LOF: identifying density-based local outliers
Open accessAbstract
For many KDD applications, such as detecting criminal activities in E-commerce, finding the rare instances or the outliers, can be more interesting than finding the common patterns. Existing work in outlier detection regards being an outlier as a binary property. In this paper, we contend that for many scenarios, it is more meaningful to assign to each object a degree of being an outlier. This degree is called the local outlier factor (LOF) of an object. It is local in that the degree depends on how isolated the object is with respect to the surrounding neighborhood. We give a detailed formal analysis showing that LOF enjoys many desirable properties. Using real-world datasets, we demonstrate that LOF can be used to find outliers which appear to be meaningful, but can otherwise not be identified with existing approaches. Finally, a careful performance evaluation of our algorithm confirms we show that our approach of finding local outliers can be practical.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
No references could be resolved yet.
Research works printed but not linked: 22
- Arning, A., Agrawal R., Raghavan P.: "A Linear Method for Deviation Detection in Large Databases", Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining, Portland, OR, AAAI Press, 1996, p. 164-169.
- Ankerst M., Breunig M. M., Kriegel H.-P., Sander J.: "OPTICS: Ordering Points To Identify the Clustering Structure", Proc. ACM SIGMOD Int. Conf. on Management of Data, Philadelphia, PA, 1999.
- Agrawal R., Gehrke J., Gunopulos D., Raghavan P.: "Automatic Subspace Clustering of High Dimensional Data for Data Mining Applications", Proc. ACM SIGMOD Int. Conf. on Management of Data, Seattle, WA, 1998, pp. 94-105.
- Berchthold S., Keim D. A., Kriegel H.-P.: "The X-Tree: An Index Structure for High-Dimensional Data", 22nd Conf. on Very Large Data Bases, Bombay, India, 1996, pp. 28-39.
- Barnett V., Lewis T.: "Outliers in statistical data", John Wiley, 1994.
- DuMouchel W., Schonlau M.: "A Fast Computer Intrusion Detection Algorithm based on Hypothesis Testing of Command Transition Probabilities", Proc. 4th Int. Conf. on Knowledge Discovery and Data Mining, New York, NY, AAAI Press, 1998, pp. 189-193.
- Ester M., Kriegel H.-P., Sander J., Xu X.: "A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise", Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining, Portland, OR, AAAI Press, 1996, pp. 226-231.
- Fawcett T., Provost F.: "Adaptive Fraud Detection", Data Mining and Knowledge Discovery Journal, Kluwer Academic Publishers, Vol. 1, No. 3, 1997, pp. 291-316.
- Fayyad U., Piatetsky-Shapiro G., Smyth P.: "Knowledge Discovery and Data Mining: Towards a Unifying Framework", Proc. 2nd Int. Conf. on Knowledge Discovery and Data Mining, Portland, OR, 1996, pp. 82-88.
- Hinneburg A., Keim D. A.: "An Efficient Approach to Clustering in Large Multimedia Databases with Noise", Proc. 4th Int. Conf. on Knowledge Discovery and Data Mining, New York City, NY, 1998,pp. 58-65.
- Johnson T., Kwok I., Ng R.: "Fast Computation of 2- Dimensional Depth Contours", Proc. 4th Int. Conf. on Knowledge Discovery and Data Mining, New York, NY, AAAI Press, 1998, pp. 224-228.
- Knorr E. M., Ng R. T.: "Algorithms for Mining Distance- Based Outliers in Large Datasets", Proc. 24th Int. Conf. on Very Large Data Bases, New York, NY, 1998, pp. 392-403.
- Knorr E. M., Ng R. T.: "Finding Intensional Knowledge of Distance-based Outliers", Proc. 25th Int. Conf. on Very Large Data Bases, Edinburgh, Scotland, 1999, pp. 211-222.
- Ng R. T., Han J.: "Efficient and Effective Clustering Methods for Spatial Data Mining", Proc. 20th Int. Conf. on Very Large Data Bases, Santiago, Chile, Morgan Kaufmann Publishers, San Francisco, CA, 1994, pp. 144-155.
- Preparata F., Shamos M.: "Computational Geometry: an Introduction", Springer, 1988.
- Ramaswamy S., Rastogi R., Kyuseok S.: "Efficient Algorithms for Mining Outliers from Large Data Sets", Proc. ACM SIDMOD Int. Conf. on Management of Data, 2000.
- Ruts I., Rousseeuw P.: "Computing Depth Contours of Bivariate Point Clouds, Journal of Computational Statistics and Data Analysis, 23, 1996, pp. 153-168.
- Sheikholeslami G., Chatterjee S., Zhang A.: "WaveCluster: A Multi-Resolution Clustering Approach for Very Large Spatial Databases", Proc. Int. Conf. on Very Large Data Bases, New York, NY, 1998, pp. 428-439.
- Tukey J. W.: "Exploratory Data Analysis", Addison-Wesley, 1977.
- Weber R., Schek Hans-J., Blott S.: "A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces", Proc. Int. Conf. on Very Large Data Bases, New York, NY, 1998, pp. 194-205.
- Wang W., Yang J., Muntz R.: "STING: A Statistical Information Grid Approach to Spatial Data Mining", Proc. 23th Int. Conf. on Very Large Data Bases, Athens, Greece, Morgan Kaufmann Publishers, San Francisco, CA, 1997, pp. 186-195.
- Zhang T., Ramakrishnan R., Linvy M.: "BIRCH: An Efficient Data Clustering Method for Very Large Databases", Proc. ACM SIGMOD Int. Conf. on Management of Data, ACM Press, New York, 1996, pp.103-114.
Cited by
Sorted by citations
Chandola, V., Banerjee, A., & Kumar, V. (2009) · ACM Computing Surveys · doi:10.1145/1541880.1541882 · Cited by 11,687 · see citing works
Deep Learning for Anomaly Detection: A Review
Pang, G., Shen, C., Cao, L., & Hengel, A. V. D. (2022) · ACM Computing Surveys · doi:10.1145/3439950 · Cited by 2,837 · see citing works
Graph based anomaly detection and description: a survey
Akoglu, L., Tong, H., & Koutra, D. (2015) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-014-0365-y · Cited by 1,504 · see citing works
Adversarially Learned One-Class Classifier for Novelty Detection
Sabokrou, M., Khalooei, M., Fathy, M., & Adeli, E. (2018) · 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2018.00356 · Cited by 765 · see citing works
Generalized Out-of-Distribution Detection: A Survey
Yang, J., Zhou, K., Li, Y., & Liu, Z. (2024) · International Journal of Computer Vision · doi:10.1007/s11263-024-02117-4 · Cited by 884 · see citing works
DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection
Yang, Y., Zhang, C., Zhou, T., Wen, Q., & Sun, L. (2023) · Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining · doi:10.1145/3580305.3599295 · Cited by 387 · see citing works
Outlier Detection: Methods, Models, and Classification
Boukerche, A., Zheng, L., & Alfandi, O. (2021) · ACM Computing Surveys · doi:10.1145/3381028 · Cited by 334 · see citing works
Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defenses
Goldblum, M., Tsipras, D., Xie, C., Chen, X., Schwarzschild, A., Song, D., Madry, A., Li, B., & Goldstein, T. (2023) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2022.3162397 · Cited by 362 · see citing works
Asymmetric Student-Teacher Networks for Industrial Anomaly Detection
Rudolph, M., Wehrbein, T., Rosenhahn, B., & Wandt, B. (2023) · 2023 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) · doi:10.1109/wacv56688.2023.00262 · Cited by 280 · see citing works
BaFFLe: Backdoor Detection via Feedback-based Federated Learning
Andreina, S., Marson, G. A., Mollering, H., & Karame, G. (2021) · 2021 IEEE 41st International Conference on Distributed Computing Systems (ICDCS) · doi:10.1109/icdcs51616.2021.00086 · Cited by 205 · see citing works
Data engineering for fraud detection
Baesens, B., Höppner, S., & Verdonck, T. (2021) · Decision Support Systems · doi:10.1016/j.dss.2021.113492 · Cited by 170 · see citing works
An incorrect data detection method for big data cleaning of machinery condition monitoring
Xu, X., Lei, Y., & Li, Z. (2020) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2019.2903774 · Cited by 134 · see citing works
A Survey on Explainable Anomaly Detection
Li, Z., Zhu, Y., & Van Leeuwen, M. (2024) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3609333 · Cited by 139 · see citing works
“For example, KNN [170] defines objects with ‘far’ 𝑘-nearest neighbours as anomalies, LOF [26] treats objects with a low local density as anomalies, and Isolation Forest [121] considers ‘easily isolated’ objects as anomalies.”
BackgroundMethodInfluentialInterpretable Anomaly Detection with DIFFI: Depth-based feature importance of Isolation Forest
Carletti, M., Terzi, M., & Susto, G. A. (2023) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2022.105730 · Cited by 118 · see citing works
Huang, J., He, T., Zhu, W., Liao, Y., Zeng, J., Xu, Q., & Niu, Y. (2025) · Computers and Electrical Engineering · doi:10.1016/j.compeleceng.2024.109930 · Cited by 113 · see citing works
Wang, F., Jiang, Y., Zhang, R., Wei, A., Xie, J., & Pang, X. (2025) · Sensors · doi:10.3390/s25010190 · Cited by 119 · see citing works
Explaining Outliers by Subspace Separability
Micenkova, B., Ng, R. T., Dang, X.-H., & Assent, I. (2013) · 2013 IEEE 13th International Conference on Data Mining · doi:10.1109/icdm.2013.132 · Cited by 104 · see citing works
Self-citationDetecting outlying properties of exceptional objects
Angiulli, F., Fassetti, F., & Palopoli, L. (2009) · ACM Transactions on Database Systems · doi:10.1145/1508857.1508864 · Cited by 88 · see citing works
An Overview of Backdoor Attacks Against Deep Neural Networks and Possible Defences
Guo, W., Tondi, B., & Barni, M. (2022) · IEEE Open Journal of Signal Processing · doi:10.1109/ojsp.2022.3190213 · Cited by 91 · see citing works
Mining outlying aspects on numeric data
Duan, L., Tang, G., Pei, J., Bailey, J., Campbell, A., & Tang, C. (2015) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-014-0398-2 · Cited by 70 · see citing works
A new data mining based network Intrusion Detection model
Gudadhe, M., Prasad, P., & Kapil Wankhade, L. (2010) · 2010 International Conference on Computer and Communication Technology (ICCCT) · doi:10.1109/iccct.2010.5640375 · Cited by 59 · see citing works
Local Outlier Detection with Interpretation
Dang, X. H., Micenková, B., Assent, I., & Ng, R. T. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-40994-3_20 · Cited by 56 · see citing works
Self-citationYepmo, V., Smits, G., & Pivert, O. (2022) · Data & Knowledge Engineering · doi:10.1016/j.datak.2021.101946 · Cited by 52 · see citing works
Jin, M., Lv, A., Zhu, Y., Wen, Z., Zhong, Y., Zhao, Z., Wu, J., Li, H., He, H., & Chen, F. (2020) · IEEE Access · doi:10.1109/access.2020.3044610 · Cited by 50 · see citing works
Detecting Malicious Model Updates from Federated Learning on Conditional Variational Autoencoder
Gu, Z., & Yang, Y. (2021) · 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS) · doi:10.1109/ipdps49936.2021.00075 · Cited by 47 · see citing works
Generating High Fidelity Data from Low-density Regions using Diffusion Models
Sehwag, V., Hazirbas, C., Gordo, A., Ozgenel, F., & Ferrer, C. C. (2022) · 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr52688.2022.01120 · Cited by 41 · see citing works
Self-Supervised Wasserstein Pseudo-Labeling for Semi-Supervised Image Classification
Taherkhani, F., Dabouei, A., Soleymani, S., Dawson, J., & Nasrabadi, N. M. (2021) · 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr46437.2021.01209 · Cited by 45 · see citing works
An adaptive weighted one-class SVM for robust outlier detection
Yang, J., Deng, T., & Sui, R. (2016) · Lecture Notes in Electrical Engineering · doi:10.1007/978-3-662-48386-2_49 · Cited by 38 · see citing works
Ahmadi-Assalemi, G., Al-Khateeb, H., Epiphaniou, G., & Aggoun, A. (2022) · IEEE Internet of Things Journal · doi:10.1109/jiot.2022.3144127 · Cited by 34 · see citing works
Outlying property detection with numerical attributes
Angiulli, F., Fassetti, F., Manco, G., & Palopoli, L. (2017) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-016-0458-x · Cited by 33 · see citing works
Explainable outlier detection: What, for Whom and Why?
Sejr, J. H., & Schneider-Kamp, A. (2021) · Machine Learning with Applications · doi:10.1016/j.mlwa.2021.100172 · Cited by 32 · see citing works
Collaborative cloud-edge computation for personalized driving behavior modeling
Zhang, X., Qiao, M., Liu, L., Xu, Y., & Shi, W. (2019) · Proceedings of the 4th ACM/IEEE Symposium on Edge Computing · doi:10.1145/3318216.3363310 · Cited by 30 · see citing works
Eliciting Latent Predictions from Transformers with the Tuned Lens
Belrose, N., Ostrovsky, I., McKinney, L., Furman, Z., Smith, L., Halawi, D., Biderman, S., & Steinhardt, J. (2023) · arXiv · doi:10.48550/arxiv.2303.08112 · Cited by 27 · see citing works
“, 2008) and local outlier factor (LOF) (Breunig et al., 2000), both implemented in scikit-learn (Pedregosa et al.”
BackgroundApplying One-Class Algorithms for Data Stream-Based Insider Threat Detection
Peccatiello, R. B., Gondim, J. J. C., & Garcia, L. P. F. (2023) · IEEE Access · doi:10.1109/access.2023.3293825 · Cited by 25 · see citing works
A Semantic-Enhanced Method Based On Deep SVDD for Pixel-Wise Anomaly Detection
Hu, C., Chen, K., & Shao, H. (2021) · 2021 IEEE International Conference on Multimedia and Expo (ICME) · doi:10.1109/icme51207.2021.9428370 · Cited by 24 · see citing works
Unsupervised detection of coordinated fake-follower campaigns on social media
Zouzou, Y., & Varol, O. (2024) · EPJ Data Science · doi:10.1140/epjds/s13688-024-00499-6 · Cited by 19 · see citing works
Auto-Validate by-History: Auto-Program Data Quality Constraints to Validate Recurring Data Pipelines
Tu, D., He, Y., Cui, W., Ge, S., Zhang, H., Han, S., Zhang, D., & Chaudhuri, S. (2023) · Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining · doi:10.1145/3580305.3599776 · Cited by 14 · see citing works
Time-Series Multi-Instance Learning for Weakly Supervised Industrial Fault Detection
Liu, C., He, S., Li, S., Shi, Z., & Meng, W. (2025) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2024.3523591 · Cited by 8 · see citing works
RAAD: Reinforced Adversarial Anomaly Detector
Woo, S. S., Yoon, D., Gim, Y., & Park, E. (2024) · Proceedings of the 39th ACM/SIGAPP Symposium on Applied Computing · doi:10.1145/3605098.3635920 · Cited by 7 · see citing works
Toward Context-Aware Anomaly Detection for AIOps in Microservices Using Dynamic Knowledge Graphs
Moens, P., Steenwinckel, B., Ongenae, F., Volckaert, B., & Hoecke, S. V. (2026) · IEEE Transactions on Network and Service Management · doi:10.1109/tnsm.2026.3652304 · Cited by 6 · see citing works
“While there are a multitude of univariate time-series AD models, three models are considered here, namely a percentile-based detector (QuantileAD), a threshold-based detector (ThresholdAD) and a local outlier detector (OutlierAD), which is a density-based technique for outlier identification [61].”
Towards Low-Barrier Cybersecurity Research and Education for Industrial Control Systems
McGuan, C., Yu, C., & Lin, Q. (2023) · 2023 IEEE International Conference on Intelligence and Security Informatics (ISI) · doi:10.1109/isi58743.2023.10297207 · Cited by 3 · see citing works
ISFL-AE: Insider-Specific Feature Learning Autoencoder for Lightweight Insider Threat Detection
Kim, Y., & Kim, Y.-G. (2026) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2026.3659000 · Cited by 1 · see citing works
Schultheis, A., Bertrand, Y., Grüger, J., Malburg, L., Bergmann, R., & Serral Asensio, E. (2025) · IoT · doi:10.3390/iot6040063 · Cited by 1 · see citing works
“This step can use techniques for DQI detection mentioned earlier, such as local outlier factor [13] or isolation forests [12].”
AnomalyMatch: Discovering Rare Objects of Interest with Semi-supervised and Active Learning
Gómez, P., Ruhberg, L. E., Nardone, M. T., & O'Ryan, D. (2025) · arXiv · doi:10.48550/arxiv.2505.03509
“Classical approaches include One-Class SVM [12], Isolation Forest [4], and Local Outlier Factor (LOF) [13], extensively available in libraries such as PyOD [11].”
- Authors
- Breunig, M. M., Kriegel, H.-P., Ng, R. T., & Sander, J.
- Affiliations
- Ludwig-Maximilians-Universität München (DE)
- University of British Columbia (CA)
- Venue
- Proceedings of the 2000 ACM SIGMOD international conference on Management of data
- Publisher
- ACM
- Published
- 2000-05-16
- Pages
- 93-104
- ISSN
- 0730-8078 (ISSN-L)
- OpenAlex
- W4254182148
- Cited by
- 4,149
- References
- 0
- Citations by year
- 2026: 445 · 2025: 595 · 2024: 512 · 2023: 499 · 2022: 355 · 2021: 328 · 2020: 243 · 2019: 147 · 2018: 148 · 2017: 102 · 2016: 89 · 2015: 69 · 2014: 76 · 2013: 64 · 2012: 68
- FWCI
- 7.61
- Type
- conference paper
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM SIGMOD International Conference on Management of Data (SIGMOD) (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Anomaly Detection Techniques and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Computer Science › Signal Processing › Data Management and Algorithms
- Keywords
- local outlier factor, outlier detection, local outliers, e-commerce fraud detection
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review