An awesome curated list of outlier (a.k.a anomaly) detection papers.
In data mining, anomaly detection (also outlier detection) is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data. - Wikipedia
- 1. Books
- 2. Research Papers
- 2.1. Survey Papers
- 2.2. State-of-the-Art Papers
- 2.3. Density Based Outlier Detection Methods
- 2.4. Distance Based Outlier Detection Methods
- 2.5. Clustering Based Outlier Detection Methods
- 2.6. Isolation Based Outlier Detection Methods
- 2.7. Subspace Outlier Detection Methods
- 2.8. Ensemble based Outlier Detection Methods
- 2.9. Deep Learning Outlier Detection Methods
- 2.10. Graph Outlier Detection
- 2.11. Outlying Aspect Mining
- 3. Tutorials
- 4. Datasets
- 5. Tools
Outlier Analysis by Charu C. Aggarwal [URL].
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
Novelty detection: a review—part 1: statistical approaches | Elsevier | 2003 | [1] | [URL] |
Novelty detection: a review—part 2:: neural network based approaches | Elsevier | 2003 | [2] | [URL] |
A Survey of Outlier Detection Methodologies | Springer | 2004 | [3] | [URL] [PDF] |
Anomaly detection: A survey | ACM | 2009 | [4] | [PDF] |
A Comprehensive Survey of Data Mining-based Fraud Detection Research | ArXiv Preprint | 2010 | [15] | [PDF] |
A survey on unsupervised outlier detection in high‐dimensional numerical data | Wiley Online Library | 2012 | [16] | [URL] |
Survey on Anomaly Detection using Data Mining Techniques | ScienceDirect | 2015 | [14] | [URL] |
Graph based anomaly detection and description: a survey | DMKD | 2015 | [47] | [URL] [PDF] |
A comparative evaluation of outlier detection algorithms: Experiments and analyses | Pattern Recognition | 2018 | [48] | [PDF] |
Progress in outlier detection techniques: A survey | IEEE Access | 2019 | [46] | [URL] |
Deep learning for anomaly detection: A survey | ArXiv | 2019 | [49] | [PDF] |
Deep learning for anomaly detection: A review | ArXiv | 2020 | [50] | [PDF] |
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
LOF: Identifying Density-Based Local Outliers | ACM SIGMOD Record | 2000 | [6] | [PDF] |
Efficient algorithms for mining outliers from large data sets | ACM SIGMOD Record | 2000 | [17] | [PDF] |
Fast outlier detection in high dimensional spaces | PKDD | 2002 | [33] | [PDF] |
Isolation Forest | IEEE | 2008 | [5] | [URL] |
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
OPTICS-OF: Identifying Local Outliers | Springer | 1999 | [9] | [URL] |
LOF: Identifying Density-Based Local Outliers | ACM SIGMOD Record | 2000 | [6] | [PDF] |
Enhancing effectiveness of outlier detections for low density patterns (COF) | PAKDD | 2002 | [55] | [URL] |
RDF: A density-based outlier detection method using vertical data representation | ICDM | 2004 | [57] | [URL] |
LOCI: fast outlier detection using the local correlation integral | IEEE | 2003 | [7] | [URL] |
LoOP: local outlier probabilities | CIKM | 2009 | [58] | [PDF] |
Resolution-based outlier factor: detecting the top-n most outlying data points in engineering data (ROF) | KAIS | 2009 | [59] | [URL] |
FastLOF: An expectation-maximization based local outlier detection algorithm | ICPR | 2012 | [60] | [URL] |
Local outlier detection reconsidered: a generalized view on locality with applications to spatial, video, and network outlier detection (SimplifiedLOF) | DMKD | 2014 | [56] | [URL] |
LiNearN: A new approach to nearest neighbour density estimator | Pattern Recognition | 2014 | [52] | [URL] |
Revisiting Attribute Independence Assumption in Probabilistic Unsupervised Anomaly Detection | Springer | 2016 | [8] | [URL] |
Hierarchical density estimates for data clustering, visualization, and outlier detection (GLOSH) | TKDD | 2015 | [61] | [URL] |
Improved histogram-based anomaly detector with the extended principal component features | arXiv preprint | 2019 | [51] | [PDF] |
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
Efficient algorithms for mining outliers from large data sets | ACM SIGMOD Record | 2000 | [17] | [PDF] |
Fast outlier detection in high dimensional spaces | PKDD | 2002 | [33] | [PDF] |
A New Local Distance-Based Outlier Detection Approach for Scattered Real-World Data | PAKDD | 2009 | [30] | [URL] |
Rapid Distance-Based Outlier Detection via Sampling | NIPS | 2013 | [32] | [PDF] |
Distance-based Outlier Detection in Data Streams | VLDB | 2016 | [31] | [PDF] |
Title | Publication | Year | Reference | URL |
---|---|---|---|---|
Clustering-Based Outlier Detection Method | FSKD | 2008 | [35] | [URL] |
Efficient Clustering-Based Outlier Detection Algorithm for Dynamic Data Stream | FSKD | 2008 | [36] | [URL] |
Cluster-based outlier detection | Annals of Operations Research | 2009 | [34] | [PDF] |
Framework of Clustering-Based Outlier Detection | FSKD | 2009 | [40] | [URL] |
An Outlier Detection Method Based on Clustering | EAIT | 2011 | [37] | [PDF] |
A Minimum Spanning Tree-Inspired Clustering-Based Outlier Detection Technique | ICDM | 2012 | [39] | [PDF] |
Cluster Based Outlier Detection Algorithm for Healthcare Data | Procedia Computer Science | 2015 | [38] | [PDF] |
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
Isolation Forest | IEEE | 2008 | [5] | [URL] |
On Detecting Clustered Anomalies Using SCiForest | Springer | 2010 | [12] | [PDF] |
Isolation-Based Anomaly Detection | ACM | 2012 | [10] | [PDF] |
Improving iForest with Relative Mass | Springer | 2014 | [11] | [URL] |
Efficient anomaly detection by isolation using nearest neighbour ensemble | ICDEW | 2014 | [42] | [URL] |
LeSiNN: Detecting anomalies by identifying Least Similar Nearest Neighbours | IEEE | 2015 | [13] | [URL] |
Isolation‐based anomaly detection using nearest‐neighbor ensembles | Computational Intelligence | 2018 | [45] | [URL] |
Anomaly Detection Technique Robust to Units and Scales of Measurement | PAKDD | 2018 | [53] | [URL] |
usfAD: a robust anomaly detector based on unsupervised stochastic forest | International Journal of Machine Learning and Cybernetics | 2020 | [54] | [URL] |
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
Outlier Detection in Axis-Parallel Subspaces of High Dimensional Data | Springer | 2009 | [28] | [URL] [PDF] |
Local Subspace Based Outlier Detection | Springer | 2009 | [24] | [URL] |
HiCS: High Contrast Subspaces for Density-Based Outlier Ranking | ACM | 2012 | [21] | [URL] |
Outlier Detection in Arbitrarily Oriented Subspaces | ICDM | 2012 | [26] | [PDF] |
An angle-based subspace anomaly detection approach to high-dimensional data: With an application to industrial fault detection | Elsevier | 2015 | [27] | [URL] [PDF] |
ZERO++: Harnessing the Power of Zero Appearances to Detect Anomalies in Large-Scale Data Sets | JAIR | 2016 | [23] | [URL] [PDF] |
Subspace Outlier Detection in Linear Time with Randomized Hashing | IEEE | 2016 | [25] | [URL] [PDF] |
Hiding outliers in high-dimensional data spaces | Springer | 2017 | [22] | [URL] |
Title | Publication | Year | Reference | URL |
---|---|---|---|---|
LODA: Lightweight on-line detector of anomalies | Machine Learning | 2016 | [62] | [PDF] |
LSCP: Locally selective combination in parallel outlier ensembles | SIAM | 2019 | [63] | [PDF] |
DCSO: dynamic combination of detector scores for outlier ensemble | ArXiv | 2019 | [64] | [PDF] |
Title | Publication | Year | Reference | URL |
---|---|---|---|---|
DeepLog: Anomaly Detection and Diagnosis from System Logs through Deep Learning | CCS conference | 2017 | [65] | [PDF] |
Title | Publication | Year | Reference | URL |
---|---|---|---|---|
Graph based anomaly detection and description: a survey | DMKD | 2015 | [67] | [PDF] |
On Using Classification Datasets to Evaluate Graph Outlier Detection: Peculiar Observations and New Insights | ArXiv | 2020 | [66] | [PDF] |
Title | Publication Venue | Year | Reference | URL |
---|---|---|---|---|
Hos-Miner: a system for detecting outlyting subspaces of high-dimensional data | VLDB | 2004 | [20] | [PDF] |
Mining outlying aspects on numeric data | Springer | 2015 | [19] | [URL] |
Discovering outlying aspects in large datasets | Springer | 2016 | [18] | [PDF] |
Scalable Outlying-Inlying Aspects Discovery via Feature Ranking | PAKDD | 2015 | [29] | [URL] |
A new effective and efficient measure for outlying aspect mining | WISE | 2020 | [41] | [URL] |
Title | Publication | Year | Reference | URL |
---|---|---|---|---|
Outlier detection techniques | KDD | 2010 | [44] | [URL] |
Which Outlier Detector Should I use? | ICDE | 2018 | [43] | [URL] |
ODDS - Outlier Detection DataSets
Tool | Language | URL |
---|---|---|
ELKI | Java | [URL] |
PyOD | Python | [URL] |
[1] | Markou, M., & Singh, S. (2003). Novelty detection: a review—part 1: statistical approaches. Signal processing, 83(12), 2481-2497. |
[2] | Markou, M., & Singh, S. (2003). Novelty detection: a review—part 2:: neural network based approaches. Signal processing, 83(12), 2499-2521. |
[3] | Hodge, V., & Austin, J. (2004). A survey of outlier detection methodologies. Artificial intelligence review, 22(2), 85-126. |
[4] | Chandola, V., Banerjee, A., & Kumar, V. (2009). Anomaly detection: A survey. ACM computing surveys (CSUR), 41(3), 1-58. |
[5] | Liu, F. T., Ting, K. M., & Zhou, Z. H. (2008, December). Isolation forest. In 2008 Eighth IEEE International Conference on Data Mining (pp. 413-422). IEEE. |
[6] | Breunig, M. M., Kriegel, H. P., Ng, R. T., & Sander, J. (2000, May). LOF: identifying density-based local outliers. In Proceedings of the 2000 ACM SIGMOD international conference on Management of data (pp. 93-104). |
[7] | Papadimitriou, S., Kitagawa, H., Gibbons, P. B., & Faloutsos, C. (2003, March). Loci: Fast outlier detection using the local correlation integral. In Proceedings 19th international conference on data engineering (Cat. No. 03CH37405) (pp. 315-326). IEEE. |
[8] | Aryal, S., Ting, K. M., & Haffari, G. (2016, April). Revisiting attribute independence assumption in probabilistic unsupervised anomaly detection. In Pacific-Asia Workshop on Intelligence and Security Informatics (pp. 73-86). Springer, Cham. |
[9] | Breunig, M. M., Kriegel, H. P., Ng, R. T., & Sander, J. (1999, September). Optics-of: Identifying local outliers. In European Conference on Principles of Data Mining and Knowledge Discovery (pp. 262-270). Springer, Berlin, Heidelberg. |
[10] | Liu, F. T., Ting, K. M., & Zhou, Z. H. (2012). Isolation-based anomaly detection. ACM Transactions on Knowledge Discovery from Data (TKDD), 6(1), 1-39. |
[11] | Aryal, S., Ting, K. M., Wells, J. R., & Washio, T. (2014, May). Improving iforest with relative mass. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 510-521). Springer, Cham. |
[12] | Liu, F. T., Ting, K. M., & Zhou, Z. H. (2010, September). On detecting clustered anomalies using SCiForest. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (pp. 274-290). Springer, Berlin, Heidelberg. |
[13] | Pang, G., Ting, K. M., & Albrecht, D. (2015, November). LeSiNN: Detecting anomalies by identifying least similar nearest neighbours. In 2015 IEEE international conference on data mining workshop (ICDMW) (pp. 623-630). IEEE. |
[14] | Agrawal, S., & Agrawal, J. (2015). Survey on anomaly detection using data mining techniques. Procedia Computer Science, 60, 708-713. |
[15] | Phua, C., Lee, V., Smith, K., & Gayler, R. (2010). A comprehensive survey of data mining-based fraud detection research. arXiv preprint arXiv:1009.6119. |
[16] | Zimek, A., Schubert, E., & Kriegel, H. P. (2012). A survey on unsupervised outlier detection in high‐dimensional numerical data. Statistical Analysis and Data Mining: The ASA Data Science Journal, 5(5), 363-387. |
[17] | Ramaswamy, S., Rastogi, R., & Shim, K. (2000, May). Efficient algorithms for mining outliers from large data sets. In Proceedings of the 2000 ACM SIGMOD international conference on Management of data (pp. 427-438). |
[18] | Vinh, N. X., Chan, J., Romano, S., Bailey, J., Leckie, C., Ramamohanarao, K., & Pei, J. (2016). Discovering outlying aspects in large datasets. Data mining and knowledge discovery, 30(6), 1520-1555. |
[19] | Duan, L., Tang, G., Pei, J., Bailey, J., Campbell, A., & Tang, C. (2015). Mining outlying aspects on numeric data. Data Mining and Knowledge Discovery, 29(5), 1116-1151. |
[20] | Zhang, J., Lou, M., Ling, T. W., & Wang, H. (2004). HOS-miner: A system for detecting outlying subspaces of high-dimensional data. In Proceedings of the 30th International Conference on Very Large Data Bases (VLDB'04) (pp. 1265-1268). Morgan Kaufmann Publishers Inc.. |
[21] | Keller, F., Muller, E., & Bohm, K. (2012, April). HiCS: High contrast subspaces for density-based outlier ranking. In 2012 IEEE 28th international conference on data engineering (pp. 1037-1048). IEEE. |
[22] | Steinbuss, G., & Böhm, K. (2017). Hiding outliers in high-dimensional data spaces. International Journal of Data Science and Analytics, 4(3), 173-189. |
[23] | Pang, G., Ting, K. M., Albrecht, D., & Jin, H. (2016). ZERO++: Harnessing the power of zero appearances to detect anomalies in large-scale data sets. Journal of Artificial Intelligence Research, 57, 593-620. |
[24] | Agrawal, A. (2009, August). Local subspace based outlier detection. In International Conference on Contemporary Computing (pp. 149-157). Springer, Berlin, Heidelberg. |
[25] | Sathe, S., & Aggarwal, C. C. (2016, December). Subspace outlier detection in linear time with randomized hashing. In 2016 IEEE 16th International Conference on Data Mining (ICDM) (pp. 459-468). IEEE. |
[26] | Kriegel, H. P., Kröger, P., Schubert, E., & Zimek, A. (2012, December). Outlier detection in arbitrarily oriented subspaces. In 2012 IEEE 12th international conference on data mining (pp. 379-388). IEEE. |
[27] | Zhang, L., Lin, J., & Karim, R. (2015). An angle-based subspace anomaly detection approach to high-dimensional data: With an application to industrial fault detection. Reliability Engineering & System Safety, 142, 482-497. |
[28] | Kriegel, H. P., Kröger, P., Schubert, E., & 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. |
[29] | Vinh, N. X., Chan, J., Bailey, J., Leckie, C., Ramamohanarao, K., & Pei, J. (2015, May). Scalable outlying-inlying aspects discovery via feature ranking. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 422-434). Springer, Cham. |
[30] | Zhang, K., Hutter, M., & Jin, H. (2009, April). A new local distance-based outlier detection approach for scattered real-world data. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 813-822). Springer, Berlin, Heidelberg. |
[31] | Tran, L., Fan, L., & Shahabi, C. (2016). Distance-based outlier detection in data streams. Proceedings of the VLDB Endowment, 9(12), 1089-1100. |
[32] | Sugiyama, M., & Borgwardt, K. (2013). Rapid distance-based outlier detection via sampling. In Advances in Neural Information Processing Systems (pp. 467-475). |
[33] | Angiulli, F., & 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). Springer, Berlin, Heidelberg. |
[34] | Duan, L., Xu, L., Liu, Y., & Lee, J. (2009). Cluster-based outlier detection. Annals of Operations Research, 168(1), 151-168. |
[35] | Jiang, S. Y., & An, Q. B. (2008, October). Clustering-based outlier detection method. In 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery (Vol. 2, pp. 429-433). IEEE. |
[36] | Elahi, M., Li, K., Nisar, W., Lv, X., & Wang, H. (2008, October). Efficient clustering-based outlier detection algorithm for dynamic data stream. In 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery (Vol. 5, pp. 298-304). IEEE. |
[37] | Pamula, R., Deka, J. K., & Nandi, S. (2011, February). An outlier detection method based on clustering. In 2011 Second International Conference on Emerging Applications of Information Technology (pp. 253-256). IEEE. |
[38] | Christy, A., Gandhi, G. M., & Vaithyasubramanian, S. (2015). Cluster based outlier detection algorithm for healthcare data. Procedia Computer Science, 50, 209-215. |
[39] | Wang, X., Wang, X. L., & Wilkes, D. M. (2012, July). A minimum spanning tree-inspired clustering-based outlier detection technique. In Industrial Conference on Data Mining (pp. 209-223). Springer, Berlin, Heidelberg. |
[40] | Jiang, S. Y., & Yang, A. M. (2009, August). Framework of clustering-based outlier detection. In 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery (Vol. 1, pp. 475-479). IEEE. |
[41] | Samariya, D., Aryal, S., Ting, K. M., & Ma, J. (2020, October). A new effective and efficient measure for outlying aspect mining. In International Conference on Web Information Systems Engineering (pp. 463-474). Springer, Cham. |
[42] | T. R. Bandaragoda, K. M. Ting, D. Albrecht, F. T. Liu and J. R. Wells, "Efficient Anomaly Detection by Isolation Using Nearest Neighbour Ensemble," 2014 IEEE International Conference on Data Mining Workshop, Shenzhen, 2014, pp. 698-705, doi: 10.1109/ICDMW.2014.70. |
[43] | Ting, K. M., Aryal, S., & Washio, T. (2018, November). Which Outlier Detector Should I use?. In 2018 IEEE International Conference on Data Mining (ICDM) (pp. 8-8). IEEE. |
[44] | Kriegel, H. P., Kröger, P., & Zimek, A. (2010). Outlier detection techniques. Tutorial at KDD, 10, 1-76. |
[45] | Bandaragoda, T. R., Ting, K. M., Albrecht, D., Liu, F. T., Zhu, Y., & Wells, J. R. (2018). Isolation‐based anomaly detection using nearest‐neighbor ensembles. Computational Intelligence, 34(4), 968-998. |
[46] | Wang, H., Bah, M. J., & Hammad, M. (2019). Progress in outlier detection techniques: A survey. IEEE Access, 7, 107964-108000. |
[47] | Akoglu, L., Tong, H., & Koutra, D. (2015). Graph based anomaly detection and description: a survey. Data mining and knowledge discovery, 29(3), 626-688. |
[48] | Domingues, R., Filippone, M., Michiardi, P., & Zouaoui, J. (2018). A comparative evaluation of outlier detection algorithms: Experiments and analyses. Pattern Recognition, 74, 406-421. |
[49] | Chalapathy, R., & Chawla, S. (2019). Deep learning for anomaly detection: A survey. arXiv preprint arXiv:1901.03407. |
[50] | Pang, G., Shen, C., Cao, L., & Hengel, A. V. D. (2020). Deep learning for anomaly detection: A review. arXiv preprint arXiv:2007.02500. |
[51] | Aryal, S., Baniya, A. A., & Santosh, K. C. (2019). Improved histogram-based anomaly detector with the extended principal component features. arXiv preprint arXiv:1909.12702. |
[52] | Wells, J. R., Ting, K. M., & Washio, T. (2014). LiNearN: A new approach to nearest neighbour density estimator. Pattern Recognition, 47(8), 2702-2720. |
[53] | Aryal, S. (2018, June). Anomaly detection technique robust to units and scales of measurement. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 589-601). Springer, Cham. |
[54] | Aryal, S., Santosh, K. C., & Dazeley, R. (2020). usfAD: a robust anomaly detector based on unsupervised stochastic forest. International Journal of Machine Learning and Cybernetics, 1-14. |
[55] | Tang, J., Chen, Z., Fu, A. W. C., & 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. |
[56] | Schubert, E., Zimek, A., & Kriegel, H. P. (2014). Local outlier detection reconsidered: a generalized view on locality with applications to spatial, video, and network outlier detection. Data mining and knowledge discovery, 28(1), 190-237. |
[57] | Ren, D., Wang, B., & Perrizo, W. (2004, November). Rdf: A density-based outlier detection method using vertical data representation. In Fourth IEEE International Conference on Data Mining (ICDM'04) (pp. 503-506). IEEE. |
[58] | Kriegel, H. P., Kröger, P., Schubert, E., & Zimek, A. (2009, November). LoOP: local outlier probabilities. In Proceedings of the 18th ACM conference on Information and knowledge management (pp. 1649-1652). |
[59] | Fan, H., Zaïane, O. R., Foss, A., & Wu, J. (2009). Resolution-based outlier factor: detecting the top-n most outlying data points in engineering data. Knowledge and Information Systems, 19(1), 31-51. |
[60] | Goldstein, M. (2012, November). FastLOF: An expectation-maximization based local outlier detection algorithm. In Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012) (pp. 2282-2285). IEEE. |
[61] | Campello, R. J., Moulavi, D., Zimek, A., & Sander, J. (2015). Hierarchical density estimates for data clustering, visualization, and outlier detection. ACM Transactions on Knowledge Discovery from Data (TKDD), 10(1), 1-51. |
[62] | Pevný, T. (2016). Loda: Lightweight on-line detector of anomalies. Machine Learning, 102(2), 275-304. |
[63] | Zhao, Y., Nasrullah, Z., Hryniewicki, M. K., & Li, Z. (2019, May). LSCP: Locally selective combination in parallel outlier ensembles. In Proceedings of the 2019 SIAM International Conference on Data Mining (pp. 585-593). Society for Industrial and Applied Mathematics. |
[64] | Zhao, Y., & Hryniewicki, M. K. (2019). DCSO: dynamic combination of detector scores for outlier ensembles. arXiv preprint arXiv:1911.10418. |
[65] | Du, M., Li, F., Zheng, G., & Srikumar, V. (2017, October). Deeplog: Anomaly detection and diagnosis from system logs through deep learning. In Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security (pp. 1285-1298). |
[66] | Zhao, L., & Akoglu, L. (2020). On Using Classification Datasets to Evaluate Graph Outlier Detection: Peculiar Observations and New Insights. arXiv preprint arXiv:2012.12931. |
[67] | Akoglu, L., Tong, H., & Koutra, D. (2015). Graph based anomaly detection and description: a survey. Data mining and knowledge discovery, 29(3), 626-688. |
More to come...
More items will be added to the repository. Please feel free to suggest other key resources by opening an issue report, submitting a pull request, or dropping me an email @ (samariya.durgesh@gmail.com). Enjoy reading!
Last updated on January 2, 2021