Abstract
Existing data collections can be large in both number of samples and in number of attributes per sample. In either case, we have found that many advanced techniques in numerical linear algebra can be used to design efficient algorithms for clustering and exploring these datasets. We illustrate this point with the method of Principal Direction Divisive Partitioning, a scalable unsupervised clustering algorithm which has been found to give high quality clusters. We show how the scalability to large sizes is achieved using those advanced linear algebra techniques. These techniques also lead to an alternate representation of the dataset which is close enough to the original for the purposes of clustering while occupying a much smaller memory footprint.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
BERRY, M.W. and DUMAIS, S.T. and O’BRIEN, G.W. (1995): Using Linear Algebra for Intelligent Information Retrieval. SIAM Review, 37, 573–595.
BOLEY, D.L. (1998): Principal Direction Divisive Partitioning. Data Mining and Knowledge Discovery, 2, 325–344.
BOLEY, D.L. and GINI, M. and GROSS, R. and HAN, E-H and HASTINGS, K. and KARYPIS, G. and KUMAR, V. and MOBASHER, B. and MOORE, J. (1999): Document Categorization and Query Generation on the World Wide Web using WebACE. AI Review, 13, 5–6, 365–391
BRADLEY, P.S. and FAYYAD, U.M. and REINA, C. (1998): Scaling Clustering Algorithms to Large Databases. In: Knowledge Discovery and Data Mining. 9–15.
CUTTING, D.R. and PEDERSEN, J.O. and KARGER, D. and TUKEY, J.W. (1992): Scatter/Gather: A Cluster-Based Approach to Browsing Large Document Collections. In: Proc. of the Fifteenth Annual International ACM SIGIR Con. on Res. and Dev. in Information Retrieval. 318–329.
DHILLON, LS. and MODHA, D.S. (2001): Concept Decomposition for Large Sparse Text Data Using Clustering. Machine Learning, 42, 1, 143–175.
GUHA, S. and RASTOGI, R. and SHIM, K. (1998): CURE: An Efficient Clustering Algorithm for Large Data Bases. In: Proc. of 1998 ACM-SIGMOD Int. Conf. on Management of Data. 73–84.
LEWIS, D. (1997): Reuters-21578.
MURPHY, P.M. and AHA, D.W. (1994): UCI Repository of Machine Learning Databases.
PENNINGTON, R.L. and HUMPHREYS, R.M. and ODEWAHN, S.C. and ZUMACH, W. and THURMES, P.M. (1993): The Automated Plate Scanner Catalog of the Palomar Sky Survey — Scanning Parameters and Procedures. P. A. S. P., 105, 521ff.
ZHANG, T. and RAMAKRISHNAN, R. and LIVNY, M. (1997): BIRCH: A New Data Clustering Algorithm and Its Applications. Data Mining and Knowledge Discovery, 1, 2 141–182.
ZHANG, Z. and ZHA, H. and SIMON, H. (2002): Low-Rank Approximation with Sparse Factors i: Basic Algorithms and Error Analysis. SIAM J. Matrix Anal., 23, 706–727.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Littau, D., Boley, D. (2003). Scalable Clustering of High Dimensional Data. In: Schader, M., Gaul, W., Vichi, M. (eds) Between Data Science and Applied Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18991-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-18991-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40354-8
Online ISBN: 978-3-642-18991-3
eBook Packages: Springer Book Archive