Abstract
The essence of uncertain data management has been well adopted since data uncertainty widely exists in lots of applications, such as Web, sensor networks, etc. Most of the uncertain data models are based on the possible world semantics. Because the number of the possible worlds will blowup exponentially with the growth of the data set, it is much more challenging to handle uncertain data than deterministic data. In this paper, we take the first attempt to study the rarity, an important statistic that describes the proportion of items with the same frequency, upon uncertain data. We have proposed three novel solutions, including an exact method and an approximate method to compute the rarity of a given frequency respectively, and a method to find the frequency of the maximum rarity. Analysis in theorem and extensive experimental results demonstrate the effectiveness and efficiency of the proposed solutions.
Similar content being viewed by others
References
Aggarwal C C. Managing and Mining Uncertain Data. Berlin/Heidelberg: Springer-Verlag, 2009. 1–494
Antova L, Koch C, Olteanu D. From complete to incomplete information and back. In: Chan C Y, Ooi B C, Zhou A, eds. Proceedings of ACM SIGMOD 2007. New York: ACM Press, 2007. 713–724
Dalvi N, Suciu D. Efficient query evaluation on probabilistic databases. Int J Very Large Data Base, 2007, 16: 523–544
Agrawal P, Benjelloun O, Sarma A D, et al. Trio: a system for data, uncertainty, and lineage. In: Dayal U, Whang K Y, Lomet D, et al., eds. Proceedings of VLDB 2006. VLDB Endowment, 2006. 1151–1154
Zhang Q, Li F, Yi K. Finding frequent items in probabilistic data. In: Wang J T, ed. Proceedings of ACM SIGMOD 2008. New York: ACM Press, 2008. 819–832
Bernecker T, Kriegel H P, Renz M, et al. Probabilistic frequent itemset mining in uncertain databases. In: Elder J F IV, Fogelman-Soulié F, Flach P A, et al., eds. Proceedings of ACM SIGKDD 2009. New York: ACM Press, 2009. 119–128
Jayram T, Kale S, Vee E. Efficient aggregation algorithms for probabilistic data. In: Bansal N, Pruhs K, Stein C, eds. Proceedings of SODA 2007. Philadelphia: SIAM, 2007. 346–355
Aggarwal C C, Yu P S. A framework for clustering uncertain data streams. In: Alonso G, Blakely J A, Chen A, eds. Proceedings of IEEE ICDE 2008. Piscataway: IEEE Press, 2008. 150–159
Datar M, Muthukrishnan S. Estimating rarity and similarity over data stream windows. In: Möhring R H, Raman R, eds. Proceedings of ESA 2002. Berlin/Heidelberg: Springer-Verlag, 2002. 323–334
Broder A. Identifying and filtering near-duplicate documents. In: Giancarlo R, Sankoff D, eds. Proceedings of CPM 2000. Berlin/Heidelberg: Springer-Verlag, 2000. 1–10
Cohen E. Size-estimation framework with applications to transitive closure and reachability. J Comput Syst Sci, 1997, 55: 441–453
Motwani R, Raghavan P. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 67–73
Chandola V, Banerjee A, Kumar V. Anomaly detection: a survey. ACM Comput Surv, 2009, 41: 15
Dong X, Halevy A Y, Yu C. Data integration with uncertainty. In: Koch C, Gehrke J, Garofalakis M N, et al., eds. Proceedings of VLDB 2007. VLDB Endowment, 2007. 687–698
Tao Y, Cheng R, Xiao X, et al. Indexing multi-dimensional uncertain data with arbitrary probability density functions. In: Bohm K, Jensen C S, Haas L M, et al., eds. Proceedings of VLDB 2005. VLDB Endowment, 2005. 922–933
Zhang M, Chen S, Jensen C S, et al. Effectively indexing uncertain moving objects for predictive queries. P VLDB Endowment, 2009, 2: 1198–1209
Benjelloun O, Sarma A D, Halevy A Y, et al. Uldbs: databases with uncertainty and lineage. In: Dayal U, Whang K Y, Lomet D B, et al., eds. Proceedings of VLDB 2006. VLDB Endowment, 2006. 953–964
Burdick D, Deshpande D M, Jayram T, et al. OLAP over uncertain and imprecise data. In: Bohm K, Jensen C S, Haas L M, et al., eds. Proceedings of VLDB 2005. VLDB Endowment, 2005. 970–981
Zhang Y, Lin X, Zhu G, et al. Efficient rank based knn query processing over uncertain data. In: Li F, Moro M M, Ghandeharizadeh S, et al., eds. Proceedings of IEEE ICDE 2010. Piscataway: IEEE Press, 2010. 28–39
Jin C, Yi K, Chen L, et al. Sliding-window top-k queries on uncertain streams. P VLDB Endowment, 2008, 1: 301–312
Cormode G, McGregor A. Approximation algorithms for clustering uncertain data. In: Lenzerini M, Lembo D, eds. Proceedings of ACM PODS 2008. New York: ACM Press, 2008. 191–200
Potamias M, Bonchi F, Gionis A, et al. k-nearest neighbors in uncertain graphs. P VLDB Endowment, 2010, 3: 997–1008
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jin, C., Zhou, M. & Zhou, A. Computing rarity on uncertain data. Sci. China Inf. Sci. 54, 2028–2039 (2011). https://doi.org/10.1007/s11432-011-4378-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-011-4378-5