Abstract
We introduce a new combination approach for the mixture of adaptive filters based on the set-membership filtering (SMF) framework. We perform SMF to combine the outputs of several parallel running adaptive algorithms and propose unconstrained, affinely constrained and convexly constrained combination weight configurations. Here, we achieve better trade-off in terms of the transient and steady-state convergence performance while providing significant computational reduction. Hence, through the introduced approaches, we can greatly enhance the convergence performance of the constituent filters with a slight increase in the computational load. In this sense, our approaches are suitable for big data applications where the data should be processed in streams with highly efficient algorithms. In the numerical examples, we demonstrate the superior performance of the proposed approaches over the state of the art using the well-known datasets in the machine learning literature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Through this paper, bold lower case letters denote column vectors and bold upper case letter denote matrices. For a vector \(\mathbf {a}\) (or matrix \(\mathbf {A}\)), \(\mathbf {a}^T\) (or \(\mathbf {A}^T\)) is its ordinary transpose. The operator \(\mathrm {col}\{\cdot \}\) produces a column vector or a matrix in which the arguments of \(\mathrm {col}\{\cdot \}\) are stacked one under the other. For a given vector \(\mathbf {w}\), \(\mathbf {w}^{(i)}\) denotes the ith individual entry of \(\mathbf {w}\). Similarly for a given matrix \(\mathbf {G}\), \(\mathbf {G}^{(i)}\) is the ith row of \(\mathbf {G}\). For a vector argument, \(\mathrm {diag}\{\cdot \}\) creates a diagonal matrix whose diagonal entries are elements of the associated vector.
References
Kozat, S.S., Erdogan, A.T., Singer, A.C., Sayed, A.H.: Steady-state MSE performance analysis of mixture approaches to adaptive filtering. IEEE Trans. Signal Process. 58, 4050–4063 (2010)
Sayed, A.H.: Fundamentals of Adaptive Filtering. Wiley, NJ (2003)
Sayin, M.O., Denizcan Vanli, N., Kozat, S.S.: A transient analysis of affine mixtures. IEEE Trans. Signal Process. 59(5), 6227–6232 (2011)
Kozat, S.S., Erdogan, A.T., Singer, A.C., Sayed, A.H.: A transient analysis of affine mixtures. IEEE Trans. Signal Process. 59(5), 6227–6232 (2011)
Donmez, M.A., Kozat, S.S.: Steady-state MSE analysis of convexly constrained mixture methods. IEEE Trans. Signal Process. 60(5), 3314–3321 (2012)
Arenas-Garcia, J., Figueiras-Vidal, A.R., Sayed, A.H.: Mean-square performance of a convex combination of two adaptive filters. IEEE Trans. Signal Process. 54(3), 1078–1090 (2006)
Arenas-Garcia, J., Gomez-Verdejo, V., Figueiras-Vidal, A.R.: New algorithms for improved adaptive convex combination of LMS transversal filters. IEEE Trans. Instrum. Meas. 54(6), 2239–2249 (2005)
Arenas-Garcia, J., Martinez-Ramon, M., Gomez-Verdejo, V., Figueiras-Vidal, A.R.: Multiple plant identifier via adaptive LMS convex combination. In: 2003 IEEE International Symposium on Intelligent Signal Processing, pp. 137–142 (2003)
Nascimento, V.H., Silva, M.T.M., Arenas-Garcia, J.: A low-cost implementation strategy for combinations of adaptive filters. In: Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5671–5675 (2013)
Lu, J., Hoi, S., Zhao, P.: Second order online collaborative filtering. In: Proceedings of Asian Conference on Machine Learning (ACML), pp. 40–55 (2013)
Ling, G., Yang, H.: Online learning for collaborative filtering. In: The International Joint Conference on Neural Networks (IJCNN), pp. 1–8 (2012)
Gollamudi, S., Nagaraj, S., Kapoor, S., Huang, Y.F.: Set-membership filtering and a set-membership normalized LMS algorithm with an adaptive step size. IEEE Signal Process. Lett. 5(5), 111–114 (1998)
Diniz, P.S.R., Werner, S.: Set-membership binormalized data-reusing LMS algorithms. IEEE Trans. Signal Process. 51(1), 124–134 (2003)
Koby, C., Ofer, D., Joseph, K., Shai, S.-S., Yoram, S.: Online passive-aggressive algorithms. J. Mach. Learn. Res. 7, 551–585 (2006)
Zhao, H., Yu, Y.: Novel adaptive vss-nlms algorithm for system identification. In: 2013 Fourth International Conference on Intelligent Control and Information Processing (ICICIP), June 2013, pp. 760–764 (2013)
Alcala-Fdez, J., Fernandez, A., Luengo, J., Derrac, J., Garca, S., Snchez, L., Herrera, F.: Keel data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. J. Mult. Valued Logic Soft Comput. 17(2–3), 255–287 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kilic, O.F., Sayin, M.O., Delibalta, I. et al. Computationally highly efficient mixture of adaptive filters. SIViP 11, 235–242 (2017). https://doi.org/10.1007/s11760-016-0925-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-016-0925-2