Abstract
A novel algorithm for finding algebraic base of singular subspace for signal information system is presented. It is based on Best Rank One Matrix (BROM) approximation for matrix representation of information system and on its subsequent matrix residua. From algebraic point of view BROM is a kind of power method for singular value problem. By attribute centering it can be used to determine principal subspace of signal information system and for this goal it is more accurate and faster than Oja’s neural algorithm for PCA while preserving its adaptivity to signal change in time and space. The concept is illustrated by an exemplary application from image processing area: adaptive computing of image energy singular trajectory which could be used for image replicas detection.
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References
Pawlak, Z.: Information Systems Theoretical Foundations. Information Systems 3, 205–218 (1981)
Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (2002)
Skarbek, W., Pietrowcew, A., Sikora, R.: The modified Oja-RLS algorithm, stochastic convergence analysis and application for image compression. Fundamenta Informaticae 36, 345–365 (1998)
Pennebaker, W.B., Mitchell, J.L.: JPEG: Still Image Data Compression Standard. Springer, Heidelberg (2006)
Maret, Y., DuFaux, F., Ebrahimi, T.: Adaptive image replica detection based on support vector classifiers. Signal Processing: Image Communication 21, 688–703 (2006)
Shnayderman, A., Gusev, A., Eskicioglu, A.M.: An SVD-Based Grayscale Image Quality Measure for Local and Global Assessment. IEEE Trans. Image Process 15, 422–429 (2006)
Golub, G., Loan, C.: Matrix Computations. The Johns Hopkins University Press, Baltimore (1989)
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Skarbek, W. (2007). Singular and Principal Subspace of Signal Information System by BROM Algorithm. In: Yao, J., Lingras, P., Wu, WZ., Szczuka, M., Cercone, N.J., Ślȩzak, D. (eds) Rough Sets and Knowledge Technology. RSKT 2007. Lecture Notes in Computer Science(), vol 4481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72458-2_19
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DOI: https://doi.org/10.1007/978-3-540-72458-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72457-5
Online ISBN: 978-3-540-72458-2
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