pyod 3.2.1

A Python library for anomaly detection across tabular, time series, graph, text, and image data. 60+ detectors, benchmark-backed ADEngine orchestration, and an agentic workflow for AI agents.

PyOD 3: Agentic Anomaly Detection At Scale

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PyOD is now agentic. Any AI agent can drive an expert-level anomaly detection investigation on your data in plain English. The classic fit/predict API stays unchanged.

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

Pillar	What it means
Multi-Modal	60+ detectors across tabular, time series, graph, text, and image data, one API
Full Lifecycle	From raw data to explained anomalies and next-step guidance in a single call
Agentic	Ask in plain English, and AI agents run expert-level detection without OD expertise
Most Used	38+ million downloads; benchmark-backed routing (ADBench, TSB-AD, BOND, NLP-ADBench)

Install

Core library (required for every activation path):

pip install pyod

Then pick the activation path that matches your agent stack:

# 1. Claude Code / Claude Desktop / Codex — enables the od-expert skill
pyod install skill              # Claude Code / Desktop: 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. 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):

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
2	ADEngine	You want PyOD to choose, compare, and assess automatically	Layer 2 walkthrough
3	Agentic Investigation	You want an AI agent to drive OD through natural conversation	Layer 3 walkthrough

Layers 2 and 3 are powered by ADEngine, PyOD’s intelligent orchestration core. Layer 3 adds two agentic activation paths: the od-expert skill for Claude Code and Codex, and an MCP server (python -m pyod.mcp_server) that works with any MCP-compatible LLM out of the box. See the Install block above for detailed setup instructions.

The figure above shows a real 5-turn agentic conversation on the UCI Cardiotocography dataset. See the full walkthrough, runnable agentic example, or interactive HTML demo.

PyOD Ecosystem & Resources: NLP-ADBench (NLP anomaly detection) | TODS (time-series) | PyGOD (graph) | ADBench (benchmark) | AD-LLM (LLM-based AD) [50] | Resources

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About PyOD

PyOD, established in 2017, is the longest-running and most widely used Python library for anomaly detection. With 38+ million downloads, it serves both academic research (featured in Analytics Vidhya, KDnuggets, and Towards Data Science) and commercial products.

V3 extends the library with ADEngine (intelligent orchestration) and the od-expert skill (agentic workflow), while keeping the classic fit/predict API fully backward-compatible. V3 is built on SUOD [55] 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 (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).
Books	Outlier Detection in Python (Brett Kennedy, Manning); Handbook of Anomaly Detection with Python (Chris Kuo, Columbia); Finding Ghosts in Your Data (Kevin Feasel, Apress).
Courses	DataCamp Anomaly Detection in Python (19M+ platform learners), Manning liveProject, O’Reilly video edition, multiple Udemy courses.
Podcasts	Talk Python To Me #497, Real Python Podcast #208.
International	Tutorials in 5 non-English languages: Chinese (CSDN, Zhihu, 搜狐, 机器之心, aidoczh.com full doc translation), Japanese, Korean, German, Spanish.

See the full impact page 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 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 is published in Journal of Machine Learning Research (JMLR) (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 [17] and ADGym.

Table of Contents:

• API Cheatsheet & Reference

• Benchmarks

• Implemented Algorithms (Tabular, Time Series, Graph, Embedding)

• Additional Topics (Model Save/Load, SUOD, Thresholding)

• Quick Start for Outlier Detection

• How to Contribute

• Inclusion Criteria

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API Cheatsheet & Reference

The full API Reference is split by modality at PyOD Documentation: Tabular, Time Series, Graph, Embedding, ADEngine, Utilities. 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) [38].

• predict_with_rejection(X): Allow the detector to reject (i.e., abstain from making) highly uncertain predictions (output = -2) [39].

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.

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Benchmarks

• ADBench [17]: 30 algorithms on 57 tabular datasets. See comparison.

• NLP-ADBench: 19 methods on 8 text datasets. Two-step (embedding + detector) beats end-to-end.

• TSB-AD [70]: 40 algorithms on 1070 time series datasets (NeurIPS 2024).

• BOND [71]: 14 graph anomaly detection algorithms on 14 datasets (NeurIPS 2022).

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Additional Topics

• Model Save & Load: Use joblib or pickle for saving and loading PyOD models. See example.

• Fast Train with SUOD: Accelerate training and prediction with the SUOD framework [55]. See example.

• Thresholding Outlier Scores: Data-driven approaches for setting contamination levels via PyThresh.

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Implemented Algorithms

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

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

Type	Abbr	Algorithm	Year	Ref
Probabilistic	ECOD	Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions (example)	2022	[31]
Probabilistic	ABOD	Angle-Based Outlier Detection (example)	2008	[24]
Probabilistic	FastABOD	Fast Angle-Based Outlier Detection using approximation (example)	2008	[24]
Probabilistic	COPOD	COPOD: Copula-Based Outlier Detection (example)	2020	[30]
Probabilistic	MAD	Median Absolute Deviation (MAD) (example)	1993	[21]
Probabilistic	SOS	Stochastic Outlier Selection (example)	2012	[22]
Probabilistic	QMCD	Quasi-Monte Carlo Discrepancy outlier detection (example)	2001	[13]
Probabilistic	KDE	Outlier Detection with Kernel Density Functions (example)	2007	[26]
Probabilistic	Sampling	Rapid distance-based outlier detection via sampling (example)	2013	[46]
Probabilistic	GMM	Probabilistic Mixture Modeling for Outlier Analysis (example)		[1] [Ch.2]
Linear Model	PCA	Principal Component Analysis (sum of weighted projected distances to eigenvector hyperplanes) (example)	2003	[45]
Linear Model	KPCA	Kernel Principal Component Analysis (example)	2007	[20]
Linear Model	MCD	Minimum Covariance Determinant (Mahalanobis distances as outlier scores) (example)	1999	[18] [41]
Linear Model	CD	Cook’s distance for outlier detection (example)	1977	[11]
Linear Model	OCSVM	One-Class Support Vector Machines (example)	2001	[44]
Linear Model	LMDD	Deviation-based Outlier Detection (LMDD) (example)	1996	[6]
Proximity-Based	LOF	Local Outlier Factor (example)	2000	[8]
Proximity-Based	COF	Connectivity-Based Outlier Factor (example)	2002	[47]
Proximity-Based	(Incr.) COF	Memory Efficient Connectivity-Based Outlier Factor (slower, reduced storage) (example)	2002	[47]
Proximity-Based	CBLOF	Clustering-Based Local Outlier Factor (example)	2003	[19]
Proximity-Based	LOCI	LOCI: Fast outlier detection via local correlation integral (example)	2003	[36]
Proximity-Based	HBOS	Histogram-based Outlier Score (example)	2012	[14]
Proximity-Based	HDBSCAN	Density-based clustering via hierarchical density estimates (example)	2013	[10]
Proximity-Based	kNN	k Nearest Neighbors (distance to k-th neighbor as outlier score) (example)	2000	[40]
Proximity-Based	AvgKNN	Average kNN (average distance to k neighbors as outlier score) (example)	2002	[5]
Proximity-Based	MedKNN	Median kNN (median distance to k neighbors as outlier score) (example)	2002	[5]
Proximity-Based	SOD	Subspace Outlier Detection (example)	2009	[25]
Proximity-Based	ROD	Rotation-based Outlier Detection (example)	2020	[4]
Outlier Ensembles	IForest	Isolation Forest (example)	2008	[32]
Outlier Ensembles	INNE	Isolation-based Anomaly Detection via Nearest-Neighbor Ensembles (example)	2018	[7]
Outlier Ensembles	DIF	Deep Isolation Forest for Anomaly Detection (example)	2023	[49]
Outlier Ensembles	FB	Feature Bagging (example)	2005	[27]
Outlier Ensembles	LSCP	LSCP: Locally Selective Combination of Parallel Outlier Ensembles (example)	2019	[54]
Outlier Ensembles	XGBOD	Extreme Boosting Based Outlier Detection (Supervised) (example)	2018	[53]
Outlier Ensembles	LODA	Lightweight On-line Detector of Anomalies (example)	2016	[37]
Outlier Ensembles	SUOD	SUOD: Accelerating Large-scale Unsupervised Heterogeneous OD (Acceleration) (example)	2021	[55]
Neural Networks	AutoEncoder	Fully connected AutoEncoder (reconstruction error as outlier score) (example)		[1] [Ch.3]
Neural Networks	VAE	Variational AutoEncoder (reconstruction error as outlier score) (example)	2013	[23]
Neural Networks	Beta-VAE	Variational AutoEncoder with customized loss (gamma and capacity) (example)	2018	[9]
Neural Networks	SO_GAAL	Single-Objective Generative Adversarial Active Learning (example)	2019	[33]
Neural Networks	MO_GAAL	Multiple-Objective Generative Adversarial Active Learning (example)	2019	[33]
Neural Networks	DeepSVDD	Deep One-Class Classification (example)	2018	[42]
Neural Networks	AnoGAN	Anomaly Detection with Generative Adversarial Networks	2017	[43]
Neural Networks	ALAD	Adversarially learned anomaly detection (example)	2018	[52]
Neural Networks	AE1SVM	Autoencoder-based One-class Support Vector Machine (example)	2019	[34]
Neural Networks	DevNet	Deep Anomaly Detection with Deviation Networks (example)	2019	[35]
Graph-based	R-Graph	Outlier detection by R-graph (example)	2017	[51]
Graph-based	LUNAR	LUNAR: Unifying Local OD Methods via Graph Neural Networks (example)	2022	[15]
Embedding-based	EmbeddingOD	Multi-modal anomaly detection via foundation model embeddings, text and image (example)	2025	[28]

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 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:

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 [70] (NeurIPS 2024, 1070 datasets):

Type	Abbr	Algorithm	Year	Ref
Windowed Bridge	TimeSeriesOD	Any PyOD detector on sliding windows (example)	2026
Subsequence	MatrixProfile	Matrix Profile via STOMP, transductive (example)	2016	[61]
Frequency	SpectralResidual	Spectral Residual: FFT-based saliency (example)	2019	[59]
Clustering	KShape	k-Shape clustering (#2 in TSB-AD) (example)	2015	[58]
Streaming	SAND	Streaming with drift adaptation, experimental (example)	2021	[56]
Deep Learning	LSTMAD	LSTM prediction error + Mahalanobis scoring	2015	[57]
Deep Learning	AnomalyTransformer	Transformer with association discrepancy (experimental)	2022	[60]

(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]):

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 [71] (NeurIPS 2022, 14 datasets):

Type	Abbr	Algorithm	Year	Ref
GCN Autoencoder	DOMINANT	GCN AE, structure + attribute reconstruction (#1 BOND deep) (dominant example)	2019	[62]
Contrastive	CoLA	Contrastive self-supervised, local neighbor context (#2 BOND deep) (cola example)	2022	[63]
Contrastive+AE	CONAD	Contrastive with anomalous-view injection + dual reconstruction (conad example)	2022	[64]
Attention AE	AnomalyDAE	GAT structure encoder + MLP attribute encoder (anomalydae example)	2020	[65]
Motif AE	GUIDE	Dual GCN AE on original + triangle-motif adjacency (guide example)	2021	[66]
Matrix Factor.	Radar	Residual analysis via matrix factorization (radar example)	2017	[67]
Matrix Factor.	ANOMALOUS	Joint MF with Laplacian regularization (anomalous example)	2018	[68]
Structural	SCAN	Structural clustering, no features needed (scan example)	2007	[69]

(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)

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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

“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)

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Reference

[1] (1,2)

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

[2]

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

[3]

Aggarwal, C.C. and Sathe, S., 2017. Outlier ensembles: An introduction. Springer.

[4]

Almardeny, Y., Boujnah, N. and Cleary, F., 2020. A Novel Outlier Detection Method for Multivariate Data. IEEE Transactions on Knowledge and Data Engineering.

[5] (1,2)

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.

[6]

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).

[7]

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.

[8]

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.

[9]

Burgess, Christopher P., et al. “Understanding disentangling in beta-VAE.” arXiv preprint arXiv:1804.03599 (2018).

[10]

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.

[11]

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

[12]

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.

[13]

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.

[14]

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.

[15]

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.

[16]

Gopalan, P., Sharan, V. and Wieder, U., 2019. PIDForest: Anomaly Detection via Partial Identification. In Advances in Neural Information Processing Systems, pp. 15783-15793.

[17] (1,2)

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

[18]

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.

[19]

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

[20]

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

[21]

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

[22]

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.

[23]

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

[24] (1,2)

Kriegel, H.P. and Zimek, A., 2008, August. Angle-based outlier detection in high-dimensional data. In KDD ‘08, pp. 444-452. ACM.

[25]

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.

[26]

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.

[27]

Lazarevic, A. and Kumar, V., 2005, August. Feature bagging for outlier detection. In KDD ‘05. 2005.

[28]

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.

[29]

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.

[30]

Li, Z., Zhao, Y., Botta, N., Ionescu, C. and Hu, X. COPOD: Copula-Based Outlier Detection. IEEE International Conference on Data Mining (ICDM), 2020.

[31]

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.

[32]

Liu, F.T., Ting, K.M. and Zhou, Z.H., 2008, December. Isolation forest. In International Conference on Data Mining, pp. 413-422. IEEE.

[33] (1,2)

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.

[34]

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.

[35]

Pang, Guansong, Chunhua Shen, and Anton Van Den Hengel. “Deep anomaly detection with deviation networks.” In KDD, pp. 353-362. 2019.

[36]

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.

[37]

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

[38]

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.

[39]

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

[40]

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.

[41]

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

[42]

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.

[43]

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.

[44]

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.

[45]

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.

[46]

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

[47] (1,2)

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.

[48]

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.

[49]

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

[50]

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.

[51]

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.

[52]

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.

[53]

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

[54]

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.

[55] (1,2,3)

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).

[56]

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.

[57]

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).

[58]

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.

[59]

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.

[60]

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).

[61]

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.

[62]

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.

[63]

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.

[64]

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.

[65]

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.

[66]

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.

[67]

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.

[68]

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.

[69]

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.

[70] (1,2)

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).

[71] (1,2)

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).