Recently the concept decomposition based on document clustering strate gies has drawn researchers' attention. These decompositions are obtained by taking the least-squares approximation onto the linear subspace spanned by all the con cept vectors. In this chapter, a new class of numerical matrix computation methods has been developed in computing the approximate decomposition matrix in concept decomposition technique. These methods utilize the knowledge of matrix sparsity pattern techniques in preconditioning field. An important advantage of these ap proaches is that they are computationally more efficient, fast in computing the rank ing vector and require much less memory than the least—squares based approach while maintaining retrieval accuracy.
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References
I. S. Dhillon and D. S. Modha. Concept decompositions for large sparse text data using clustering. Mach. Learn., 42(1):143–175, 2001
G. H. Golub and C. F. van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, MD, 3rd edition, 1996
J. Gao and J. Zhang. Clustered SVD strategies in latent semantic indexing. Inform. Process. Manage., 41(5):1051–1063, 2005
E. Chow. A priori sparsity patterns for parallel sparse approximate inverse preconditioners. SIAM J. Sci. Comput., 21(5):1804–1822, 2000
M. Grote and T. Huckle. Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput., 18:838–853, 1997
J. Hartigan. Clustering Algorithms. Wiley, New York, 1975
J. Hartigan and M. Wong. Algorithm AS136: A k—means clustering algorithm. Appl. Stat., 28:100–108, 1979
A. K. Jain, M. N. Murty, and P. J. Flynn. Data clustering: a review. ACM Comput. Surv., 31(3):264–323, 1999
E. Chow and Y. Saad. Approximate inverse preconditioners via sparse—sparse iterations. SIAM J. Sci. Comput., 19(3):995–1023, 1998
J. D. F. Cosgrove, J. C. Diaz, and A. Griewank. Approximate inverse preconditionings for sparse linear systems. Int. J. Comput. Math., 44:91–110, 1992
L. Y. Kolotilina. Explicit preconditioning of systems of linear algebraic equations with dense matrices. J. Soviet Math., 43:2566–2573, 1988
K. Wang, J. Zhang, and C. Shen. A class of parallel multilevel sparse approximate inverse preconditioners for sparse linear systems. J. Scalable Comput. Pract. Exper., 7:93–106, 2006
K. Wang and J. Zhang. MSP: a class of parallel multistep successive sparse approximate inverse preconditioning strategies. SIAM J. Sci. Comput., 24(4):1141–1156, 2003
S. T. Barnard, L. M. Bernardo, and H. D. Simon. An MPI implementation of the SPAI pre-conditioner on the T3E. Int. J. High Perform Comput. Appl., 13:107–128, 1999
J. Gao and J. Zhang. Text retrieval using sparsified concept decomposition matrix. Technical Report No. 412-04, Department of Computer Science, University of Kentucky, KY, 2004
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Shen, C., Williams, D. (2009). Sparse Matrix Computational Techniques in Concept Decomposition Matrix Approximation. In: Ao, SI., Rieger, B., Chen, SS. (eds) Advances in Computational Algorithms and Data Analysis. Lecture Notes in Electrical Engineering, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8919-0_10
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