A survey on unsupervised outlier detection in high-dimensional numerical data

Statistical Analysis and Data Mining

Volumn 5, Issue 5, 2012, Pages 363-387

  Zimek, Arthur ^a   Schubert, Erich ^b   Kriegel, Hans Peter ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Anomalies in high dimensional data; Approximate outlier detection; Correlation outlier detection; Curse of dimensionality; Outlier detection in high dimensional data; Subspace outlier detection

Indexed keywords

CLUSTERING ALGORITHMS; DATA MINING; EFFICIENCY; GEOMETRY; STATISTICS;

ANOMALIES IN HIGH-DIMENSIONAL DATUM; APPROXIMATE OUTLIER DETECTIONS; CORRELATION OUTLIER DETECTIONS; CURSE OF DIMENSIONALITY; EUCLIDEAN SPACES; HIGH DIMENSIONAL DATA; HIGH-DIMENSIONAL; OUTLIER DETECTION; OUTLIER DETECTION IN HIGH-DIMENSIONAL DATUM; SUBSPACE OUTLIER DETECTIONS;

SURVEYS;

EID: 84866458840     PISSN: 19321872     EISSN: 19321864     Source Type: Journal    
DOI: 10.1002/sam.11161     Document Type: Review

References (154)

1. M. Markou and S. Singh, Novelty detection: a review-part 1: statistical approaches, Signal Process 83 (2003), 2481-2497.
2. M. Markou and S. Singh, Novelty detection: A review-part 2: neural network based approaches, Signal Process 83 (2003), 2499-2521.
3. V. J. Hodge and J. Austin, A survey of outlier detection methodologies, Artif Intell Rev 22 (2004), 85-126.
4. M. Agyemang, K. Barker, and R. Alhajj, A comprehensive survey of numeric and symbolic outlier mining techniques, Intell Data Anal 10 (2006), 521-538.
5. A. Patcha and J.-M. Park, An overview of anomaly detection techniques: Existing solutions and latest technological trends, Comput Netw 51 (2007), 3448-3470.
6. A. S. Hadi, A. H. M. Rahmatullah Imon, and M. Werner, Detection of outliers, Wiley Interdiscip Rev: Comput Stat 1(1) (2009), 57-70.
7. V. Chandola, A. Banerjee, and V. Kumar, Anomaly detection: a survey, ACM Comput Surv 41 (3) (2009), Article 15, 1-58.
8. X. Su and C.-L. Tsai, Outlier detection, Wiley Interdiscip Rev: Data Mining Knowledge Disc 1(3) (2011), 261-268.
9. J. Han, M. Kamber, and J. Pei, Data Mining: Concepts and Techniques, (3rd ed.), Morgan Kaufmann, Amsterdam, 2011.
10. V. Chandola, A. Banerjee, and V. Kumar, Anomaly detection for discrete sequences: A survey, IEEE Trans Knowledge Data Eng 24(5) (2012), 823-839.
11. C. C. Aggarwal and P. S. Yu, Outlier detection for high dimensional data, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Santa Barbara, CA, 2001, 37-46.
12. K. Beyer, J. Goldstein, R. Ramakrishnan, and U. Shaft, When is "nearest neighbor" meaningful? In Proceedings of the 7th International Conference on Database Theory (ICDT), Jerusalem, Israel, 1999, 217-235.
13. K. Lin, H. V. Jagadish, and C. Faloutsos, The TV-Tree: an index structure for high-dimensional data, The VLDB J 3 (1995), 517-542.
14. S. Brin, Near neighbor search in large metric spaces, In Proceedings of the 21st International Conference on Very Large Data Bases (VLDB), Zurich, Switzerland, 1995, 574-584.
15. S. Berchtold, D. A. Keim, and H.-P. Kriegel, The X-Tree: an index structure for high-dimensional data, In Proceedings of the 22nd International Conference on Very Large Data Bases (VLDB), Bombay, India, 1996, 28-39.
16. S. Berchtold, C. Böhm, B. Braunmüller, D. A. Keim, and H.-P. Kriegel, Fast parallel similarity search in multimedia databases, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Tucson, AZ, 1997, 1-12.
17. N. Katayama and S. Satoh, The SR-tree: an index structure for high-dimensional nearest neighbor queries, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Tucson, AZ, 1997, 369-380.
18. S. Berchtold, C. Böhm, D. A. Keim, and H.-P. Kriegel, A cost model for nearest neighbor search in high-dimensional data space, In Proceedings of the 16th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Tucson, AZ, 1997, 78-86.
19. P. Indyk and R. Motwani, Approximate nearest neighbors: towards removing the curse of dimensionality, In Proceedings of the thirtieth annual ACM symposium on Theory of computing (STOC), Dallas, TX, 1998, 604-613.
20. R. Weber, H.-J. Schek, and S. Blott, A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces, In Proceedings of the 24th International Conference on Very Large Data Bases (VLDB), New York City, NY, 1998, 194-205.
21. C. Böhm, S. Berchtold, and D. A. Keim, Searching in high-dimensional spaces: Index structures for improving the performance of multimedia databases, ACM Comput Surv 33(3) (2001), 322-373.
22. V. Pestov, On the geometry of similarity search: dimensionality curse and concentration of measure, Inform Process Lett 73(1-2) (2000), 47-51.
23. A. Hinneburg, C. C. Aggarwal, and D. A. Keim, What is the nearest neighbor in high dimensional spaces? In Proceedings of the 26th International Conference on Very Large Data Bases (VLDB), Cairo, Egypt, 2000, 506-515.
24. C. C. Aggarwal, A. Hinneburg, and D. Keim, On the surprising behavior of distance metrics in high dimensional space, In Proceedings of the 8th International Conference on Database Theory (ICDT), London, UK, 2001, 420-434.
25. D. Francois, V. Wertz, and M. Verleysen, The concentration of fractional distances, IEEE Trans Knowledge Data Eng 19(7) (2007), 873-886.
26. M. Radovanović, A. Nanopoulos, and M. Ivanović, On the existence of obstinate results in vector space models, In Proceedings of the 33rd International Conference on Research and Development in Information Retrieval (SIGIR), Geneva, Switzerland, 2010, 186-193.
27. S. Ramaswamy, R. Rastogi, and K. Shim, Efficient algorithms for mining outliers from large data sets, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Dallas, TX, 2000, 427-438.
28. M. M. Breunig, H.-P. Kriegel, R. Ng, and J. Sander, LOF: identifying density-based local outliers, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Dallas, TX, 2000, 93-104.
29. U. Shaft and R. Ramakrishnan, Theory of nearest neighbors indexability, ACM Trans Database Syst (TODS) 31(3) (2006), 814-838.
30. K. P. Bennett, U. Fayyad, and D. Geiger, Density-based indexing for approximate nearest-neighbor queries, In Proceedings of the 5th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), San Diego, CA, 1999, 233-243.
31. H.-P. Kriegel, P. Kröger, and A. Zimek, Clustering high dimensional data: a survey on subspace clustering, pattern-based clustering, and correlation clustering, ACM Trans Knowledge Disc Data (TKDD) 3(1) (2009), 1-58.
32. P. Kröger and A. Zimek, Subspace clustering techniques. In Encyclopedia of Database Systems, L. Liu and M. T. Özsu, eds. Springer, New York, 2009, 2873-2875.
33. H.-P. Kriegel, P. Kröger, and A. Zimek, Subspace clustering, Wiley Interdiscip Rev: Data Mining Knowledge Disc 2(4) (2012), 351-364.
34. I. Assent, Clustering high dimensional data, Wiley Interdiscip Rev: Data Mining Knowledge Disc 2(4) (2012), 340-350.
35. C. Domeniconi, D. Papadopoulos, D. Gunopulos, and S. Ma, Subspace clustering of high dimensional data, In Proceedings of the 4th SIAM International Conference on Data Mining (SDM), Lake Buena Vista, FL, 2004.
36. K.-G. Woo, J.-H. Lee, M.-H. Kim, and Y.-J. Lee, FINDIT: a fast and intelligent subspace clustering algorithm using dimension voting, Inform Softw Technol 46(4) (2004), 255-271.
37. L. Parsons, E. Haque, and H. Liu, Subspace clustering for high dimensional data: a review, ACM SIGKDD Explor 6(1) (2004), 90-105.
38. M. L. Yiu and N. Mamoulis, Iterative projected clustering by subspace mining, IEEE Trans Knowledge Data Eng 17(2) (2005), 176-189.
39. G. Liu, J. Li, K. Sim, and L. Wong, Distance based subspace clustering with flexible dimension partitioning, In Proceedings of the 23rd International Conference on Data Engineering (ICDE), Istanbul, Turkey, 2007, 1250-1254.
40. H.-P. Kriegel, P. Kröger, E. Schubert, and A. Zimek, A general framework for increasing the robustness of PCA-based correlation clustering algorithms, In Proceedings of the 20th International Conference on Scientific and Statistical Database Management (SSDBM), Hong Kong, China, 2008, 418-435.
41. G. Moise and J. Sander, Finding non-redundant, statistically significant regions in high dimensional data: a novel approach to projected and subspace clustering, In Proceedings of the 14th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Las Vegas, NV, 2008, 533-541.
42. E. Achtert, C. Böhm, J. David, P. Kröger, and A. Zimek, Global correlation clustering based on the Hough transform, Stat Anal Data Mining 1(3) (2008), 111-127.
43. C. Zhu, H. Kitagawa, and C. Faloutsos, Example-based robust outlier detection in high dimensional datasets, In Proceedings of the 5th IEEE International Conference on Data Mining (ICDM), Houston, TX, 2005, 829-832.
44. H.-P. Kriegel, M. Schubert, and A. Zimek, Angle-based outlier detection in high-dimensional data, In Proceedings of the 14th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Las Vegas, NV, 2008, 444-452.
45. E. Müller, I. Assent, U. Steinhausen, and T. Seidl, OutRank: ranking outliers in high dimensional data, In Proceedings of the 24th International Conference on Data Engineering (ICDE) Workshop on Ranking in Databases (DBRank), Cancun, Mexico, 2008, 600-603.
46. C. C. Aggarwal, Re-designing distance functions and distance-based applications for high dimensional data, ACM SIGMOD Record 30(1) (2001), 13-18.
47. N. Katayama and S. Satoh, Distinctiveness-sensitive nearest-neighbor search for efficient similarity retrieval of multimedia information, In Proceedings of the 17th International Conference on Data Engineering (ICDE), Heidelberg, Germany, 2001, 493-502.
48. C. C. Aggarwal and P. S. Yu, Finding generalized projected clusters in high dimensional space, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Dallas, TX, 2000, 70-81.
49. S. Berchtold, C. Böhm, H. V. Jagadish, H.-P. Kriegel, and J. Sander, Independent Quantization: an index compression technique for high-dimensional data spaces, In Proceedings of the 16th International Conference on Data Engineering (ICDE), San Diego, CA, 2000, 577-588.
50. H. Jin, B. C. Ooi, H. T. Shen, C. Yu, and A. Y. Zhou, An adaptive and efficient dimensionality reduction algorithm for high-dimensional indexing, In Proceedings of the 19th International Conference on Data Engineering (ICDE), Bangalore, India, 2003, 87-98.
51. C. C. Aggarwal and P. S. Yu, On high dimensional indexing of uncertain data, In Proceedings of the 24th International Conference on Data Engineering (ICDE), Cancun, Mexico, 2008, 1460-1461.
52. S. France and D. Carrol, Is the distance compression effect overstated? Some theory and experimentation, In Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition (MLDM), Leipzig, Germany, 2009, 280-294.
53. M. E. Houle, H.-P. Kriegel, P. Kröger, E. Schubert, and A. Zimek, Can shared-neighbor distances defeat the curse of dimensionality? In Proceedings of the 22nd International Conference on Scientific and Statistical Database Management (SSDBM), Heidelberg, Germany, 2010, 482-500.
54. P. Hall, J. S. Marron, and A. Neeman, Geometric representation of high dimension, low sample size data, J Royal Stat Soc: Ser B 67 (2005), 427-444.
55. F. Murtagh, The remarkable simplicity of very high dimensional data: application of model-based clustering, J Classif 26 (2009), 249-277.
56. S. France, D. Carrol, and H. Xiong, Distance metrics for high dimensional nearest neighborhood recovery: compression and normalization, Inform Sci 184 (2012), 92-110.
57. R. J. Durrant and A. Kabán, When is 'nearest neighbour' meaningful: a converse theorem and implications, J Complex 25(4) (2009), 385-397.
58. F. Korn, B.-U. Pagel, and C. Faloutsos, On the "dimensionality curse" and the "self-similarity blessing", IEEE Trans Knowledge Data Eng 13(1) (2001), 96-111.
59. R. Clarke, H. W. Ressom, A. Wang, J. Xuan, M. C. Liu, E. A. Gehan, and Y. Wang, The properties of high-dimensional data spaces: implications for exploring gene and protein expression data, Nature Rev Cancer 8 (2008), 37-49.
60. K. Sim, V. Gopalkrishnan, A. Zimek, and G. Cong, A survey on enhanced subspace clustering, Data Mining Knowledge Disc (2012). DOI:10.1007/s10618-012-0258-x.
61. H.-P. Kriegel and A. Zimek, Subspace clustering, ensemble clustering, alternative clustering, multiview clustering: What can we learn from each other? In MultiClust: 1st International Workshop on Discovering, Summarizing and Using Multiple Clusterings Held in Conjunction with KDD 2010, Washington, DC, 2010.
62. T. Bernecker, M. E. Houle, H.-P. Kriegel, P. Kröger, M. Renz, E. Schubert, and A. Zimek, Quality of similarity rankings in time series, In Proceedings of the 12th International Symposium on Spatial and Temporal Databases (SSTD), Minneapolis, MN, 2011, 422-440.
63. M. Verleysen and D. François, The curse of dimensionality in data mining and time series prediction, In Proceedings of the 8th International Work-Conference on Artificial Neural Networks (IWANN), Barcelona, Spain, 2005, 758-770.
64. D. Hawkins, Identification of Outliers, Chapman and Hall, New York, 1980.
65. M. Radovanović, A. Nanopoulos, and M. Ivanović, Nearest neighbors in high-dimensional data: the emergence and influence of hubs, In Proceedings of the 26th International Conference on Machine Learning (ICML), Montreal, Canada, 2009. 865-872.
66. M. Radovanović, A. Nanopoulos, and M. Ivanović, Hubs in space: Popular nearest neighbors in high-dimensional data, J Mach Learn Res 11 (2010), 2487-2531.
67. M. Radovanović, A. Nanopoulos, and M. Ivanović, Time-series classification in many intrinsic dimensions, In Proceedings of the 10th SIAM International Conference on Data Mining (SDM), Columbus, OH, 2010, 677-688.
68. N. Tomašev, M. Radovanović, D. Mladenić, and M. Ivanović, The role of hubness in clustering high-dimensional data, In Proceedings of the 15th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Shenzhen, China, 2011, 183-195.
69. A.-L. Barabási, Scale-free networks: a decade and beyond, Science 325(5939) (2009), 412-413.
70. E. M. Knorr and R. T. Ng, A unified approach for mining outliers, In Proceedings of the conference of the Centre for Advanced Studies on Collaborative research (CASCON), Toronto, Canada, 1997, 11-23.
71. E. M. Knorr, R. T. Ng, and V. Tucanov, Distance-based outliers: algorithms and applications, VLDB J 8(3-4) (2000), 237-253.
72. F. Angiulli and C. Pizzuti, Fast outlier detection in high dimensional spaces, In Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discoverys (PKDD), Helsinki, Finland, 2002, 15-26.
73. G. Kollios, D. Gunopulos, N. Koudas, and S. Berchthold, Efficient biased sampling for approximate clustering and outlier detection in large datasets, IEEE Trans Knowledge Data Eng 15(5) (2003), 1170-1187.
74. S. D. Bay and M. Schwabacher, Mining distance-based outliers in near linear time with randomization and a simple pruning rule, In Proceedings of the 9th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Washington, DC, 2003, 29-38.
75. Y. Pei, O. Zaïane, and Y. Gao, An efficient reference-based approach to outlier detection in large datasets, In Proceedings of the 6th IEEE International Conference on Data Mining (ICDM), Hong Kong, China, 2006, 478-487.
76. J. Tang, Z. Chen, A. W.-C. Fu, and D. W. Cheung, Enhancing effectiveness of outlier detections for low density patterns, In Proceedings of the 6th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Taipei, Taiwan, 2002, 535-548.
77. W. Jin, A. Tung, and J. Han, Mining top-n local outliers in large databases, In Proceedings of the 7th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), San Francisco, CA, 2001, 293-298.
78. W. Jin, A. K. H. Tung, J. Han, and W. Wang, Ranking outliers using symmetric neighborhood relationship, In Proceedings of the 10th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Singapore, 2006, 577-593.
79. C.-C. Szeto and E. Hung, Mining outliers with faster cutoff update and space utilization, Pattern Recogn Lett 31(11) (2010), 1292-1301.
80. G. H. Orair, C. Teixeira, Y. Wang, W. Meira, Jr., and S. Parthasarathy, Distance-based outlier detection: consolidation and renewed bearing, Proc VLDB Endowment 3(2) (2010), 1469-1480.
81. A. Guttman, R-Trees: a dynamic index structure for spatial searching, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Boston, MA, 1984, 47-57.
82. N. Beckmann, H.-P. Kriegel, R. Schneider, and B. Seeger, The R*-Tree: an efficient and robust access method for points and rectangles, In Proceedings of the ACM International Conference on Management of Data (SIGMOD), Atlantic City, NJ, 1990, 322-331.
83. A. Gionis, P. Indyk, and R. Motwani, Similarity search in high dimensions via hashing, In Proceedings of the 25th International Conference on Very Large Data Bases (VLDB), Edinburgh, Scotland, 1999, 518-529.
84. P. Indyk, Nearest neighbors in high-dimensional spaces. In Handbook of Discrete and Computational Geometry, chapter 39, (2nd ed.), J. E. Goodman and J. O'Rourke, eds. CRC Press, Boca Raton, 2004, 877-892.
85. A. Andoni and P. Indyk, Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions, In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), Berkeley, CA, 2006, 459-468.
86. W. B. Johnson and J. Lindenstrauss, Extensions of Lipschitz mappings into a Hilbert space, In Conference in Modern Analysis and Probability, volume 26 of Contemporary Mathematics, American Mathematical Society, 1984, 189-206.
87. J. Matoušek, On variants of the Johnson-Lindenstrauss lemma, Random Struct Algor 33(2) (2008), 142-156.
88. D. Achlioptas, Database-friendly random projections, In Proceedings of the 20th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Santa Barbara, CA, 2001.
89. D. Achlioptas, Database-friendly random projections: Johnson-Lindenstrauss with binary coins, J Comput Syst Sci 66 (2003), 671-687.
90. S. Venkatasubramanian and Q. Wang, The Johnson- Lindenstrauss transform: an empirical study, In Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX) SIAM, San Francisco, CA, 2011, 164-173.
91. A. Kabán, On the distance concentration awareness of certain data reduction techniques, Pattern Recogn 44(2) (2011), 265-277.
92. G. Peano, Sur une courbe, qui remplit toute une aire plane, Mathe Ann 36(1) (1890), 157-160.
93. G. M. Morton, A computer oriented geodetic data base and a new technique in file sequencing, Technical report, International Business Machines Co., 1966.
94. D. Hilbert, Ueber die stetige Abbildung einer Linie auf ein Flächenstück, Math Ann 38(3) (1891), 459-460.
95. I. Kamel and C. Faloutsos, Hilbert R-tree: an improved R-tree using fractals, In Proceedings of the 20th International Conference on Very Large Data Bases (VLDB), Santiago de Chile, Chile, 1994, 500-509.
96. N. H. Vu and V. Gopalkrishnan, Efficient pruning schemes for distance-based outlier detection, In Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD), Bled, Slovenia, 2009, 160-175.
97. A. Ghoting, S. Parthasarathy, and M. E. Otey, Fast mining of distance-based outliers in high-dimensional datasets, Data Mining Knowledge Disc 16(3) (2008), 349-364.
98. J. A. Hartigan, Clustering Algorithms, John Wiley & Sons, New York, 1975.
99. Y. Wang, S. Parthasarathy, and S. Tatikonda, Locality sensitive outlier detection: A ranking driven approach, In Proceedings of the 27th International Conference on Data Engineering (ICDE), Hannover, Germany, 2011, 410-421.
100. T. de Vries, S. Chawla, and M. E. Houle, Finding local anomalies in very high dimensional space, In Proceedings of the 10th IEEE International Conference on Data Mining (ICDM), Sydney, Australia, 2010, 128-137.
101. N. Pham and R. Pagh, A near-linear time approximation algorithm for angle-based outlier detection in high-dimensional data, In Proceedings of the 18th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Beijing, China, 2012.
102. S. Papadimitriou, H. Kitagawa, P. Gibbons, and C. Faloutsos, LOCI: Fast outlier detection using the local correlation integral, In Proceedings of the 19th International Conference on Data Engineering (ICDE), Bangalore, India, 2003, 315-326.
103. F. Angiulli and C. Pizzuti, Outlier mining in large high-dimensional data sets, IEEE Trans Knowledge Data Eng 17(2) (2002), 203-215.
104. B. Moon, H. V. Jagadish, C. Faloutsos, and J. H. Saltz, Analysis of the clustering properties of the Hilbert space-filling curve, IEEE Trans Knowledge Data Eng 13(1) (2001), 124-141.
105. S. Liao, M. A. Lopez, and S. T. Leutenegger, High dimensional similarity search with space filling curves, In Proceedings of the 17th International Conference on Data Engineering (ICDE), Heidelberg, Germany, 2001, 615-622.
106. L. Yang, Distance-preserving dimensionality reduction, Wiley Interdiscip Rev: Data Mining Knowledge Disc 1(5) (2011), 369-380.
107. R. Gnanadesikan and J. R. Kettenring, Robust estimates, residuals, and outlier detection with multiresponse data, Biometrics 28(1) (1972), 81-124.
108. I. T. Jolliffe, Principal Component Analysis (2nd ed.), Springer, New York, 2002.
109. P. Filzmoser, R. Maronna, and M. Werner, Outlier identification in high dimensions, Comput Stat Data Anal 52(3) (2008), 1694-1711.
110. J. A. Lee and M. Verleysen, Quality assessment of dimensionality reduction: rank-based criteria, Neurocomputing 72(7-9) (2009), 1431-1443.
111. N. H. Vu and V. Gopalkrishnan, Feature extraction for outlier detection in high-dimensional spaces, J Mach Learn Res, Proc Track 10 (2010), 66-75.
112. F. Keller, E. Müller, and K. Böhm, HiCS: high contrast subspaces for density-based outlier ranking, In Proceedings of the 28th International Conference on Data Engineering (ICDE), Washington, DC, 2012.
113. A. Lazarevic and V. Kumar, Feature bagging for outlier detection, In Proceedings of the 11th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Chicago, IL, 2005, 157-166.
114. H. V. Nguyen, H. H. Ang, and V. Gopalkrishnan, Mining outliers with ensemble of heterogeneous detectors on random subspaces, In Proceedings of the 15th International Conference on Database Systems for Advanced Applications (DASFAA), Tsukuba, Japan, 2010, 368-383.
115. J. Gao and P.-N. Tan, Converting output scores from outlier detection algorithms into probability estimates, In Proceedings of the 6th IEEE International Conference on Data Mining (ICDM), Hong Kong, China, 2006. 212-221.
116. H.-P. Kriegel, P. Kröger, E. Schubert, and A. Zimek, Interpreting and unifying outlier scores, In Proceedings of the 11th SIAM International Conference on Data Mining (SDM), Mesa, AZ, 2011, 13-24.
117. E. Schubert, R. Wojdanowski, A. Zimek, and H.-P. Kriegel, On evaluation of outlier rankings and outlier scores, In Proceedings of the 12th SIAM International Conference on Data Mining (SDM), Anaheim, CA, 2012, 1047-1058.
118. E. M. Knorr and R. T. Ng, Finding intensional knowledge of distance-based outliers, In Proceedings of the 25th International Conference on Very Large Data Bases (VLDB), Edinburgh, Scotland, 1999, 211-222.
119. H.-P. Kriegel, P. Kröger, J. Sander, and A. Zimek, Density-based clustering, Wiley Interdiscip Rev: Data Mining and Knowledge Disc 1(3) (2011), 231-240.
120. R. Agrawal and R. Srikant, Fast algorithms for mining association rules, In Proceedings of the 20th International Conference on Very Large Data Bases (VLDB), Santiago de Chile, Chile, 1994, 487-499.
121. I. Färber, S. Günnemann, H.-P. Kriegel, P. Kröger, E. Müller, E. Schubert, T. Seidl, and A. Zimek, On using class-labels in evaluation of clusterings, In MultiClust: 1st International Workshop on Discovering, Summarizing and Using Multiple Clusterings Held in Conjunction with KDD 2010, Washington, DC, 2010.
122. H.-P. Kriegel, E. Schubert, and A. Zimek, Evaluation of multiple clustering solutions, In 2nd MultiClust Workshop: Discovering, Summarizing and Using Multiple Clusterings Held in Conjunction with ECML PKDD 2011, Athens, Greece, 2011, 55-66.
123. C. C. Aggarwal and P. S. Yu, An effective and efficient algorithm for high-dimensional outlier detection, VLDB J 14(2) (2005), 211-221.
124. J. Zhang, M. Lou, T. W. Ling, and H. Wang, 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), Toronto, Canada, 2004, 1265-1268.
125. H. V. Nguyen, V. Gopalkrishnan, and I. Assent, An unbiased distance-based outlier detection approach for high-dimensional data, In Proceedings of the 16th International Conference on Database Systems for Advanced Applications (DASFAA), Hong Kong, China, 2011, 138-152.
126. I. Assent, R. Krieger, E. Müller, and T. Seidl, Subspace outlier mining in large multimedia databases, In Parallel Universes and Local Patterns, 2007.
127. I. Assent, R. Krieger, E. Müller, and T. Seidl, DUSC: dimensionality unbiased subspace clustering, In Proceedings of the 7th IEEE International Conference on Data Mining (ICDM), Omaha, NE, 2007, 409-414.
128. I. Assent, R. Krieger, E. Müller, and T. Seidl, EDSC: efficient density-based subspace clustering, In Proceedings of the 17th ACM Conference on Information and Knowledge Management (CIKM), Napa Valley, CA, 2008, 1093-1102.
129. H.-P. Kriegel, P. Kröger, E. Schubert, and A. Zimek, Outlier detection in axis-parallel subspaces of high dimensional data, In Proceedings of the 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Bangkok, Thailand, 2009, 831-838.
130. E. Müller, M. Schiffer, and T. Seidl, Adaptive outlierness for subspace outlier ranking, In Proceedings of the 19th ACM Conference on Information and Knowledge Management (CIKM), Toronto, Canada, 2010, 1629-1632.
131. E. Müller, M. Schiffer, and T. Seidl, Statistical selection of relevant subspace projections for outlier ranking, In Proceedings of the 27th International Conference on Data Engineering (ICDE), Hannover, Germany, 2011, 434-445.
132. H.-P. Kriegel, P. Kröger, M. Schubert, and Z. Zhu, Efficient query processing in arbitrary subspaces using vector approximations, In Proceedings of the 18th International Conference on Scientific and Statistical Database Management (SSDBM), Vienna, Austria, 2006, 184-190.
133. W. Müller and A. Henrich, Faster exact histogram intersection on large data collections using inverted VA-files, In Proceedings of the 3rd International Conference on Image and Video Retrieval (CIVR), Dublin, Ireland, 2004, 455-463.
134. p-norm, In Proceedings of the 24th International Conference on Data Engineering (ICDE), Cancun, Mexico, 2008, 317-326.
135. T. Bernecker, T. Emrich, F. Graf, H.-P. Kriegel, P. Kröger, M. Renz, E. Schubert, and A. Zimek, Subspace similarity search using the ideas of ranking and top-k retrieval, In Proceedings of the 26th International Conference on Data Engineering (ICDE) Workshop on Ranking in Databases (DBRank), Long Beach, CA, 2010, 4-9.
136. T. Bernecker, T. Emrich, F. Graf, H.-P. Kriegel, P. Kröger, M. Renz, E. Schubert, and A. Zimek, Subspace similarity search: Efficient k-nn queries in arbitrary subspaces, In Proceedings of the 22nd International Conference on Scientific and Statistical Database Management (SSDBM), Heidelberg, Germany, 2010, 555-564.
137. T. Bernecker, F. Graf, H.-P. Kriegel, C. Moennig, and A. Zimek, BeyOND -unleashing BOND, In Proceedings of the 37th International Conference on Very Large Data Bases (VLDB) Workshop on Ranking in Databases (DBRank), Seattle, WA, 2011, 34-39.
138. H.-P. Kriegel, P. Kröger, E. Schubert, and A. Zimek, LoOP: local outlier probabilities, In Proceedings of the 18th ACM Conference on Information and Knowledge Management (CIKM), Hong Kong, China, 2009, 1649-1652.
139. V. A. Epanechnikov, Non-parametric estimation of a multivariate probability density, Theory Prob Appl 14(1) (1969), 153-158.
140. A. Zimek, Correlation clustering, PhD thesis, Ludwig-Maximilians-Universität München, Munich, Germany, 2008.
141. A. Zimek, Correlation clustering, ACM SIGKDD Explor 11(1) (2009), 53-54.
142. E. Achtert, C. Böhm, H.-P. Kriegel, P. Kröger, and A. Zimek, Deriving quantitative models for correlation clusters, In Proceedings of the 12th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Philadelphia, PA, 2006, 4-13.
143. E. Müller, M. Schiffer, P. Gerwert, M. Hannen, T. Jansen, and T. Seidl, SOREX: Subspace outlier ranking exploration toolkit, In Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD), Barcelona, Spain, 2010, 607-610.
144. E. Müller, S. Günnemann, I. Assent, and T. Seidl, Evaluating clustering in subspace projections of high dimensional data, In Proceedings of the 35th International Conference on Very Large Data Bases (VLDB), Lyon, France, 2009, 1270-1281.
145. M. Hall, E. Frank, G. Holmes, B. Pfahringer, P. Reutemann, and I. H. Witten, The WEKA data mining software: an update, ACM SIGKDD Explor 11(1) (2009), 10-18.
146. E. Achtert, H.-P. Kriegel, L. Reichert, E. Schubert, R. Wojdanowski, and A. Zimek, Visual evaluation of outlier detection models, In Proceedings of the 15th International Conference on Database Systems for Advanced Applications (DASFAA), Tsukuba, Japan, 2010, 396-399.
147. E. Achtert, A. Hettab, H.-P. Kriegel, E. Schubert, and A. Zimek, Spatial outlier detection: data, algorithms, visualizations. In Proceedings of the 12th International Symposium on Spatial and Temporal Databases (SSTD), Minneapolis, MN, 2011, 512-516.
148. K. Zhang, M. Hutter, and H. Jin, A new local distance-based outlier detection approach for scattered real-world data, In Proceedings of the 13th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Bangkok, Thailand, 2009, 813-822.
149. S. Shekhar, C.-T. Lu, and P. Zhang, A unified approach to detecting spatial outliers, GeoInformatica 7(2) (2003), 139-166.
150. S. Chawla and P. Sun, SLOM: a new measure for local spatial outliers, Knowledge Inform Syst (KAIS) 9(4) (2006), 412-429.
151. F. Chen, C.-T. Lu, and A. P. Boedihardjo, GLS-SOD: a generalized local statistical approach for spatial outlier detection, In Proceedings of the 16th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD), Washington, DC, 2010, 1069-1078.
152. E. Achtert, S. Goldhofer, H.-P. Kriegel, E. Schubert, and A. Zimek, Evaluation of clusterings -metrics and visual support, In Proceedings of the 28th International Conference on Data Engineering (ICDE), Washington, DC, 2012.
153. C. C. Aggarwal and P. S. Yu, Redefining clustering for high-dimensional applications, IEEE Trans Knowledge Data Eng 14(2) (2002), 210-225.
154. G. Moise, A. Zimek, P. Kröger, H.-P. Kriegel, and J. Sander, Subspace and projected clustering: experimental evaluation and analysis, Knowledge and Inform Syst (KAIS) 21(3) (2009), 299-326.