Abstract
Starting from an extended Rayleigh quotient defined on the noncompact Stiefel manifold, in this paper, we present a novel dual purpose subspace flows for subspace tracking. The proposed algorithm can switch from principal subspace to minor subspace tracking with a simple sign change of its stepsize parameter. More interestingly, the proposed dual purpose gradient system behaves the same invariant property as that of the well-known Chen-Amari-Lin system. The stability of the discrete version of the proposed subspace flow is guaranteed by an additional added stabilizing term. No tunable parameter is required for the proposed algorithm as opposed to the modified Oja algorithm. The strengths of the proposed algorithm is demonstrated using a de facto benchmark example.
Supported by National Natural Science Foundation of China ( No. 61002039 ) and The Fundamental Research Funds for the Central Universities ( No. DC10040121, DC12010216).
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References
Abed-Meraim, K., Attallah, S., Chkeif, A., Hua, Y.: Orthogonal Oja Algorithm. IEEE Signal Processing Letters 7(5), 116–119 (2000)
Absil, P.A., Mahony, R., Sepulchre, R., Dooren, P.V.: A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces. SIAM Review 44(1), 57–73 (2002)
Chen, T.: Modified Oja’s Algorithms for Principal Subspace and Minor Subspace Extraction. Neural Processing Letters (1), 105–110 (1997)
Chen, T., Amari, S.I.: Unified stabilization approach to principal and minor components extraction algorithms. Neural Networks 14, 1377–1387 (2001)
Chen, T., Amari, S.I., Lin, Q.: A unified algorithm for principal and minor components extraction. Neural Networks 11, 385–390 (1998)
Darken, C., Chang, J., Moody, J.: Learning rate schedules for faster stochastic gradient search. In: Neural Networks for Signal Processing, pp. 3–12 (1992)
Delmas, J.: Subspace tracking for signal processing. In: Adali, T., Haykin, S. (eds.) Adaptive Signal Processing: Next Generation Solution, pp. 211–270. Wiley (2010)
Douglas, S.C., Kung, S., Amari, S.I.: A self-stabilized minor subspace rule. IEEE Signal Processing Letters 5(12), 328–330 (1998)
Helmke, U., Moore, J.B.: Optimization and dynamical systems. Springer, Heidelberg (1993)
Kong, X., Hu, C., Han, C.: A Dual Purpose Principal and Minor Subspace Gradient Flow. IEEE Transactions on Signal Processing 60(1), 197–210 (2012)
Manton, J.H., Helmke, U., Mareels, I.M.: A dual purpose principal and minor component flow. Systems & Control Letters 54(8), 759–769 (2005)
Oja, E.: Principal components, minor components, and linear neural networks. Neural Networks 5(6), 927–935 (1992)
Xu, L.: Least mean square error reconstruction principle for self-organizing neural-nets. Neural Networks 6(5), 627–648 (1993)
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Liu, L., Xu, Y., Liu, Q. (2013). A Stable Dual Purpose Adaptive Algorithm for Subspace Tracking on Noncompact Stiefel Manifold. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39065-4_77
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DOI: https://doi.org/10.1007/978-3-642-39065-4_77
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