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This paper proposes a new Newton-based adaptive filtering algorithm, namely the Quasi-Newton Least-Mean Fourth (QNLMF) algorithm. The main goal is to have a higher order adaptive filter that usually fits the non-Gaussian signals with an improved performance behavior, which is achieved using the Newton numerical method. Both the convergence analysis and the steady-state performance analysis are derived...
This paper describes new algorithms that incorporates the non-uniform norm constraint into the zero-attracting and reweighted modified filtered-x affine projection or pseudo affine projection algorithms for active noise control. The simulations indicate that the proposed algorithms can obtain better performance for primary and secondary paths with various sparseness levels with insignificant numerical...
In this paper, we develop a greedy algorithm for sparse learning over a doubly stochastic network. In the proposed algorithm, nodes of the network perform sparse learning by exchanging their individual intermediate variables. The algorithm is iterative in nature. We provide a restricted isometry property (RIP)-based theoretical guarantee both on the performance of the algorithm and the number of iterations...
We present the theory of sequences of random graphs and their convergence to limit objects. Sequences of random dense graphs are shown to converge to their limit objects in both their structural properties and their spectra. The limit objects are bounded symmetric functions on [0,1]2. The kernel functions define an equivalence class and thus identify collections of large random graphs who are spectrally...
This work examines the mean-square error performance of diffusion stochastic algorithms under a generalized coordinate-descent scheme. In this setting, the adaptation step by each agent is limited to a random subset of the coordinates of its stochastic gradient vector. The selection of which coordinates to use varies randomly from iteration to iteration and from agent to agent across the network....
This work develops a distributed optimization algorithm with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown to have a wider stability range and superior convergence performance than the EXTRA consensus strategy. The exact diffusion solution is also applicable to non-symmetric left-stochastic combination matrices,...
In hearing aids (HAs), the acoustic coupling between the microphone and the receiver results in the system becoming unstable under certain conditions and causes artifacts commonly referred to as whistling or howling. The least mean square (LMS) class of algorithms is commonly used to mitigate this by providing adaptive feedback cancellation (AFC). The speech quality after AFC and the amount of added...
The estimation of means of data points lying on the Riemannian manifold of symmetric positive-definite (SPD) matrices is of great utility in classification problems and is currently heavily studied. The power means of SPD matrices with exponent p in the interval [−1, 1] interpolate in between the Harmonic (p = −1) and the Arithmetic mean (p = 1), while the Geometric (Karcher) mean corresponds to their...
Compressive sensing (CS) has been shown useful for reducing dimensionality, by exploiting signal sparsity inherent to specific domain representations of data. Traditional CS approaches represent the signal as a sparse linear combination of basis vectors from a prescribed dictionary. However, it is often impractical to presume accurate knowledge of the basis, which motivates data-driven dictionary...
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily smooth. Our framework can handle stochastic approximations of the gradient of the smooth function and allows for stochastic errors in the evaluation of the proximity...
The approximation of linear time-invariant (LTI) systems by sampling series is a central task of signal processing. For the Paley-Wiener space PW1π of bandlimited signals with absolutely integrable Fourier transform, it is known that there exist signals and stable LTI systems such that the canonical approximation process diverges. In this paper we analyze the structure of the sets of signals and systems...
Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error...
The distribution theory serves as an important theoretical foundation for some approaches arose from the engineering intuition. Particular examples are approaches based on the delta-“function”. In this work, we show that the usual construction of a band-limited interpolation (BLI) of signals “vanishing” at infinity (e.g., in [1], [2]), using the delta-“function”, is erroneous, both in the distributional...
The stochastic dual coordinate-ascent (S-DCA) technique is a useful alternative to the traditional stochastic gradient-descent algorithm for solving large-scale optimization problems due to its scalability to large data sets and strong theoretical guarantees. However, the available S-DCA formulation is limited to finite sample sizes and relies on performing multiple passes over the same data. This...
In this work, a novel algorithm named sign regressor least mean mixed-norm (SRLMMN) algorithm is proposed as an alternative to the well-known least mean mixed-norm (LMMN) algorithm. The SRLMMN algorithm is a hybrid version of the sign regressor least mean square (SRLMS) and sign regressor least mean fourth (SRLMF) algorithms. Analytical expressions are derived to describe the convergence, steady-state,...
Recovering low-rank tensors from undercomplete linear measurements is a computationally challenging problem of great practical importance. Most existing approaches circumvent the intractability of the tensor rank by considering instead the multilinear rank. Among them, the recently proposed tensor iterative hard thresholding (TIHT) algorithm is simple and has low cost per iteration, but converges...
The solution of many applied problems relies on finding the minimizer of a sum of smooth and/or nonsmooth convex functions possibly involving linear operators. In the last years, primal-dual methods have shown their efficiency to solve such minimization problems, their main advantage being their ability to deal with linear operators with no need to invert them. However, when the problem size becomes...
A non-linear active noise control (ANC) scheme, which is based on an even mirror Fourier non-linear filter has been developed in this paper. A new weight update mechanism for the proposed scheme has been suggested and the range of the learning rate which ensures stability has been derived. The noise mitigation achieved using the new scheme has been compared with that obtained using a functional link...
We provide a time-domain analysis of the stability for two adaptive algorithms of gradient type that interfere with each other via their update errors. Such coupling can occur naturally as well as by desire of the designer. Especially, system identification algorithms that combine two adaptive schemes can often be described by such a structure. We derive precise statements on local contracting/expanding...
In this paper, we present an improved version of the second order sequential best rotation algorithm (SBR2) for polynomial matrix eigenvalue decomposition of para-Hermitian matrices. The improved algorithm is entitled multiple shift SBR2 (MS-SBR2) which is developed based on the original SBR2 algorithm. It can achieve faster convergence than the original SBR2 algorithm by means of transferring more...
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