yzhao062/pyod

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Python Outlier Detection (PyOD) 3

PyOD 3: Agentic Anomaly Detection At Scale

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---

**PyOD is agent-ready.** Claude Code and Codex can use the ``od-expert`` skill to drive ADEngine investigations, while MCP-compatible agents can query PyOD's detector knowledge and planning tools. The classic ``fit``/``predict`` API stays unchanged.

---

PyOD 3 is the most comprehensive Python library for anomaly detection. Four pillars:

=========================== ======================================================================================== Pillar What it means =========================== ======================================================================================== Multi-Modal 61 detectors across tabular, time series, graph, text, image, and audio data, one API Full Lifecycle From raw data to explained anomalies and next-step guidance in a single call Agentic od-expert turns natural-language requests into ADEngine workflows; MCP exposes structured tools for other agents Most Used 46+ million downloads; benchmark-backed routing (ADBench, TSB-AD, BOND, NLP-ADBench) =========================== ========================================================================================

Install ^^^^^^^

Core library (required for every activation path):

.. code-block:: bash

pip install pyod

Then pick the activation path that matches your agent stack:

.. code-block:: bash

# 1. Claude Code / Codex — enables the od-expert skill
pyod install skill              # Claude Code: user-global (~/.claude/skills/)
pyod install skill --project    # Codex: project-local (./skills/, Codex has no user-global dir)

# 2. Any MCP-compatible LLM — requires the optional mcp extra
pip install pyod[mcp]
pyod mcp serve                 # alias for `python -m pyod.mcp_server`

# 3. Pure Python — no extra step
#    from pyod.utils.ad_engine import ADEngine

Run pyod info at any time to see version, detector counts, and the install state of each activation path. pyod info also detects which agent stack you have installed (~/.claude/ for Claude Code, ~/.codex/ for Codex) and recommends the right install command.

For conda, source install, dependency details, and troubleshooting, see the full installation guide <https://pyod.readthedocs.io/en/latest/install.html>__. The legacy pyod-install-skill command from v3.0.0 still works as an alias for pyod install skill.

Outlier Detection with 5 Lines of Code (pip install pyod):

.. code-block:: python

from pyod.models.iforest import IForest
clf = IForest()
clf.fit(X_train)
y_train_scores = clf.decision_scores_          # training anomaly scores
y_test_scores = clf.decision_function(X_test)   # test anomaly scores

Three ways to use PyOD:

========= ===================== ====================================================================== ======================================= Layer Name When to use Entry point ========= ===================== ====================================================================== ======================================= 1 Classic API You know which detector you want Layer 1 examples <https://pyod.readthedocs.io/en/latest/examples/tabular.html>__ 2 ADEngine You want PyOD to choose, compare, and assess automatically Layer 2 walkthrough <https://pyod.readthedocs.io/en/latest/examples/adengine.html>__ 3 Agentic Investigation You want an AI agent to drive OD through natural conversation Layer 3 walkthrough <https://pyod.readthedocs.io/en/latest/examples/agentic.html>__ ========= ===================== ====================================================================== =======================================

Layers 2 and 3 are powered by ADEngine, PyOD's lifecycle orchestration core. The full multi-turn Layer 3 investigation flow is available through the od-expert skill for Claude Code and Codex. The MCP server (python -m pyod.mcp_server) exposes ten stateless tools for MCP-compatible LLMs, spanning knowledge queries (list_detectors, explain_detector, compare_detectors, get_benchmarks), planning (profile_data, plan_detection, build_detector), and detection (run_detection, analyze_results, explain_findings); stateful investigate / iterate MCP tools are deferred.

.. image:: https://raw.githubusercontent.com/yzhao062/pyod/development/docs/figs/agentic-demo.png :alt: PyOD 3 agentic investigation demo on cardiotocography dataset :align: center :width: 720

The figure above shows a real 5-turn agentic conversation on the UCI Cardiotocography dataset. See the full walkthrough <https://pyod.readthedocs.io/en/latest/examples/agentic.html>, runnable agentic example <https://github.com/yzhao062/pyod/blob/development/examples/agentic_example.py>, or interactive HTML demo <https://htmlpreview.github.io/?https://github.com/yzhao062/pyod/blob/development/examples/agentic_demo.html>__.

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, is the longest-running and most widely used Python library for anomaly detection. With 46+ million downloads <https://pepy.tech/project/pyod>, it serves both academic research (featured in 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>) and commercial products.

V3 extends the library with ADEngine (lifecycle orchestration) and the od-expert skill (agentic workflow), while keeping the classic fit/predict API fully backward-compatible. V3 is built on SUOD [#Zhao2021SUOD]_ for fast parallel training and numba JIT for per-model speedups.

Impact & Recognition:

=================================== =========================================================================== Area Examples =================================== =========================================================================== Space & science European Space Agency OPS-SAT spacecraft telemetry benchmark <https://www.nature.com/articles/s41597-025-05035-3>__ (Nature Scientific Data, 2025) uses PyOD for all 30 algorithms. Enterprise deployment Walmart (1M+ daily pricing updates, KDD 2019), Databricks (Kakapo framework integrating PyOD with MLflow/Hyperopt; insider-threat detection solution), IQVIA (123K+ pharmacy claims), Altair AI Studio, Ericsson (patent WO2023166515A1 <https://patents.google.com/patent/WO2023166515A1>). Books Outlier Detection in Python <https://www.manning.com/books/outlier-detection-in-python> (Brett Kennedy, Manning); Handbook of Anomaly Detection with Python (Chris Kuo, Columbia); Finding Ghosts in Your Data <https://link.springer.com/book/10.1007/978-1-4842-8870-2>__ (Kevin Feasel, Apress). Courses DataCamp Anomaly Detection in Python <https://www.datacamp.com/courses/anomaly-detection-in-python>__ (19M+ platform learners), Manning liveProject <https://www.manning.com/liveproject/using-pyod-and-ensembles-methods>, O'Reilly video edition, multiple Udemy courses. Podcasts Talk Python To Me #497 <https://talkpython.fm/episodes/show/497/outlier-detection-with-python>, Real Python Podcast #208 <https://realpython.com/podcasts/rpp/208/>. International Tutorials in 5 non-English languages: Chinese (CSDN, Zhihu, 搜狐, 机器之心, aidoczh.com <https://www.aidoczh.com> full doc translation), Japanese, Korean, German, Spanish. =================================== ===========================================================================

See the full impact page <https://pyod.readthedocs.io/en/latest/impact.html>__ on Read the Docs for the complete list of citations, enterprise deployments, patents, and media coverage.

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:

• API Cheatsheet & Reference <#api-cheatsheet--reference>__
• Benchmarks <#benchmarks>__
• Implemented Algorithms <#implemented-algorithms>__ (Tabular, Time Series, Graph, Embedding)
• Additional Topics <#additional-topics>__ (Model Save/Load, SUOD, Thresholding)
• Quick Start for Outlier Detection <#quick-start-for-outlier-detection>__
• How to Contribute <#how-to-contribute>__
• Inclusion Criteria <#inclusion-criteria>__

---

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

The full API Reference is split by modality at PyOD Documentation <https://pyod.readthedocs.io/en/latest/>: Tabular <https://pyod.readthedocs.io/en/latest/pyod.models.tabular.html>, Time Series <https://pyod.readthedocs.io/en/latest/pyod.models.timeseries.html>, Graph <https://pyod.readthedocs.io/en/latest/pyod.models.graph.html>, Embedding <https://pyod.readthedocs.io/en/latest/pyod.models.embedding.html>, ADEngine <https://pyod.readthedocs.io/en/latest/pyod.ad_engine.html>, Utilities <https://pyod.readthedocs.io/en/latest/pyod.utils.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.

---

Benchmarks ^^^^^^^^^^

• ADBench <https://github.com/Minqi824/ADBench>__ [#Han2022ADBench]_: 30 algorithms on 57 tabular datasets. See comparison <https://github.com/yzhao062/pyod/blob/master/examples/compare_all_models.py>__.
• NLP-ADBench <https://github.com/USC-FORTIS/NLP-ADBench>__: 19 methods on 8 text datasets. Two-step (embedding + detector) beats end-to-end.
• TSB-AD <https://github.com/TheDatumOrg/TSB-AD>__ [#Liu2024TSB]_: 40 algorithms on 1070 time series datasets (NeurIPS 2024).
• BOND <https://arxiv.org/abs/2206.10071>__ [#Liu2022BOND]_: 14 graph anomaly detection algorithms on 14 datasets (NeurIPS 2022).

---

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 is organized into two functional groups: (i) Detection Algorithms, with dedicated subsections for tabular, time series, graph, and audio data (EmbeddingOD inside the tabular table adds text and image support via foundation model encoders); and (ii) Utility Functions for data generation, evaluation, and lifecycle orchestration.

(i-a) Tabular & Multi-Modal Detection Algorithms :

.. list-table:: :widths: 15 14 58 5 8 :header-rows: 1

• • Type
  • Abbr
  • Algorithm
  • Year
  • Ref
• • Probabilistic
  • ECOD
  • Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions (example <https://github.com/yzhao062/pyod/blob/development/examples/ecod_example.py>__)
  • 2022
  • [#Li2021ECOD]_
• • Probabilistic
  • ABOD
  • Angle-Based Outlier Detection (example <https://github.com/yzhao062/pyod/blob/development/examples/abod_example.py>__)
  • 2008
  • [#Kriegel2008Angle]_
• • Probabilistic
  • FastABOD
  • Fast Angle-Based Outlier Detection using approximation (example <https://github.com/yzhao062/pyod/blob/development/examples/abod_example.py>__)
  • 2008
  • [#Kriegel2008Angle]_
• • Probabilistic
  • COPOD
  • COPOD: Copula-Based Outlier Detection (example <https://github.com/yzhao062/pyod/blob/development/examples/copod_example.py>__)
  • 2020
  • [#Li2020COPOD]_
• • Probabilistic
  • MAD
  • Median Absolute Deviation (MAD) (example <https://github.com/yzhao062/pyod/blob/development/examples/mad_example.py>__)
  • 1993
  • [#Iglewicz1993How]_
• • Probabilistic
  • SOS
  • Stochastic Outlier Selection (example <https://github.com/yzhao062/pyod/blob/development/examples/sos_example.py>__)
  • 2012
  • [#Janssens2012Stochastic]_
• • Probabilistic
  • QMCD
  • Quasi-Monte Carlo Discrepancy outlier detection (example <https://github.com/yzhao062/pyod/blob/development/examples/qmcd_example.py>__)
  • 2001
  • [#Fang2001Wrap]_
• • Probabilistic
  • KDE
  • Outlier Detection with Kernel Density Functions (example <https://github.com/yzhao062/pyod/blob/development/examples/kde_example.py>__)
  • 2007
  • [#Latecki2007Outlier]_
• • Probabilistic
  • Sampling
  • Rapid distance-based outlier detection via sampling (example <https://github.com/yzhao062/pyod/blob/development/examples/sampling_example.py>__)
  • 2013
  • [#Sugiyama2013Rapid]_
• • Probabilistic
  • GMM
  • Probabilistic Mixture Modeling for Outlier Analysis (example <https://github.com/yzhao062/pyod/blob/development/examples/gmm_example.py>__)
  • [#Aggarwal2015Outlier]_ [Ch.2]
• • Linear Model
  • PCA
  • Principal Component Analysis (sum of weighted projected distances to eigenvector hyperplanes) (example <https://github.com/yzhao062/pyod/blob/development/examples/pca_example.py>__)
  • 2003
  • [#Shyu2003A]_
• • Linear Model
  • KPCA
  • Kernel Principal Component Analysis (example <https://github.com/yzhao062/pyod/blob/development/examples/kpca_example.py>__)
  • 2007
  • [#Hoffmann2007Kernel]_
• • Linear Model
  • MCD
  • Minimum Covariance Determinant (Mahalanobis distances as outlier scores) (example <https://github.com/yzhao062/pyod/blob/development/examples/mcd_example.py>__)
  • 1999
  • [#Hardin2004Outlier]_ [#Rousseeuw1999A]_
• • Linear Model
  • CD
  • Cook's distance for outlier detection (example <https://github.com/yzhao062/pyod/blob/development/examples/cd_example.py>__)
  • 1977
  • [#Cook1977Detection]_
• • Linear Model
  • OCSVM
  • One-Class Support Vector Machines (example <https://github.com/yzhao062/pyod/blob/development/examples/ocsvm_example.py>__)
  • 2001
  • [#Scholkopf2001Estimating]_
• • Linear Model
  • LMDD
  • Deviation-based Outlier Detection (LMDD) (example <https://github.com/yzhao062/pyod/blob/development/examples/lmdd_example.py>__)
  • 1996
  • [#Arning1996A]_
• • Proximity-Based
  • LOF
  • Local Outlier Factor (example <https://github.com/yzhao062/pyod/blob/development/examples/lof_example.py>__)
  • 2000
  • [#Breunig2000LOF]_
• • Proximity-Based
  • COF
  • Connectivity-Based Outlier Factor (example <https://github.com/yzhao062/pyod/blob/development/examples/cof_example.py>__)
  • 2002
  • [#Tang2002Enhancing]_
• • Proximity-Based
  • (Incr.) COF
  • Memory Efficient Connectivity-Based Outlier Factor (slower, reduced storage) (example <https://github.com/yzhao062/pyod/blob/development/examples/cof_example.py>__)
  • 2002
  • [#Tang2002Enhancing]_
• • Proximity-Based
  • CBLOF
  • Clustering-Based Local Outlier Factor (example <https://github.com/yzhao062/pyod/blob/development/examples/cblof_example.py>__)
  • 2003
  • [#He2003Discovering]_
• • Proximity-Based
  • LOCI
  • LOCI: Fast outlier detection via local correlation integral (example <https://github.com/yzhao062/pyod/blob/development/examples/loci_example.py>__)
  • 2003
  • [#Papadimitriou2003LOCI]_
• • Proximity-Based
  • HBOS
  • Histogram-based Outlier Score (example <https://github.com/yzhao062/pyod/blob/development/examples/hbos_example.py>__)
  • 2012
  • [#Goldstein2012Histogram]_
• • Proximity-Based
  • HDBSCAN
  • Density-based clustering via hierarchical density estimates (example <https://github.com/yzhao062/pyod/blob/development/examples/hdbscan_example.py>__)
  • 2013
  • [#Campello2013Density]_
• • Proximity-Based
  • kNN
  • k Nearest Neighbors (distance to k-th neighbor as outlier score) (example <https://github.com/yzhao062/pyod/blob/development/examples/knn_example.py>__)
  • 2000
  • [#Ramaswamy2000Efficient]_
• • Proximity-Based
  • AvgKNN
  • Average kNN (average distance to k neighbors as outlier score) (example <https://github.com/yzhao062/pyod/blob/development/examples/knn_example.py>__)
  • 2002
  • [#Angiulli2002Fast]_
• • Proximity-Based
  • MedKNN
  • Median kNN (median distance to k neighbors as outlier score) (example <https://github.com/yzhao062/pyod/blob/development/examples/knn_example.py>__)
  • 2002
  • [#Angiulli2002Fast]_
• • Proximity-Based
  • SOD
  • Subspace Outlier Detection (example <https://github.com/yzhao062/pyod/blob/development/examples/sod_example.py>__)
  • 2009
  • [#Kriegel2009Outlier]_
• • Proximity-Based
  • ROD
  • Rotation-based Outlier Detection (example <https://github.com/yzhao062/pyod/blob/development/examples/rod_example.py>__)
  • 2020
  • [#Almardeny2020A]_
• • Outlier Ensembles
  • IForest
  • Isolation Forest (example <https://github.com/yzhao062/pyod/blob/development/examples/iforest_example.py>__)
  • 2008
  • [#Liu2008Isolation]_
• • Outlier Ensembles
  • INNE
  • Isolation-based Anomaly Detection via Nearest-Neighbor Ensembles (example <https://github.com/yzhao062/pyod/blob/development/examples/inne_example.py>__)
  • 2018
  • [#Bandaragoda2018Isolation]_
• • Outlier Ensembles
  • DIF
  • Deep Isolation Forest for Anomaly Detection (example <https://github.com/yzhao062/pyod/blob/development/examples/dif_example.py>__)
  • 2023
  • [#Xu2023Deep]_
• • Outlier Ensembles
  • FB
  • Feature Bagging (example <https://github.com/yzhao062/pyod/blob/development/examples/feature_bagging_example.py>__)
  • 2005
  • [#Lazarevic2005Feature]_
• • Outlier Ensembles
  • LSCP
  • LSCP: Locally Selective Combination of Parallel Outlier Ensembles (example <https://github.com/yzhao062/pyod/blob/development/examples/lscp_example.py>__)
  • 2019
  • [#Zhao2019LSCP]_
• • Outlier Ensembles
  • XGBOD
  • Extreme Boosting Based Outlier Detection (Supervised) (example <https://github.com/yzhao062/pyod/blob/development/examples/xgbod_example.py>__)
  • 2018
  • [#Zhao2018XGBOD]_
• • Outlier Ensembles
  • LODA
  • Lightweight On-line Detector of Anomalies (example <https://github.com/yzhao062/pyod/blob/development/examples/loda_example.py>__)
  • 2016
  • [#Pevny2016Loda]_
• • Outlier Ensembles
  • SUOD
  • SUOD: Accelerating Large-scale Unsupervised Heterogeneous OD (Acceleration) (example <https://github.com/yzhao062/pyod/blob/development/examples/suod_example.py>__)
  • 2021
  • [#Zhao2021SUOD]_
• • Neural Networks
  • AutoEncoder
  • Fully connected AutoEncoder (reconstruction error as outlier score) (example <https://github.com/yzhao062/pyod/blob/development/examples/auto_encoder_example.py>__)
  • [#Aggarwal2015Outlier]_ [Ch.3]
• • Neural Networks
  • VAE
  • Variational AutoEncoder (reconstruction error as outlier score) (example <https://github.com/yzhao062/pyod/blob/development/examples/vae_example.py>__)
  • 2013
  • [#Kingma2013Auto]_
• • Neural Networks
  • Beta-VAE
  • Variational AutoEncoder with customized loss (gamma and capacity) (example <https://github.com/yzhao062/pyod/blob/development/examples/vae_example.py>__)
  • 2018
  • [#Burgess2018Understanding]_
• • Neural Networks
  • SO_GAAL
  • Single-Objective Generative Adversarial Active Learning (example <https://github.com/yzhao062/pyod/blob/development/examples/so_gaal_example.py>__)
  • 2019
  • [#Liu2019Generative]_
• • Neural Networks
  • MO_GAAL
  • Multiple-Objective Generative Adversarial Active Learning (example <https://github.com/yzhao062/pyod/blob/development/examples/mo_gaal_example.py>__)
  • 2019
  • [#Liu2019Generative]_
• • Neural Networks
  • DeepSVDD
  • Deep One-Class Classification (example <https://github.com/yzhao062/pyod/blob/development/examples/deepsvdd_example.py>__)
  • 2018
  • [#Ruff2018Deep]_
• • Neural Networks
  • AnoGAN
  • Anomaly Detection with Generative Adversarial Networks
  • 2017
  • [#Schlegl2017Unsupervised]_
• • Neural Networks
  • ALAD
  • Adversarially learned anomaly detection (example <https://github.com/yzhao062/pyod/blob/development/examples/alad_example.py>__)
  • 2018
  • [#Zenati2018Adversarially]_
• • Neural Networks
  • AE1SVM
  • Autoencoder-based One-class Support Vector Machine (example <https://github.com/yzhao062/pyod/blob/development/examples/ae1svm_example.py>__)
  • 2019
  • [#Nguyen2019scalable]_
• • Neural Networks
  • DevNet
  • Deep Anomaly Detection with Deviation Networks (example <https://github.com/yzhao062/pyod/blob/development/examples/devnet_example.py>__)
  • 2019
  • [#Pang2019Deep]_
• • Graph-based
  • R-Graph
  • Outlier detection by R-graph (example <https://github.com/yzhao062/pyod/blob/development/examples/rgraph_example.py>__)
  • 2017
  • [#You2017Provable]_
• • Graph-based
  • LUNAR
  • LUNAR: Unifying Local OD Methods via Graph Neural Networks (example <https://github.com/yzhao062/pyod/blob/development/examples/lunar_example.py>__)
  • 2022
  • [#Goodge2022Lunar]_
• • Embedding-based
  • EmbeddingOD
  • Multi-modal anomaly detection via foundation model embeddings, text, image, and audio (example <https://github.com/yzhao062/pyod/blob/development/examples/embedding_od_example.py>__)
  • 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.models.tabular.html>__ for details.

(i-b) Time Series Anomaly Detection :

All time series detectors use the same fit/predict/decision_function API as tabular detectors, with one exception: MatrixProfile is transductive (train-only; use decision_scores_ and labels_ after fit(), no out-of-sample predict).

Input format: numpy array of shape (n_timestamps,) for univariate or (n_timestamps, n_channels) for multivariate. Each row is one timestep; columns are channels/features. Pandas DataFrames and lists are auto-converted. Output: decision_scores_ of shape (n_timestamps,) with one anomaly score per timestep.

Time series detection in 3 lines:

.. code-block:: python

from pyod.models.ts_kshape import KShape      # or any TS detector
clf = KShape(window_size=20)
clf.fit(X_train)                               # shape (n_timestamps,) or (n_timestamps, n_channels)
scores = clf.decision_scores_                  # per-timestamp anomaly scores

Algorithm rankings from TSB-AD benchmark <https://github.com/TheDatumOrg/TSB-AD>__ [#Liu2024TSB]_ (NeurIPS 2024, 1070 datasets):

.. list-table:: :widths: 15 18 50 5 12 :header-rows: 1

• • Type
  • Abbr
  • Algorithm
  • Year
  • Ref
• • Windowed Bridge
  • TimeSeriesOD
  • Any PyOD detector on sliding windows (example <https://github.com/yzhao062/pyod/blob/development/examples/ts_od_example.py>__)
  • 2026
• • Subsequence
  • MatrixProfile
  • Matrix Profile via STOMP, transductive (example <https://github.com/yzhao062/pyod/blob/development/examples/ts_matrix_profile_example.py>__)
  • 2016
  • [#Yeh2016Matrix]_
• • Frequency
  • SpectralResidual
  • Spectral Residual: FFT-based saliency (example <https://github.com/yzhao062/pyod/blob/development/examples/ts_spectral_residual_example.py>__)
  • 2019
  • [#Ren2019Time]_
• • Clustering
  • KShape
  • k-Shape clustering (#2 in TSB-AD) (example <https://github.com/yzhao062/pyod/blob/development/examples/ts_kshape_example.py>__)
  • 2015
  • [#Paparrizos2015KShape]_
• • Streaming
  • SAND
  • Streaming with drift adaptation, experimental (example <https://github.com/yzhao062/pyod/blob/development/examples/ts_sand_example.py>__)
  • 2021
  • [#Boniol2021SAND]_
• • Deep Learning
  • LSTMAD
  • LSTM prediction error + Mahalanobis scoring
  • 2015
  • [#Malhotra2015Long]_
• • Deep Learning
  • AnomalyTransformer
  • Transformer with association discrepancy (experimental)
  • 2022
  • [#Xu2022Anomaly]_

(i-c) Graph Anomaly Detection (pip install pyod[graph]):

All graph detectors are transductive in v1: use decision_scores_ and labels_ after fit(). No out-of-sample predict. Input: PyG Data object with x (node features) and edge_index (COO edges). SCAN works without features.

Graph detection in 3 lines (pip install pyod[graph]):

.. code-block:: python

from pyod.models.pyg_dominant import DOMINANT
clf = DOMINANT(hidden_dim=64, epochs=100)
clf.fit(data)                                  # PyG Data object
scores = clf.decision_scores_                  # per-node anomaly scores

Algorithm rankings from BOND benchmark <https://arxiv.org/abs/2206.10071>__ [#Liu2022BOND]_ (NeurIPS 2022, 14 datasets):

.. list-table:: :widths: 18 18 45 5 14 :header-rows: 1

• • Type
  • Abbr
  • Algorithm
  • Year
  • Ref
• • GCN Autoencoder
  • DOMINANT
  • GCN AE, structure + attribute reconstruction (#1 BOND deep) (dominant example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_dominant_example.py>__)
  • 2019
  • [#Ding2019DOMINANT]_
• • Contrastive
  • CoLA
  • Contrastive self-supervised, local neighbor context (#2 BOND deep) (cola example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_cola_example.py>__)
  • 2022
  • [#Liu2022CoLA]_
• • Contrastive+AE
  • CONAD
  • Contrastive with anomalous-view injection + dual reconstruction (conad example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_conad_example.py>__)
  • 2022
  • [#Xu2022CONAD]_
• • Attention AE
  • AnomalyDAE
  • GAT structure encoder + MLP attribute encoder (anomalydae example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_anomalydae_example.py>__)
  • 2020
  • [#Fan2020AnomalyDAE]_
• • Motif AE
  • GUIDE
  • Dual GCN AE on original + triangle-motif adjacency (guide example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_guide_example.py>__)
  • 2021
  • [#Yuan2021GUIDE]_
• • Matrix Factor.
  • Radar
  • Residual analysis via matrix factorization (radar example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_radar_example.py>__)
  • 2017
  • [#Li2017Radar]_
• • Matrix Factor.
  • ANOMALOUS
  • Joint MF with Laplacian regularization (anomalous example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_anomalous_example.py>__)
  • 2018
  • [#Peng2018ANOMALOUS]_
• • Structural
  • SCAN
  • Structural clustering, no features needed (scan example <https://github.com/yzhao062/pyod/blob/development/examples/pyg_scan_example.py>__)
  • 2007
  • [#Xu2007SCAN]_

(i-d) Audio Anomaly Detection (pip install pyod[audio]):

Audio clips use the same fit/decision_function API. Two paths are available: a lightweight embed-then-detect path (EmbeddingOD.for_audio() turns each clip into a 74-dimensional handcrafted acoustic vector and runs any classical detector), and a dedicated deep detector (AudioAE, a log-mel reconstruction autoencoder). Inputs are file paths, waveform arrays, or (waveform, sample_rate) tuples. Output: one anomaly score per clip.

Audio detection in 3 lines (pip install pyod[audio]):

.. code-block:: python

from pyod.models.embedding import EmbeddingOD
clf = EmbeddingOD.for_audio('balanced')        # 74-dim handcrafted features + KNN
clf.fit(train_clips)                            # list of file paths or waveform arrays
scores = clf.decision_scores_                  # per-clip anomaly scores

.. list-table:: :widths: 18 18 45 5 14 :header-rows: 1

• • Type
  • Abbr
  • Algorithm
  • Year
  • Ref
• • Embed then Detect
  • EmbeddingOD
  • for_audio(): 74-dim MFCC, chroma, and spectral features with any detector
  • 2026
• • Deep AE
  • AudioAE
  • Log-mel reconstruction autoencoder (DCASE 2020 Task 2 baseline)
  • 2020

(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
   from pyod.utils.data import generate_data

   contamination = 0.1  # percentage of outliers
   n_train = 200  # number of training points
   n_test = 100  # number of testing points

   # generate sample data
   X_train, X_test, y_train, y_test = generate_data(
       n_train=n_train, n_test=n_test, n_features=2,
       contamination=contamination, random_state=42)

   # 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:0.9992, precision @ rank n:0.95

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

.. code-block:: python

   from pyod.utils.example import visualize

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

---

Acknowledgments ^^^^^^^^^^^^^^^

This material is based upon work supported by the National Science Foundation under Award No. 2346158 <https://www.nsf.gov/awardsearch/showAward?AWD_ID=2346158>_ for "NSF POSE: Phase II: OpenAD: An Integrated Open-Source Ecosystem for Anomaly Detection." The award lists the University of Illinois Chicago as the lead organization and Illinois Institute of Technology, Lehigh University, and the University of Southern California as sub-awardee organizations.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

---

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).

.. [#Boniol2021SAND] Boniol, P., Paparrizos, J., Palpanas, T. and Franklin, M.J., 2021. SAND: Streaming Subsequence Anomaly Detection. Proceedings of the VLDB Endowment, 14(10), pp.1717-1729.

.. [#Malhotra2015Long] Malhotra, P., Vig, L., Shroff, G. and Agarwal, P., 2015. Long Short Term Memory Networks for Anomaly Detection in Time Series. In European Symposium on Artificial Neural Networks (ESANN).

.. [#Paparrizos2015KShape] Paparrizos, J. and Gravano, L., 2015. k-Shape: Efficient and Accurate Clustering of Time Series. In Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, pp.1855-1870.

.. [#Ren2019Time] Ren, H., Xu, B., Wang, Y., Yi, C., Huang, C., Kou, X., Xing, T., Yang, M., Tong, J. and Zhang, Q., 2019. Time-Series Anomaly Detection Service at Microsoft. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp.3009-3017.

.. [#Xu2022Anomaly] Xu, J., Wu, H., Wang, J. and Long, M., 2022. Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy. In International Conference on Learning Representations (ICLR).

.. [#Yeh2016Matrix] Yeh, C.C.M., Zhu, Y., Ulanova, L., Begum, N., Ding, Y., Dau, H.A., Silva, D.F., Mueen, A. and Keogh, E., 2016. Matrix Profile I: All Pairs Similarity Joins for Time Series Subsequences. In 2016 IEEE 16th International Conference on Data Mining (ICDM), pp.1317-1322.

.. [#Ding2019DOMINANT] Ding, K., Li, J., Bhanushali, R. and Liu, H., 2019. Deep Anomaly Detection on Attributed Networks. In Proceedings of the 2019 SIAM International Conference on Data Mining, pp.594-602. SIAM.

.. [#Liu2022CoLA] Liu, Y., Li, Z., Pan, S., Gool, T., Xiang, T. and Gong, B., 2022. Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning. In Proceedings of the ACM Web Conference 2022, pp.2137-2147.

.. [#Xu2022CONAD] Xu, Z., Huang, X., Zhao, Y., Dong, Y. and Li, J., 2022. Contrastive Attributed Network Anomaly Detection with Data Augmentation. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp.444-457. Springer.

.. [#Fan2020AnomalyDAE] Fan, H., Zhang, F. and Li, Z., 2020. AnomalyDAE: Dual Autoencoder for Anomaly Detection on Attributed Networks. In Proceedings of the 29th ACM International Conference on Information and Knowledge Management, pp.747-756.

.. [#Yuan2021GUIDE] Yuan, X., Zhou, N., Yu, S., Huang, H., Chen, Z. and Xia, F., 2021. Higher-Order Structure Based Anomaly Detection on Attributed Networks. In 2021 IEEE International Conference on Big Data, pp.2691-2700. IEEE.

.. [#Li2017Radar] Li, J., Dani, H., Hu, X. and Liu, H., 2017. Radar: Residual Analysis for Anomaly Detection in Attributed Networks. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, pp.2152-2158.

.. [#Peng2018ANOMALOUS] Peng, Z., Luo, M., Li, J., Liu, H. and Zheng, Q., 2018. ANOMALOUS: A Joint Modeling Approach for Anomaly Detection on Attributed Networks. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, pp.3529-3535.

.. [#Xu2007SCAN] Xu, X., Yuruk, N., Feng, Z. and Schweiger, T.A.J., 2007. SCAN: A Structural Clustering Algorithm for Networks. In Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp.824-833.

.. [#Liu2024TSB] Liu, Q., Boniol, P., Palpanas, T. and Paparrizos, J., 2024. TSB-AD: Towards A Reliable Time-Series Anomaly Detection Benchmark. In Advances in Neural Information Processing Systems (NeurIPS).

.. [#Liu2022BOND] Liu, K., Dou, Y., Zhao, Y., Ding, X., Hu, X., Zhang, R., Ding, K., Chen, C., Peng, H., Shu, K., Sun, L., Li, J., Chen, G.H., Jia, Z. and Yu, P.S., 2022. BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs. In Advances in Neural Information Processing Systems (NeurIPS).