{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T21:14:07Z","timestamp":1776374047236,"version":"3.51.2"},"reference-count":126,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2015,7,22]],"date-time":"2015-07-22T00:00:00Z","timestamp":1437523200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000038","name":"NSERC","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001807","name":"FAPESP","doi-asserted-by":"crossref","award":["#2013\/18698-4 and #2010\/20032-6"],"award-info":[{"award-number":["#2013\/18698-4 and #2010\/20032-6"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"crossref","award":["#304137\/2013-8 and#201239\/2012-4"],"award-info":[{"award-number":["#304137\/2013-8 and#201239\/2012-4"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Knowl. Discov. Data"],"published-print":{"date-parts":[[2015,7,27]]},"abstract":"<jats:p>An integrated framework for density-based cluster analysis, outlier detection, and data visualization is introduced in this article. The main module consists of an algorithm to compute hierarchical estimates of the level sets of a density, following Hartigan\u2019s classic model of density-contour clusters and trees. Such an algorithm generalizes and improves existing density-based clustering techniques with respect to different aspects. It provides as a result a complete clustering hierarchy composed of all possible density-based clusters following the nonparametric model adopted, for an infinite range of density thresholds. The resulting hierarchy can be easily processed so as to provide multiple ways for data visualization and exploration. It can also be further postprocessed so that: (i) a normalized score of \u201coutlierness\u201d can be assigned to each data object, which unifies both the global and local perspectives of outliers into a single definition; and (ii) a \u201cflat\u201d (i.e., nonhierarchical) clustering solution composed of clusters extracted from local cuts through the cluster tree (possibly corresponding to different density thresholds) can be obtained, either in an unsupervised or in a semisupervised way. In the unsupervised scenario, the algorithm corresponding to this postprocessing module provides a global, optimal solution to the formal problem of maximizing the overall stability of the extracted clusters. If partially labeled objects or instance-level constraints are provided by the user, the algorithm can solve the problem by considering both constraints violations\/satisfactions and cluster stability criteria. An asymptotic complexity analysis, both in terms of running time and memory space, is described. Experiments are reported that involve a variety of synthetic and real datasets, including comparisons with state-of-the-art, density-based clustering and (global and local) outlier detection methods.<\/jats:p>","DOI":"10.1145\/2733381","type":"journal-article","created":{"date-parts":[[2015,7,22]],"date-time":"2015-07-22T18:49:50Z","timestamp":1437590990000},"page":"1-51","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":671,"title":["Hierarchical Density Estimates for Data Clustering, Visualization, and Outlier Detection"],"prefix":"10.1145","volume":"10","author":[{"given":"Ricardo J. G. B.","family":"Campello","sequence":"first","affiliation":[{"name":"Department of Computer Sciences, University of S\u00e3o Paulo, Brazil"}]},{"given":"Davoud","family":"Moulavi","sequence":"additional","affiliation":[{"name":"Department of Computing Science, University of Alberta, Canada"}]},{"given":"Arthur","family":"Zimek","sequence":"additional","affiliation":[{"name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Germany"}]},{"given":"J\u00f6rg","family":"Sander","sequence":"additional","affiliation":[{"name":"Department of Computing Science, University of Alberta, Canada"}]}],"member":"320","published-online":{"date-parts":[[2015,7,22]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1150402.1150459"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2463676.2463696"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/375663.375668"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/1609942.1609946"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1497577.1497581"},{"key":"e_1_2_1_6_1","volume-title":"Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD)","author":"Angiulli F.","unstructured":"F. Angiulli and C. Pizzuti . 2002. Fast outlier detection in high dimensional spaces . In Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD) . Helsinki, Finland. 15--26. DOI:http:\/\/dx.doi.org\/10.1007\/3-540-45681-3_2 F. Angiulli and C. Pizzuti. 2002. Fast outlier detection in high dimensional spaces. In Proceedings of the 6th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD). Helsinki, Finland. 15--26. DOI:http:\/\/dx.doi.org\/10.1007\/3-540-45681-3_2"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/304182.304187"},{"key":"e_1_2_1_8_1","unstructured":"K. Bache and M. Lichman. 2013. UCI Machine Learning Repository. (2013). http:\/\/archive.ics.uci.edu\/ml. K. Bache and M. Lichman. 2013. UCI Machine Learning Repository. (2013). http:\/\/archive.ics.uci.edu\/ml."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.2307\/2347159"},{"key":"e_1_2_1_10_1","unstructured":"V. Barnett and T. Lewis. 1994. Outliers in Statistical Data (3rd ed.). John Wiley & Sons. V. Barnett and T. Lewis. 1994. Outliers in Statistical Data (3rd ed.). John Wiley & Sons."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.5555\/1404506"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/956750.956758"},{"key":"e_1_2_1_13_1","first-page":"119","article-title":"Outlier..........s","volume":"25","author":"Beckman R. J.","year":"1983","unstructured":"R. J. Beckman and R. D. Cook . 1983 . Outlier..........s . Technometrics 25 , 2 (1983), 119 -- 149 . R. J. Beckman and R. D. Cook. 1983. Outlier..........s. Technometrics 25, 2 (1983), 119--149.","journal-title":"Technometrics"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015330.1015360"},{"key":"e_1_2_1_15_1","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop C. M.","unstructured":"C. M. Bishop . 2006. Pattern Recognition and Machine Learning . Springer . C. M. Bishop. 2006. Pattern Recognition and Machine Learning. Springer."},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 4th SIAM International Conference on Data Mining (SDM). Lake Buena Vista, FL. 400--412","author":"Brecheisen S.","unstructured":"S. Brecheisen , H.-P. Kriegel , P. Kr\u00f6ger , and M. Pfeifle . 2004. Visually mining through cluster hierarchies . In Proceedings of the 4th SIAM International Conference on Data Mining (SDM). Lake Buena Vista, FL. 400--412 . S. Brecheisen, H.-P. Kriegel, P. Kr\u00f6ger, and M. Pfeifle. 2004. Visually mining through cluster hierarchies. In Proceedings of the 4th SIAM International Conference on Data Mining (SDM). Lake Buena Vista, FL. 400--412."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/375663.375672"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/342009.335388"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1353343.1353398"},{"key":"e_1_2_1_20_1","volume-title":"Proceedings of the 17th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD)","author":"Campello R. J. G. B.","unstructured":"R. J. G. B. Campello , D. Moulavi , and J. Sander . 2013a. Density-based clustering based on hierarchical density estimates . In Proceedings of the 17th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD) . Gold Coast, Australia. 160--172. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-37456-2_14 R. J. G. B. Campello, D. Moulavi, and J. Sander. 2013a. Density-based clustering based on hierarchical density estimates. In Proceedings of the 17th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD). Gold Coast, Australia. 160--172. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-37456-2_14"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-013-0311-4"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.datak.2008.06.006"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s100440050011"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-2670(01)83197-4"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.2307\/3315985"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(00)00052-9"},{"key":"e_1_2_1_27_1","volume-title":"Proceedings of the 30th International Conference on Data Engineering (ICDE)","author":"Dang X. H.","year":"2014","unstructured":"X. H. Dang , I. Assent , R. T. Ng , A. Zimek , and E. Schubert . 2014. Discriminative features for identifying and interpreting outliers . In Proceedings of the 30th International Conference on Data Engineering (ICDE) , Chicago, IL. 88--99. DOI:http:\/\/dx.doi.org\/10.1109\/ICDE. 2014 .6816642 X. H. Dang, I. Assent, R. T. Ng, A. Zimek, and E. Schubert. 2014. Discriminative features for identifying and interpreting outliers. In Proceedings of the 30th International Conference on Data Engineering (ICDE), Chicago, IL. 88--99. DOI:http:\/\/dx.doi.org\/10.1109\/ICDE.2014.6816642"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7439(01)00111-3"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.5555\/3120676.3120693"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2010.151"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10115-011-0430-4"},{"key":"e_1_2_1_33_1","volume-title":"Workshop on Clustering High Dimensional Data and its Applications at 2nd SIAM International Conference on Data Mining. 105--115","author":"Ert\u00f6z L.","unstructured":"L. Ert\u00f6z , M. Steinbach , and V. Kumar . 2002. A new shared nearest neighbor clustering algorithm and its applications . In Workshop on Clustering High Dimensional Data and its Applications at 2nd SIAM International Conference on Data Mining. 105--115 . L. Ert\u00f6z, M. Steinbach, and V. Kumar. 2002. A new shared nearest neighbor clustering algorithm and its applications. In Workshop on Clustering High Dimensional Data and its Applications at 2nd SIAM International Conference on Data Mining. 105--115."},{"key":"e_1_2_1_34_1","volume-title":"Proceedings of the 3rd SIAM International Conference on Data Mining (SDM)","author":"Ert\u00f6z L.","unstructured":"L. Ert\u00f6z , M. Steinbach , and V. Kumar . 2003. Finding clusters of different sizes, shapes, and densities in noisy, high dimensional data . In Proceedings of the 3rd SIAM International Conference on Data Mining (SDM) , San Francisco, CA. L. Ert\u00f6z, M. Steinbach, and V. Kumar. 2003. Finding clusters of different sizes, shapes, and densities in noisy, high dimensional data. In Proceedings of the 3rd SIAM International Conference on Data Mining (SDM), San Francisco, CA."},{"key":"e_1_2_1_35_1","volume-title":"Encyclopedia of Database Systems, L. Liu and M. T. \u00d6zsu (Eds.)","author":"Ester M.","unstructured":"M. Ester . 2009. Density-based Clustering . In Encyclopedia of Database Systems, L. Liu and M. T. \u00d6zsu (Eds.) . Springer , 795--799. DOI:http:\/\/dx.doi.org\/10.1007\/978-0-387-39940-9_605 M. Ester. 2009. Density-based Clustering. In Encyclopedia of Database Systems, L. Liu and M. T. \u00d6zsu (Eds.). Springer, 795--799. DOI:http:\/\/dx.doi.org\/10.1007\/978-0-387-39940-9_605"},{"key":"e_1_2_1_36_1","volume-title":"Proceedings of the 2nd ACM International Conference on Knowledge Discovery and Data Mining (KDD)","author":"Ester M.","unstructured":"M. Ester , H.-P. Kriegel , J. Sander , and X. Xu . 1996. A density-based algorithm for discovering clusters in large spatial databases with noise . In Proceedings of the 2nd ACM International Conference on Knowledge Discovery and Data Mining (KDD) . Portland, OR. 226--231. M. Ester, H.-P. Kriegel, J. Sander, and X. Xu. 1996. A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the 2nd ACM International Conference on Knowledge Discovery and Data Mining (KDD). Portland, OR. 226--231."},{"key":"e_1_2_1_37_1","doi-asserted-by":"crossref","unstructured":"B. S. Everitt S. Landau and M. Leese. 2001. Cluster Analysis (4th ed.). Arnold. B. S. Everitt S. Landau and M. Leese. 2001. Cluster Analysis (4th ed.). Arnold.","DOI":"10.1002\/9781118887486.ch6"},{"key":"e_1_2_1_38_1","volume-title":"Proceedings of the 2nd IEEE International Conference on Data Mining (ICDM), Maebashi City. Japan. 179--186","author":"Foss A.","unstructured":"A. Foss and O. R. Za\u00efane . 2002. A parameterless method for efficiently discovering clusters of arbitrary shape in large datasets . In Proceedings of the 2nd IEEE International Conference on Data Mining (ICDM), Maebashi City. Japan. 179--186 . A. Foss and O. R. Za\u00efane. 2002. A parameterless method for efficiently discovering clusters of arbitrary shape in large datasets. In Proceedings of the 2nd IEEE International Conference on Data Mining (ICDM), Maebashi City. Japan. 179--186."},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.113"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1975.1055330"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2006.43"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000042993.50813.60"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729885"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDMW.2006.92"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2008.32"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1002\/wics.6"},{"key":"e_1_2_1_47_1","volume-title":"6th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)","volume":"5","author":"Hang S.","unstructured":"S. Hang , Z. You , and L. Y. Chun . 2009. Incorporating biological knowledge into density-based clustering analysis of gene expression data . In 6th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD) , Vol. 5 . Tianjin, China, 52--56. S. Hang, Z. You, and L. Y. Chun. 2009. Incorporating biological knowledge into density-based clustering analysis of gene expression data. In 6th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), Vol. 5. Tianjin, China, 52--56."},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.1148\/radiology.143.1.7063747"},{"key":"e_1_2_1_49_1","volume-title":"Clustering Algorithms","author":"Hartigan J. A.","unstructured":"J. A. Hartigan . 1975. Clustering Algorithms . John Wiley & Sons , New York , London, Sydney, Toronto. J. A. Hartigan. 1975. Clustering Algorithms. John Wiley & Sons, New York, London, Sydney, Toronto."},{"key":"e_1_2_1_50_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1987.10478428"},{"key":"e_1_2_1_51_1","volume-title":"Identification of Outliers","author":"Hawkins D.","unstructured":"D. Hawkins . 1980. Identification of Outliers . Chapman and Hall . D. Hawkins. 1980. Identification of Outliers. Chapman and Hall."},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(01)00103-9"},{"key":"e_1_2_1_53_1","volume-title":"Proceedings of the 7th International Symposium on Intelligent Data Analysis (IDA)","author":"Hinneburg A.","unstructured":"A. Hinneburg and H. H. Gabriel . 2007. Denclue 2.0: Fast clustering based on kernel density estimation . In Proceedings of the 7th International Symposium on Intelligent Data Analysis (IDA) . Ljubljana, Slovenia. 70--80. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-540-74825-0_7 A. Hinneburg and H. H. Gabriel. 2007. Denclue 2.0: Fast clustering based on kernel density estimation. In Proceedings of the 7th International Symposium on Intelligent Data Analysis (IDA). Ljubljana, Slovenia. 70--80. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-540-74825-0_7"},{"key":"e_1_2_1_54_1","volume-title":"Proceedings of the 4th ACM International Conference on Knowledge Discovery and Data Mining (KDD)","author":"Hinneburg A.","unstructured":"A. Hinneburg and D. A. Keim . 1998. An efficient approach to clustering in large multimedia databases with noise . In Proceedings of the 4th ACM International Conference on Knowledge Discovery and Data Mining (KDD) . New York City, NY. 58--65. A. Hinneburg and D. A. Keim. 1998. An efficient approach to clustering in large multimedia databases with noise. In Proceedings of the 4th ACM International Conference on Knowledge Discovery and Data Mining (KDD). New York City, NY. 58--65."},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10115-003-0086-9"},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:AIRE.0000045502.10941.a9"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2012.05.011"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01908075"},{"key":"e_1_2_1_59_1","doi-asserted-by":"publisher","DOI":"10.1109\/78.324744"},{"key":"e_1_2_1_60_1","unstructured":"A. K. Jain and R. C. Dubes. 1988. Algorithms for Clustering Data. Prentice Hall Englewood Cliffs. A. K. Jain and R. C. Dubes. 1988. Algorithms for Clustering Data. Prentice Hall Englewood Cliffs."},{"key":"e_1_2_1_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/502512.502554"},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.1007\/11731139_68"},{"key":"e_1_2_1_63_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289588"},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDE.2012.88"},{"key":"e_1_2_1_65_1","volume-title":"Proceedings of the conference of the Centre for Advanced Studies on Collaborative research (CASCON)","author":"Knorr E. M.","year":"2010","unstructured":"E. M. Knorr and R. T. Ng . 1997a. A unified approach for mining outliers . In Proceedings of the conference of the Centre for Advanced Studies on Collaborative research (CASCON) . Toronto, ON, Canada. 11--23. DOI:http:\/\/dx.doi.org\/10.1145\/78 2010 .782021 E. M. Knorr and R. T. Ng. 1997a. A unified approach for mining outliers. In Proceedings of the conference of the Centre for Advanced Studies on Collaborative research (CASCON). Toronto, ON, Canada. 11--23. DOI:http:\/\/dx.doi.org\/10.1145\/782010.782021"},{"key":"e_1_2_1_66_1","volume-title":"Proceedings of the 3rd ACM International Conference on Knowledge Discovery and Data Mining (KDD)","author":"Knorr E. M.","year":"2010","unstructured":"E. M. Knorr and R. T. Ng . 1997b. A unified notion of outliers: Properties and computation . In Proceedings of the 3rd ACM International Conference on Knowledge Discovery and Data Mining (KDD) . Newport Beach, CA. 219--222. DOI:http:\/\/dx.doi.org\/10.1145\/78 2010 .782021 E. M. Knorr and R. T. Ng. 1997b. A unified notion of outliers: Properties and computation. In Proceedings of the 3rd ACM International Conference on Knowledge Discovery and Data Mining (KDD). Newport Beach, CA. 219--222. DOI:http:\/\/dx.doi.org\/10.1145\/782010.782021"},{"key":"e_1_2_1_67_1","volume-title":"Proceedings of the 24th International Conference on Very Large Data Bases (VLDB)","author":"Knorr E. M.","unstructured":"E. M. Knorr and R. T. Ng . 1998. Algorithms for mining distance-based outliers in large datasets . In Proceedings of the 24th International Conference on Very Large Data Bases (VLDB) . New York City, NY. 392--403. E. M. Knorr and R. T. Ng. 1998. Algorithms for mining distance-based outliers in large datasets. In Proceedings of the 24th International Conference on Very Large Data Bases (VLDB). New York City, NY. 392--403."},{"key":"e_1_2_1_68_1","doi-asserted-by":"publisher","DOI":"10.1007\/s007780050006"},{"key":"e_1_2_1_69_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2003.1232271"},{"key":"e_1_2_1_70_1","doi-asserted-by":"publisher","DOI":"10.1002\/widm.30"},{"key":"e_1_2_1_71_1","doi-asserted-by":"publisher","DOI":"10.1145\/1645953.1646195"},{"key":"e_1_2_1_72_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01307-2_86"},{"key":"e_1_2_1_73_1","volume-title":"Proceedings of the 11th SIAM International Conference on Data Mining (SDM) Mesa, AZ. 13--24","author":"Kriegel H.-P.","unstructured":"H.-P. Kriegel , P. Kr\u00f6ger , E. Schubert , and A. Zimek . 2011a. Interpreting and unifying outlier scores . In Proceedings of the 11th SIAM International Conference on Data Mining (SDM) Mesa, AZ. 13--24 . H.-P. Kriegel, P. Kr\u00f6ger, E. Schubert, and A. Zimek. 2011a. Interpreting and unifying outlier scores. In Proceedings of the 11th SIAM International Conference on Data Mining (SDM) Mesa, AZ. 13--24."},{"key":"e_1_2_1_74_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2012.21"},{"key":"e_1_2_1_75_1","unstructured":"H.-P. Kriegel P. Kr\u00f6ger and A. Zimek. 2010. Outlier Detection Techniques. Tutorial at the 16th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD). Washington DC. (2010). H.-P. Kriegel P. Kr\u00f6ger and A. Zimek. 2010. Outlier Detection Techniques. Tutorial at the 16th ACM International Conference on Knowledge Discovery and Data Mining (SIGKDD). Washington DC. (2010)."},{"key":"e_1_2_1_76_1","doi-asserted-by":"publisher","DOI":"10.1145\/1401890.1401946"},{"key":"e_1_2_1_77_1","doi-asserted-by":"publisher","DOI":"10.1145\/312129.312186"},{"key":"e_1_2_1_78_1","doi-asserted-by":"publisher","DOI":"10.1145\/1081870.1081891"},{"key":"e_1_2_1_79_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2009.143"},{"key":"e_1_2_1_80_1","doi-asserted-by":"publisher","DOI":"10.1145\/2133360.2133363"},{"key":"e_1_2_1_81_1","volume-title":"International Conference on Service Systems and Service Management (ICSSSM)","author":"Liu P.","unstructured":"P. Liu , D. Zhou , and N. Wu . 2007. VDBSCAN: Varied density based spatial clustering of applications with noise . In International Conference on Service Systems and Service Management (ICSSSM) . Chengdu, China. 1--4. P. Liu, D. Zhou, and N. Wu. 2007. VDBSCAN: Varied density based spatial clustering of applications with noise. In International Conference on Service Systems and Service Management (ICSSSM). Chengdu, China. 1--4."},{"key":"e_1_2_1_82_1","volume-title":"Proceedings of the 13th IEEE International Conference on Data Mining (ICDM)","author":"Micenkov\u00e1 B.","unstructured":"B. Micenkov\u00e1 , R. T. Ng , X. H. Dang , and I. Assent . 2013. Explaining outliers by subspace separability . In Proceedings of the 13th IEEE International Conference on Data Mining (ICDM) . Dallas, TX. 518--527. B. Micenkov\u00e1, R. T. Ng, X. H. Dang, and I. Assent. 2013. Explaining outliers by subspace separability. In Proceedings of the 13th IEEE International Conference on Data Mining (ICDM). Dallas, TX. 518--527."},{"key":"e_1_2_1_83_1","first-page":"738","article-title":"Excess mass estimates and tests for multimodality","volume":"86","author":"Muller D. W.","year":"1991","unstructured":"D. W. Muller and G. Sawitzki . 1991 . Excess mass estimates and tests for multimodality . J. Amer. Statist. Assoc. 86 , 415 (1991), 738 -- 746 . D. W. Muller and G. Sawitzki. 1991. Excess mass estimates and tests for multimodality. J. Amer. Statist. Assoc. 86, 415 (1991), 738--746.","journal-title":"J. Amer. Statist. Assoc."},{"key":"e_1_2_1_84_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2012.112"},{"key":"e_1_2_1_85_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDEW.2008.4498387"},{"key":"e_1_2_1_86_1","doi-asserted-by":"publisher","DOI":"10.1145\/1871437.1871690"},{"key":"e_1_2_1_87_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDE.2011.5767916"},{"key":"e_1_2_1_88_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2010.06.010"},{"key":"e_1_2_1_89_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12026-8_29"},{"key":"e_1_2_1_90_1","doi-asserted-by":"publisher","DOI":"10.5555\/3121646.3121658"},{"key":"e_1_2_1_91_1","volume-title":"Proceedings of the 16th International Conference on Database Systems for Advanced Applications (DASFAA)","author":"Nguyen H. V.","year":"2014","unstructured":"H. V. Nguyen , V. Gopalkrishnan , and I. Assent . 2011. 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. 138--152. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642- 2014 9-3_12 H. V. Nguyen, V. Gopalkrishnan, and I. Assent. 2011. 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. 138--152. DOI:http:\/\/dx.doi.org\/10.1007\/978-3-642-20149-3_12"},{"key":"e_1_2_1_92_1","doi-asserted-by":"publisher","DOI":"10.14778\/1920841.1921021"},{"key":"e_1_2_1_93_1","volume-title":"Proceedings of the 19th International Conference on Data Engineering (ICDE)","author":"Papadimitriou S.","year":"2003","unstructured":"S. Papadimitriou , H. Kitagawa , P. B. Gibbons , and C. Faloutsos . 2003. LOCI: Fast outlier detection using the local correlation integral . In Proceedings of the 19th International Conference on Data Engineering (ICDE) . Bangalore, India. 315--326. DOI:http:\/\/dx.doi.org\/10.1109\/ICDE. 2003 .1260802 S. Papadimitriou, H. Kitagawa, P. B. Gibbons, and C. Faloutsos. 2003. LOCI: Fast outlier detection using the local correlation integral. In Proceedings of the 19th International Conference on Data Engineering (ICDE). Bangalore, India. 315--326. DOI:http:\/\/dx.doi.org\/10.1109\/ICDE.2003.1260802"},{"key":"e_1_2_1_94_1","doi-asserted-by":"publisher","DOI":"10.1007\/11875581_81"},{"key":"e_1_2_1_95_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/28.3-4.308"},{"key":"e_1_2_1_96_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-008-0120-3"},{"key":"e_1_2_1_97_1","doi-asserted-by":"publisher","DOI":"10.1080\/13658810500399654"},{"key":"e_1_2_1_98_1","doi-asserted-by":"publisher","DOI":"10.1145\/2339530.2339669"},{"key":"e_1_2_1_99_1","doi-asserted-by":"publisher","DOI":"10.1145\/342009.335437"},{"key":"e_1_2_1_100_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72530-5_25"},{"key":"e_1_2_1_101_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-009-0157-y"},{"key":"e_1_2_1_102_1","volume-title":"Encyclopedia of Machine Learning","author":"Sander J.","unstructured":"J. Sander . 2010. Density-based clustering . In Encyclopedia of Machine Learning , C. Sammut and G. I. Webb (Eds.). Springer , US , 270--273. J. Sander. 2010. Density-based clustering. In Encyclopedia of Machine Learning, C. Sammut and G. I. Webb (Eds.). Springer, US, 270--273."},{"key":"e_1_2_1_103_1","volume-title":"Proceedings of the 7th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD)","author":"Sander J.","unstructured":"J. Sander , X. Qin , Z. Lu , N. Niu , and A. Kovarsky . 2003. Automatic extraction of clusters from hierarchical clustering representations . In Proceedings of the 7th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD) . Seoul, Korea. 75--87. DOI:http:\/\/dx.doi.org\/10.1007\/3-540-36175-8_8 J. Sander, X. Qin, Z. Lu, N. Niu, and A. Kovarsky. 2003. Automatic extraction of clusters from hierarchical clustering representations. In Proceedings of the 7th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD). Seoul, Korea. 75--87. DOI:http:\/\/dx.doi.org\/10.1007\/3-540-36175-8_8"},{"key":"e_1_2_1_104_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611972825.90"},{"key":"e_1_2_1_105_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611973440.63"},{"key":"e_1_2_1_106_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-012-0300-z"},{"key":"e_1_2_1_107_1","volume-title":"Density Estimation for Statistics and Data Analysis","author":"Silverman B. W.","unstructured":"B. W. Silverman . 1986. Density Estimation for Statistics and Data Analysis . Chapman & Hall\/CRC. B. W. Silverman. 1986. Density Estimation for Statistics and Data Analysis. Chapman & Hall\/CRC."},{"key":"e_1_2_1_108_1","doi-asserted-by":"publisher","DOI":"10.1099\/00221287-17-1-184"},{"key":"e_1_2_1_109_1","volume-title":"ASP-ACSM Convention. 393--406","author":"Soler T.","unstructured":"T. Soler and M. Chin . 1985. On transformation of covariance matrices between local Cartesian coordinate systems and commutative diagrams . In ASP-ACSM Convention. 393--406 . T. Soler and M. Chin. 1985. On transformation of covariance matrices between local Cartesian coordinate systems and commutative diagrams. In ASP-ACSM Convention. 393--406."},{"key":"e_1_2_1_110_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00357-003-0004-6"},{"key":"e_1_2_1_111_1","doi-asserted-by":"publisher","DOI":"10.1198\/jcgs.2009.07049"},{"key":"e_1_2_1_112_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICDM.2010.69"},{"key":"e_1_2_1_113_1","unstructured":"P.-N. Tan M. Steinbach and V. Kumar. 2006. Introduction to Data Mining. Addison Wesley. P.-N. Tan M. Steinbach and V. Kumar. 2006. Introduction to Data Mining. Addison Wesley."},{"key":"e_1_2_1_114_1","volume-title":"Proceedings of the 6th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD)","author":"Tang J.","unstructured":"J. Tang , Z. Chen , A. W.-C. Fu , and D. W. Cheung . 2002. 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. 535--548. DOI:http:\/\/dx.doi.org\/10.1007\/3-540-47887-6_53 J. Tang, Z. Chen, A. W.-C. Fu, and D. W. Cheung. 2002. 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. 535--548. DOI:http:\/\/dx.doi.org\/10.1007\/3-540-47887-6_53"},{"key":"e_1_2_1_116_1","unstructured":"D. Wishart. 1969. Mode analysis: A generalization of nearest neighbor which reduces chaining effects. In Numerical Taxonomy A. J. Cole (Ed.). 282--311. D. Wishart. 1969. Mode analysis: A generalization of nearest neighbor which reduces chaining effects. In Numerical Taxonomy A. J. Cole (Ed.). 282--311."},{"key":"e_1_2_1_117_1","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1111\/j.2517-6161.1983.tb01262.x","article-title":"A kth nearest neighbour clustering procedure","volume":"45","author":"Wong M. A.","year":"1983","unstructured":"M. A. Wong and T. Lane . 1983 . A kth nearest neighbour clustering procedure . Journal of the Royal Statistical Society: Series B (Statistical Methodology) 45 , 3 (1983), 362 -- 368 . M. A. Wong and T. Lane. 1983. A kth nearest neighbour clustering procedure. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 45, 3 (1983), 362--368.","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"e_1_2_1_118_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2005.845141"},{"key":"e_1_2_1_119_1","doi-asserted-by":"crossref","unstructured":"R. Xu and D. Wunsch II. 2009. Clustering. IEEE Press. R. Xu and D. Wunsch II. 2009. Clustering. IEEE Press.","DOI":"10.1002\/9780470382776"},{"key":"e_1_2_1_120_1","doi-asserted-by":"publisher","DOI":"10.1145\/1401890.1401983"},{"key":"e_1_2_1_121_1","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/17.10.977"},{"key":"e_1_2_1_122_1","doi-asserted-by":"publisher","DOI":"10.1186\/gb-2003-4-5-r34"},{"key":"e_1_2_1_123_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01307-2_84"},{"key":"e_1_2_1_124_1","doi-asserted-by":"publisher","DOI":"10.1145\/233269.233324"},{"key":"e_1_2_1_125_1","doi-asserted-by":"publisher","DOI":"10.1145\/2594473.2594476"},{"key":"e_1_2_1_126_1","doi-asserted-by":"publisher","DOI":"10.1145\/2618243.2618257"},{"key":"e_1_2_1_127_1","doi-asserted-by":"publisher","DOI":"10.1145\/2487575.2487676"},{"key":"e_1_2_1_128_1","doi-asserted-by":"publisher","DOI":"10.1002\/sam.11161"}],"container-title":["ACM Transactions on Knowledge Discovery from Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2733381","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2733381","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:17:02Z","timestamp":1750227422000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2733381"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,22]]},"references-count":126,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,7,27]]}},"alternative-id":["10.1145\/2733381"],"URL":"https:\/\/doi.org\/10.1145\/2733381","relation":{},"ISSN":["1556-4681","1556-472X"],"issn-type":[{"value":"1556-4681","type":"print"},{"value":"1556-472X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,22]]},"assertion":[{"value":"2013-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-07-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}