https://pyod.readthedocs.io/en/latest/model_persistence.html>: Use joblib or pickle for saving and loading PyOD models. See example <https://github.com/yzhao062/pyod/blob/master/examples/save_load_model_example.py>.
• Fast Train with SUOD <https://pyod.readthedocs.io/en/latest/fast_train.html>: Accelerate training and prediction with the SUOD framework [#Zhao2021SUOD]. See example <https://github.com/yzhao062/pyod/blob/master/examples/suod_example.py>_.
• Thresholding Outlier Scores <https://pyod.readthedocs.io/en/latest/thresholding.html>: Data-driven approaches for setting contamination levels via PyThresh <https://github.com/KulikDM/pythresh>.

---

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 HDBSCAN Density-based clustering based on hierarchical density estimates 2013 [#Campello2013Density]_ 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]_ Embedding-based EmbeddingOD Multi-modal anomaly detection via foundation model embeddings (text, image) 2025 [#Li2024NLPADBench]_ =================== ================== ====================================================================================================== ===== ========================================

Ensemble methods (IForest, INNE, DIF, FB, LSCP, LODA, SUOD, XGBOD) are included in the table above. Score combination functions (average, maximization, AOM, MOA, median, majority vote) are in pyod.models.combination. See API docs <https://pyod.readthedocs.io/en/latest/pyod.html>_ for details.

(ii) Utility Functions:

=================== ============================ ===================================================================================================================================================== Type Name Function =================== ============================ ===================================================================================================================================================== Data generate_data Synthesized data generation; normal data from multivariate Gaussian, outliers from uniform distribution Data generate_data_clusters Synthesized data generation in clusters for more complex patterns Evaluation evaluate_print Print ROC-AUC and Precision @ Rank n for a detector Evaluation precision_n_scores Calculate Precision @ Rank n Utility get_label_n Turn raw outlier scores into binary labels by assigning 1 to the top n scores Stat wpearsonr Calculate the weighted Pearson correlation of two samples Encoding resolve_encoder Resolve an encoder from a string name, BaseEncoder instance, or callable Encoding SentenceTransformerEncoder Encode text via sentence-transformers models (e.g., MiniLM, mpnet) Encoding OpenAIEncoder Encode text via OpenAI Embeddings API (text-embedding-3-small/large) Encoding HuggingFaceEncoder Encode text or images via HuggingFace transformers (BERT, DINOv2, CLIP) =================== ============================ =====================================================================================================================================================

---

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).

.. [#Campello2013Density] Campello, R.J.G.B., Moulavi, D. and Sander, J., 2013, April. Density-based clustering based on hierarchical density estimates. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 160-172). Springer.

.. [#Cook1977Detection] Cook, R.D., 1977. Detection of influential observation in linear regression. Technometrics, 19(1), pp.15-18.

.. [#Chen2024PyOD] Chen, S., Qian, Z., Siu, W., Hu, X., Li, J., Li, S., Qin, Y., Yang, T., Xiao, Z., Ye, W. and Zhang, Y., 2024. PyOD 2: A Python Library for Outlier Detection with LLM-powered Model Selection. arXiv preprint arXiv:2412.12154.

.. [#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.

.. [#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.

.. [#Han2022ADBench] Han, S., Hu, X., Huang, H., Jiang, M. and Zhao, Y., 2022. ADBench: Anomaly Detection Benchmark. arXiv preprint arXiv:2206.09426.

.. [#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.

.. [#He2003Discovering] He, Z., Xu, X. and Deng, S., 2003. Discovering cluster-based local outliers. Pattern Recognition Letters\ , 24(9-10), pp.1641-1650.

.. [#Hoffmann2007Kernel] Hoffmann, H., 2007. Kernel PCA for novelty detection. Pattern recognition, 40(3), pp.863-874.

.. [#Iglewicz1993How] Iglewicz, B. and Hoaglin, D.C., 1993. How to detect and handle outliers (Vol. 16). Asq Press.

.. [#Janssens2012Stochastic] Janssens, J.H.M., Huszár, 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.

.. [#Kingma2013Auto] Kingma, D.P. and Welling, M., 2013. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114.

.. [#Kriegel2008Angle] Kriegel, H.P. and Zimek, A., 2008, August. Angle-based outlier detection in high-dimensional data. In KDD '08\ , pp. 444-452. ACM.

.. [#Kriegel2009Outlier] Kriegel, H.P., Kröger, 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.

.. [#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.

.. [#Lazarevic2005Feature] Lazarevic, A. and Kumar, V., 2005, August. Feature bagging for outlier detection. In KDD '05. 2005.

.. [#Li2024NLPADBench] Li, Y., Li, J., Xiao, Z., Yang, T., Nian, Y., Hu, X. and Zhao, Y., 2025. NLP-ADBench: NLP Anomaly Detection Benchmark. In Findings of the Association for Computational Linguistics: EMNLP 2025.

.. [#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.

.. [#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.

.. [#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.

.. [#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.

.. [#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.

.. [#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.

.. [#Pang2019Deep] Pang, Guansong, Chunhua Shen, and Anton Van Den Hengel. "Deep anomaly detection with deviation networks." In KDD, pp. 353-362. 2019.

.. [#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.

.. [#Pevny2016Loda] Pevný, T., 2016. Loda: Lightweight on-line detector of anomalies. Machine Learning, 102(2), pp.275-304.

.. [#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.

.. [#Perini2023Rejection] Perini, L., Davis, J. Unsupervised anomaly detection with rejection. In Proceedings of the Thirty-Seven Conference on Neural Information Processing Systems (NeurIPS), 2023.

.. [#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.

.. [#Rousseeuw1999A] Rousseeuw, P.J. and Driessen, K.V., 1999. A fast algorithm for the minimum covariance determinant estimator. Technometrics\ , 41(3), pp.212-223.

.. [#Ruff2018Deep] Ruff, L., Vandermeulen, R., Goernitz, N., Deecke, L., Siddiqui, S.A., Binder, A., Müller, E. and Kloft, M., 2018, July. Deep one-class classification. In International conference on machine learning (pp. 4393-4402). PMLR.

.. [#Schlegl2017Unsupervised] Schlegl, T., Seeböck, 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.

.. [#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.

.. [#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.

.. [#Sugiyama2013Rapid] Sugiyama, M. and Borgwardt, K., 2013. Rapid distance-based outlier detection via sampling. Advances in neural information processing systems, 26.

.. [#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.

.. [#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.

.. [#Xu2023Deep] Xu, H., Pang, G., Wang, Y., Wang, Y., 2023. Deep isolation forest for anomaly detection. IEEE Transactions on Knowledge and Data Engineering.

.. [#Yang2024ad] Yang, T., Nian, Y., Li, S., Xu, R., Li, Y., Li, J., Xiao, Z., Hu, X., Rossi, R., Ding, K. and Hu, X., 2024. AD-LLM: Benchmarking Large Language Models for Anomaly Detection. arXiv preprint arXiv:2412.11142.

.. [#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.

.. [#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.

.. [#Zhao2018XGBOD] Zhao, Y. and Hryniewicki, M.K. XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning. IEEE International Joint Conference on Neural Networks\ , 2018.

.. [#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.

.. [#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).

PyOD 快速上手指南

PyOD (Python Outlier Detection) 是一个功能强大且易于使用的 Python 库，专为检测多元数据中的异常值（离群点）而设计。它集成了从经典算法到最新深度学习模型在内的 45+ 种检测方法，并提供统一的 API 接口。

1. 环境准备

在开始之前，请确保您的开发环境满足以下要求：

• 操作系统：Linux, macOS, Windows
• Python 版本：3.8 或更高
• 核心依赖：
  • numpy >= 1.19
  • scipy >= 1.5.1
  • scikit-learn >= 0.22.0
  • numba >= 0.51
  • joblib
  • matplotlib

注意：如果您计划使用深度学习模型（如 AutoEncoder）或文本/图像异常检测功能，还需额外安装 torch、transformers 或 sentence-transformers 等可选依赖。

2. 安装步骤

推荐使用 pip 进行安装。国内用户建议使用清华或阿里镜像源以加速下载。

方式一：使用 pip 安装（推荐）

使用国内镜像源加速安装：

pip install pyod -i https://pypi.tuna.tsinghua.edu.cn/simple

或使用官方源安装/更新：

pip install pyod
pip install --upgrade pyod

方式二：使用 Conda 安装

如果您使用 Anaconda 或 Miniconda 环境：

conda install -c conda-forge pyod

方式三：从源码安装

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

3. 基本使用

PyOD 的核心优势在于其统一的 API。只需 5 行代码即可完成模型的训练与预测。

场景一：表格数据异常检测（以 ECOD 算法为例）

ECOD 是一种无需参数调节且高效的无监督算法，适合作为入门首选。

# 引入必要的库
from pyod.models.ecod import ECOD
import numpy as np

# 假设 X_train 和 X_test 是您的训练集和测试集 (numpy array)
# X_train shape: (n_samples, n_features)

# 1. 初始化检测器
clf = ECOD()

# 2. 拟合模型 (训练)
clf.fit(X_train)

# 3. 获取训练数据的异常分数 (分数越高越可能是异常)
y_train_scores = clf.decision_scores_ 

# 4. 预测测试数据的异常分数
y_test_scores = clf.decision_function(X_test)

# 5. 获取二分类标签 (0 表示正常，1 表示异常)
y_test_pred = clf.predict(X_test) 

场景二：文本数据异常检测（EmbeddingOD）

PyOD V2 新增了基于嵌入的模型，可直接处理文本数据。需先安装额外依赖：

pip install pyod sentence-transformers -i https://pypi.tuna.tsinghua.edu.cn/simple

使用示例：

from pyod.models.embedding import EmbeddingOD

# 准备文本数据 (字符串列表)
train_texts = ["normal text 1", "normal text 2", ...]
test_texts = ["normal text", "abnormal spam text", ...]

# 初始化：自动结合预训练编码器 (MiniLM) 和检测器 (KNN)
clf = EmbeddingOD.for_text(quality='fast')

# 拟合与预测
clf.fit(train_texts)
scores = clf.decision_function(test_texts)  # 异常分数
labels = clf.predict(test_texts)            # 0 或 1

核心 API 速查

所有检测器均遵循以下标准接口：

方法/属性	说明
fit(X)	训练模型（无监督学习通常忽略 y 标签）。
decision_function(X)	返回原始异常分数，分数越高代表越异常。
predict(X)	返回二分类标签（0=正常，1=异常）。
decision_scores_	属性：训练数据的异常分数。
labels_	属性：训练数据的二分类标签。

提示：对于未知的表格数据集，建议优先尝试 ECOD 或 IsolationForest；若涉及文本或图像，请使用 EmbeddingOD。