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Computationally highly efficient mixture of adaptive filters

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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.

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  1. 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.


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Correspondence to O. Fatih Kilic.

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Kilic, O.F., Sayin, M.O., Delibalta, I. et al. Computationally highly efficient mixture of adaptive filters. SIViP 11, 235–242 (2017).

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