Abstract
A data cube is a popular organization for summary data. A cube is simply a multidimensional structure that contains in each cell an aggregate value, i.e., the result of applying an aggregate function to an underlying relation. In practical situations, cubes can require a large amount of storage, so, compressing them is of practical importance. In this paper, we propose an approximation technique that reduces the storage cost of the cube at the price of getting approximate answers for the queries posed against the cube. The idea is to characterize regions of the cube by using statistical models whose description take less space than the data itself. Then, the model parameters can be used to estimate the cube cells with a certain level of accuracy. To increase the accuracy, and to guarantee the level of error in the query answers, some of the “outliers” (i.e., cells that incur in the largest errors when estimated), are retained. The storage taken by the model parameters and the retained cells, of course, should take a fraction of the space of the full cube and the estimation procedure should be faster than computing the data from the underlying relations. We use loglinear models to model the cube regions. Experiments show that the errors introduced in typical queries are small even when the description is substantially smaller than the full cube. The models also offer information about the underlying structure of the data modeled by them. Moreover, these models are relatively easy to update dynamically as data is added to the warehouse.
This work has been supported by NSF grant IIS-9732113
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Acharya, P. B. Gibbons, V. Poosala, and S. Ramaswamy. Join Synopses for Approximate Query Answering. In Proceedings of the 1999 ACM-SIGMOD International Conference on Management of Data, Philadelphia, PA, June 1999.
S. Agarwal, R. Agrawal, P. M. Deshpande, A. Gupta, J. F. Naughton, R. Ramakrishnan, and S. Sarawagi. On the Computation of Multidimensional Aggregates. In Proceedings of the 22nd International Conference on Very Large Data Bases, Bombay, India, pages 506–521, September 1996.
R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan. Automatic Subspace Clustering of High Dimensional Data for Data Mining Applications. In Proceedings of the ACM SIGMOD International Conference on Management of Data, Seattle, June 1998.
A. Agresti. An Introduction to Categorical Data Analysis. John Wiley, New York, 1996.
E. B. Andersen. Introduction to the Statistical Analysis of Categorical Data. Springer Verlag, New York, 1997.
D. Barbará, W. DuMouchel, C. Faloutsos, P. J. Haas, J. M. Hellerstein, Y. Ioannidis, H. V. Jagadish, T. Johnson, R. Ng, V. Poosala, K. A. Ross, and K. G. Sevcik. The New Jersey Data Reduction Report. Bulletin of the Technial Committee on Data Engineering, 20(4):3–45, December 1997.
D. Barbará and M. Sullivan. Quasi-Cubes: A space-efficient way to support approximate multidimensional databases. Technical Report, Department of Information and Software Systems Engineering, George Mason University, 1997.
D. Barbará and M. Sullivan. Quasi-cubes: Exploiting approximations in multidimensional databases. SIGMOD Record, 26(3), September 1997.
D. Barbará and X. Wu. Using loglinear models to compress datacubes. Technical Report, Department of Information and Software Systems Engineering, George Mason University, 1999.
U. S. Census Bureau. Population data. http://www.census.gov/main/www/access.html.
B. Fingleton. Models of Category Counts. Cambridge University Press, 1984.
J. Gray, A. Bosworth, A. Layman, and H. Pirahesh. Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals. In Proceedings of the International Conference on Data Engineering, New Orleans, 1996.
V. Harinarayan, A. Rajaraman, and J. D. Ullman. Implementing Data Cubes Efficiently. In Proceedings of the ACM-SIGMOD Conference, Montreal, Canada, 1996.
A. K. Jain and R. C. Dubes. Algorithms for Clustering Data. Prentice Hall, 1988.
MicroStrategy. DSS Server[tm] Features. http://www.microstrategy.com/products/ server/features.htm.
K. A. Ross and D. Srivastava. Fast Computation of Sparse Datacubes. In Proceedings of the 23rd VLDB Conference, Athens, Greece, 1997.
S. Sarawagi, R. Agrawal, and N. Meggido. Discovery-driven Exploration of OLAP Data Cubes. In Proceedings of the International Conference on Extending Data Base Technology, pages 168–182, 1998.
J. Shanmugasundaram, U. Fayyad, and P. S. Bradley. Compressed Data Cubes for OLAP Aggregate Query Approximation on Continuous Dimensions. In Proceedings of the ACM-SIGKDD International Conference on Knowledge Discovery and Data Mining, San Diego, CA, August 1999.
B. W. Silverman. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, UK, 1994.
J. S. Vitter and M. Wang. Approximate Computation of Multidimensional Aggregates of Sparse Data Using Wavelets. In Proceedings of the 1999 ACM-SIGMOD International Conference on Management of Data, Philadelphia, PA, June 1999.
Y. Zhao, P. M. Deshpande, and J. F. Naughton. An Array-Based Algorithm for Simultaneous Multidimensional Aggregates. In Proceedings of the ACM-SIGMOD International Conference on Management of Data, Tucson, Arizona, pages 159–170, May 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barbará, D., Wu, X. (2000). Using Loglinear Models to Compress Datacubes. In: Lu, H., Zhou, A. (eds) Web-Age Information Management. WAIM 2000. Lecture Notes in Computer Science, vol 1846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45151-X_30
Download citation
DOI: https://doi.org/10.1007/3-540-45151-X_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67627-0
Online ISBN: 978-3-540-45151-8
eBook Packages: Springer Book Archive