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In applications where large-order filters are needed, the computational load of adaptive filtering algorithms can become prohibitively expensive. In this paper, a comprehensive analysis of a selective partial-update least mean squares, named SPU-LMS-M-min, is developed. By employing the partial-update strategy for a non-normalized adaptive scheme, the designer can choose an appropriate number of update blocks considering a trade-off between convergence rate and computational complexity, which can result in a more than 40% reduction in the number of multiplications in some configurations compared to the traditional LMS algorithm. Based on the principle of minimum distortion, a selection criterion is proposed that is based on the input signal's blocks with the lowest energy, whereas typical Selective Partial Update (SPU) algorithms use a selection criterion based on blocks with highest energy. Stochastic models are developed for the mean weights and mean and mean squared behaviour of the proposed algorithm, which are further extended to accommodate scenarios involving time-varying dynamics and suboptimal filter lengths. Simulation results show that the theoretical predictions are in good agreement with the experimental outcomes. Furthermore, it is demonstrated that the proposed selection criterion can be easily extended to active noise cancellation algorithms as well as algorithms utilizing variable filter length. This allows for the reduction of computational costs for these algorithms without compromising their asymptotic performance. [ABSTRACT FROM AUTHOR]

Video streaming takes the largest share of internet traffic today, and MPEG dynamic adaptive streaming over HTTP (DASH) has become dominant among other video streaming standards and protocols. According to the DASH standard, multimedia content is encoded in different quality levels with different bitrates located on the server, and users can request multimedia content of any available bitrate. The user side determines the desired bitrate in the unit called adaptation bitrate (ABR) logic. Many ABR algorithms have been proposed to improve the quality of experience (QoE). The main criteria for determining QoE are average bitrate, number of switches between resolutions, and number of buffer underflows. This paper presents a hybrid DASH adaptation algorithm that uses the following input values: current buffer occupancy level, network throughput value calculated on the last downloaded DASH segment, and Takagi-Sugeno-Kang model output that represents expected throughput in the next segment download iteration. We compared the proposed algorithm with several other algorithms and the results show that it outperforms others in average bitrate and number of bitrate switches. Furthermore, our algorithm prevented all buffer underflows. [ABSTRACT FROM AUTHOR]

This paper introduces an online centered normalized least mean squares (OC-NLMS) algorithm for linear adaptive finite impulse response (FIR) filters and neural networks. As an extension of the normalized least mean squares (NLMS), the OC-NLMS algorithm features an approach of online input centering according to the introduced filter memory. This key feature can compensate the effect of concept drift in data streams, because such a centering makes the filter independent from the nonzero mean value of signal. This approach is beneficial for applications of adaptive filtering of data with offsets. Furthermore, it can be useful for real-time applications like data stream processing where it is impossible to normalize the measured data with respect to its unknown statistical attributes. The OC-NLMS approach holds superior performance in comparison to the NLMS for data with large offsets and dynamical ranges, due to its input centering feature that deals with the nonzero mean value of the input data. In this paper, the derivation of this algorithm is presented. Several simulation results with artificial and real data are also presented and analysed to demonstrate the capability of the proposed algorithm in comparison with NLMS. [ABSTRACT FROM AUTHOR]

This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear PDEs. The main idea of these algorithms is to utilize the solutions on the kth-level adaptive meshes to find the solutions on the (k + 1)th-level adaptive meshes which are constructed by performing adaptive element bisections on the k th-level adaptive meshes. These algorithms transform nonsymmetric positive definite (non-SPD) PDEs (resp., nonlinear PDEs) into symmetric positive definite (SPD) PDEs (resp., linear PDEs). The proposed algorithms are both accurate and efficient due to the following advantages: They do not need to solve the nonsymmetric or nonlinear systems; the degrees of freedom are very small, they are easily implemented, and the interpolation errors are very small. Next, this paper constructs residual-type a posteriori error estimators which are shown to be reliable and efficient. The key ingredient in proving the efficiency is to establish an upper bound of the oscillation terms, which may not be higher-order terms due to the low regularity of the numerical solution. Furthermore, the convergence of the algorithms is proved when bisection is used for the mesh refinements. Finally, numerical experiments are provided to verify the accuracy and efficiency of the ATG finite element algorithms compared to regular adaptive finite element algorithms and two-grid finite element algorithms [J. Xu, SIAM J. Numer. Anal., 33 (1996), pp. 1759-1777]. [ABSTRACT FROM AUTHOR]

When dealing with complex nonlinear signals in intelligent system, by defining the inner product of two data vectors in the feature space, the kernel function can reflect the nonlinear mapping relationship between reproducing kernel Hilbert space (RKHS) and original data space. Therefore, by implementing classical linear adaptive filtering in RKHS space, the filtering operation can be expressed as a special relation of inner product with kernel function, which is referred to as “kernel trick.” As long as these algorithms can be expressed in the form of inner product, not only the convex least squares problem can be solved iteratively, but also the nonlinear adaptive filtering algorithms can be obtained, which have both general approximation characteristics and convexity. Therefore, the combination of kernel method and adaptive filtering algorithm is realized. On the other hand, since the Gram matrix is used, the dimension of kernel adaptive algorithm is determined by the number of data samples. When the number of observation sample point is increasing, the size of the state space increases exponentially with the growth of the dimension. Thereby, the kernel adaptive algorithm should solve the problem of online sparsification to avoid “curse of dimensionality.” As part II, based on online sparse kernel learning and the classical adaptive filtering algorithm, the kernel adaptive algorithms and online sparse algorithms are investigated in this paper. The main works of this paper have two aspects. First, combined with classical adaptive algorithm and kernel feature mapping, this paper investigates the basic concept of kernel adaptive algorithm and the realization mechanism of four kernel adaptive algorithm intensively: 1) kernel least mean squares; 2) kernel recursive least squares; 3) kernel affine projection algorithm; and 4) kernel principal component analysis. Second, in order to reduce the computational complexity, this paper studies some online sparse algorithms which include novel criterion, approximate linear dependency, sliding window, coherence criterion, surprise criterion, and so on. Finally, this paper summarizes the essence of existing conclusions of above algorithms and perspectives the future research direction. [ABSTRACT FROM AUTHOR]

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic trace estimation in a second phase. In turn, Hutch++ only requires O \bigl(\varepsilon 1 \bigr) matrix-vector products to approximate the trace within a relative error \varepsilon with high probability, provided that the matrix is symmetric positive semidefinite. This compares favorably with the O \bigl(\varepsilon 2 \bigr) matrix-vector products needed when using stochastic trace estimation alone. In Hutch++, the number of matrix-vector products is fixed a priori and distributed in a prescribed fashion among the two phases. In this work, we derive an adaptive variant of Hutch++, which outputs an estimate of the trace that is within some prescribed error tolerance with a controllable failure probability, while splitting the matrix-vector products in a near-optimal way among the two phases. For the special case of a symmetric positive semidefinite matrix, we present another variant of Hutch++, called Nystr\"om++, which utilizes the so-called Nystr\"om approximation and requires only one pass over the matrix, as compared to two passes with Hutch++. We extend the analysis of Hutch++ to Nystr\"om++. Numerical experiments demonstrate the effectiveness of our two new algorithms. [ABSTRACT FROM AUTHOR]

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta }$ (with $\theta \in (0,1)$), with $n$ individuals among which $k$ are infected. However, the required number of tests may increase substantially under real-world practical constraints, notably including bounds on the maximum number $\Delta $ of tests an individual can be placed in, or the maximum number $\Gamma $ of individuals in a given test. While previous works have given recovery guarantees for these settings, significant gaps remain between the achievability and converse bounds. In this paper, we substantially or completely close several of the most prominent gaps. In the case of $\Delta $ -divisible items, we show that the definite defectives (DD) algorithm coupled with a random regular design is asymptotically optimal in dense scaling regimes, and optimal to within a factor of e more generally; we establish this by strengthening both the best known achievability and converse bounds. In the case of $\Gamma $ -sized tests, we provide a comprehensive analysis of the regime $\Gamma = \Theta (1)$ , and again establish a precise threshold proving the asymptotic optimality of SCOMP (a slight refinement of DD) equipped with a tailored pooling scheme. Finally, for each of these two settings, we provide near-optimal adaptive algorithms based on sequential splitting, and provably demonstrate gaps between the performance of optimal adaptive and non-adaptive algorithms. [ABSTRACT FROM AUTHOR]

Given a binary sequence with length $n$ , determining its minimal rational fraction representation (MRFR) has important applications in the design and cryptanalysis of stream ciphers. There are many studies of this problem since Klapper and Goresky first introduced an adaptive rational approximation algorithm with a time complexity of $O(n^{2}\log n\log \log n)$. In this paper, we revisit this problem by considering both adaptive and non-adaptive efficient algorithms. Compared with the state-of-art methods, we make several contributions to the problem of finding MRFR. Firstly, we find a general and precise recursive relationship between the minimal bases for two adjacent lattices generated by successive truncation sequences. This enables us to improve the currently fastest adaptive algorithm proposed by Li et al.. Secondly, by optimizing a time-consuming step of the well-known Lagrange reduction algorithm for 2-dimensional lattices, we obtain a non-adaptive, and yet practically faster MRFR-solving algorithm named global Euclidean algorithm. Thirdly, we identify theoretical flaws on some non-adaptive methods in the literature by counter-examples and correct the problems by designing modified Euclidean algorithm named partial Euclidean algorithm. Meanwhile, we further reduce the time complexity of existing algorithm from $O(n^{2})$ to $O(n\log ^{2}n\log \log n)$ by invoking the half-gcd algorithm. We also conduct a comprehensive experimental comparative analysis on the above algorithms to validate our theoretical analysis. [ABSTRACT FROM AUTHOR]

The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and many more. One of the defining features of the group testing problem is the distinction between the non-adaptive and adaptive settings. In the non-adaptive case, all tests must be designed in advance, whereas in the adaptive case, each test can be designed based on the previous outcomes. While tight information-theoretic limits and near-optimal practical algorithms are known for the adaptive setting in the absence of noise, surprisingly little is known in the noisy adaptive setting. In this paper, we address this gap by providing information-theoretic achievability and converse bounds under various noise models, as well as a slightly weaker achievability bound for a computationally efficient variant. These bounds are shown to be tight or near-tight in a broad range of scaling regimes, particularly at low noise levels. The algorithms used for the achievability results have the notable feature of only using two or three stages of adaptivity. [ABSTRACT FROM AUTHOR]

In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts. [ABSTRACT FROM AUTHOR]

This paper focuses on C0IPG adaptive algorithms for the biharmonic eigenvalue problem with the clamped boundary condition. We prove the reliability and efficiency of the a posteriori error indicator of the approximating eigenfunctions and analyze the reliability of the a posteriori error indicator of the approximating eigenvalues. We present two adaptive algorithms, and numerical experiments indicate that both algorithms are efficient. [ABSTRACT FROM AUTHOR]

Based on the minimum noise subspace (MNS) method previously introduced in the context of blind channel identification, generalized minimum noise subspace (GMNS) is proposed in this paper for array processing that generalizes MNS with respect to the availability of only a fixed number of parallel computing units. Different batch and adaptive algorithms are then introduced for fast and parallel computation of signal (principal) and noise (minor) subspaces. The computational complexity of GMNS and its related estimation accuracy are investigated by simulated experiments and a real-life experiment in radio astronomy. It is shown that GMNS represents an excellent tradeoff between the computational gain and the subspace estimation accuracy, as compared to several standard subspace methods. [ABSTRACT FROM PUBLISHER]

First-order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great practical success in deep learning, their behavior and performance on more general loss functions are not well understood. In this paper, we derive a non-autonomous system of differential equations, which is the continuous time limit of adaptive optimization methods. We study the convergence of its trajectories and give conditions under which the differential system, underlying all adaptive algorithms, is suitable for optimization. We discuss convergence to a critical point in the non-convex case and give conditions for the dynamics to avoid saddle points and local maxima. For convex loss function, we introduce a suitable Lyapunov functional which allows us to study its rate of convergence. Several other properties of both the continuous and discrete systems are brie y discussed. The differential system studied in the paper is general enough to encompass many other classical algorithms (such as Heavy Ball and Nesterov's accelerated method) and allow us to recover several known results for these algorithms. [ABSTRACT FROM AUTHOR]

Background: Due to the high susceptivity of the walking pattern to be affected by several disorders, accurate analysis methods are necessary. Given the complexity and relevance of such assessment, the utilization of methods to facilitate it plays a significant role, provided that they do not compromise the outcomes.Research Questions: This paper aimed at identifying the standards for the application of adaptive predictive systems to gait analysis, given the extensive research on this field. Furthermore, we also intended to check whether such methods can effectively support clinicians in determining the number of physiotherapy sessions necessary to recover gait-related dysfunctions.Methods: Through a screening process of scientific databases, we considered studies encompassed from 1968 to April 2019. Within these 50 years, we found 24 papers that met our inclusion criteria. They were analyzed according to their data acquisition and processing methods via ad hoc questionnaires. Additionally, we examined quantitatively the adaptive approaches.Results: Concerning data acquisition, the included papers presented a mean score of 6.1 SD 1.0, most of them applying optoelectronic systems, and the ground reaction force (GRF) was the most used parameter. The AI quality assessment showed an above-average rate of 7.8 SD 1.0, and artificial neural networks (ANN) being the paradigm most frequently utilized. Our systematic review identified only one study that addressed therapeutics including a predictive method.Significance: While much progress has been identified to predict assessment aspects, there is little effort to assist healthcare professionals in establishing the rehabilitation duration and prognostics. Therefore, future studies should focus on accomplishing the production of applications of predictive methods to therapeutics and prognosis, not lingering extremely on the analysis of gait features. [ABSTRACT FROM AUTHOR]

The least mean squared (LMS) algorithm and its variants have been the most often used algorithms in adaptive signal processing. However the LMS algorithm suffers from a high computational complexity, especially with large filter lengths. The Fourier transform-based block normalized LMS (FBNLMS) reduces the computation count by using the discrete Fourier transform (DFT) and exploiting the fast algorithms for implementing the DFT. Even though the savings achieved with the FBNLMS over the direct-LMS implementation are significant, the computational requirements of FBNLMS are still very high, rendering many real-time applications, like audio and video estimation, infrasible. The Hartley transform-based BNLMS (HBNLMS) is found to have a computational complexity much less than, and a memory requirement almost of the same order as, that of the FBNLMS. This paper is based on the cosine and sine symmetric implementation of the discrete Hartley transform (DHT), which is the key in reducing the computational complexity of the FBNLMS by 33% asymptotically (with respect to multiplications). The parallel implementation of the discrete cosine transform (DCT) in turn can lead to more efficient implementations of the HBNLMS. [ABSTRACT FROM AUTHOR]

This paper compares the performance of the popular adaptive h -refinement ( h\text{R} ) technique for the finite-element method (FEM) with the adaptive version of the recently presented operator-customized wavelet basis (OCWB). This new method is a combination of the second-generation wavelet theory with hierarchical basis, which is a multi-resolution basis, and, when applied to the FEM, the solution is split into different levels of detail. These levels, also referred to as scales, are composed by compactly supported functions, allowing the detail to be added only on the chosen regions. Although this strategy reduces the total system dimension with sufficiently small error, all the scales are naturally coupled, which means that there are interactions between functions composing different detail levels. This coupling forces the whole multi-resolution system to be recomputed when a detail is added, a kind of redundancy that also occurs on the h\text{R}$ method. Using the second-generation wavelet theory, functions are custom-designed to decouple the system, which means the interactions between the functions of different levels are eliminated, and it is possible to solve for further detail independently of previous scales. This property significantly increases the performance of the algorithm. Conversely, the formulation—and, consequently, the algorithm design—complexity is also increased, which is the reason why there are such few applications on the subject. Like the h\text{R} method, an adaptive OCWB can be programmed with various strategies; since the results are shown in terms of processing time on a regular PC, both the algorithms have been developed with similar structures. [ABSTRACT FROM AUTHOR]

In hearing aid (HA) systems, amplification of speech signals is done to compensate the hearing loss of patients. Background noise and feedback signals may also get amplified which degrade the intelligibility and quality of speech. To achieve high de-noise efficiency, signal processing unit in HA system has voice activity detector (VAD). The conventional VAD detects voice based on zero crossing rate or energy of input signals. However, these methods cannot perform well at low SNR or non-stationary noise environments. Since pitch is a special characteristic of speech and is basically independent of noise intensity, VAD based on pitch can have high accuracy even when the noise spectrum is changing drastically. In this paper, pitch-based VAD is presented and its accuracy is checked against zero crossing rate-based VAD (ZCR-VAD). For noise reduction, an improved multi-band spectral over-subtraction algorithm is employed along with the high accurate pitch-based VAD. For feedback cancellation, the performance of adaptive algorithms like NLMS, RLS and affine projection (AP) algorithms with pitch-based VAD is compared and it is observed that AP is suitable for feedback cancellation. The proposed noise reduction and feedback cancellation algorithm with pitch-based VAD method is tested with NOIZEUS speech database and with real-time noisy speech signals. The simulation results show that the accuracy of pitch-VAD is about 23% higher than that of ZCR-VAD. The SNR for the proposed noise reduction and feedback cancellation with pitch-VAD method is improved by 10 dB than conventional spectral subtraction and adaptive algorithms. Mean opinion score (MOS) obtained for the proposed method is 4.3 out of 5. [ABSTRACT FROM AUTHOR]

This paper introduces the graph-structured recursive least squares (GS-RLS) algorithm, which is a very efficient means to track a linear time-varying system when the inputs to the system have structure that can be modeled using a decomposable Gaussian graphical model. For graphs with small clique sizes, it is shown that GS-RLS can achieve tracking performance very close to that of the conventional RLS algorithm for a fraction of the computational cost. In particular, after proving that the outputs of wide-sense stationary time-varying communication channels have graphical model structure if the inputs are cyclostationary, significant computational gains are realized for adaptive equalization of the time-varying underwater acoustic communication channel using the GS-RLS algorithm. This is verified using field data from the SPACE08 underwater acoustic communication experiment. [ABSTRACT FROM AUTHOR]

This paper introduces an anti-jamming technology for satellite communication that can cancel terrestrial jammers. In this paper, we first consider the Conjugate Gradient Method (CGM) as the first adaptive algorithm. Using this method, the attainment of the depth of the nulls and the rate of convergence are shown to be excellent. We also introduce a second novel adaptive algorithm, the hardware complexity of which for real-time implementation remains within the capacity of an off-the-shelf serial processor. A simulator based on the proposed adaptive algorithms is then illustrated to verify the performance of an adaptive system designed for implementation on a geostationary satellite. Finally, we demonstrate a hardware implementation of the adaptive system for canceling terrestrial jammers. Detailed hardware descriptions of an implemented adaptive system - such as the antenna array module, the beamforming module, and the controller module - are illustrated, along with the results of the performance obtained in laboratory tests. [ABSTRACT FROM AUTHOR]

Smart antenna systems are used in a wide range of fixed and mobile communication applications. Generally smart antennas are made of antenna arrays and signal processors. The antenna array can have any kind of shape, from linear to circular or rectangular. For simplicity considerations in this paper we studied the linear antenna array. The main characteristic of a smart antenna system is the digital signal processing feature. The system processes the signals in order to obtain a desired radiation pattern. In this paper we will describe some of the most significant algorithms used for processing the signal received by every element of the array along with some of the advantages and disadvantages for each of them. The algorithms described are the LMS (Least Mean Squares), the RLS (Recursive Least Squares) and CMA (Constant Modulus Algorithm). [ABSTRACT FROM AUTHOR]

In this paper, the problem of the simultaneous estimation of frequency and power components is investigated. It is solved through a new recursive estimator capable of estimating the unknown model parameters during severe dynamic changes in the system. By this, a simple nonlinear parameter model for the instantaneous power, taking into account the fundamental components of voltage and current, is used as a starting point for the power components and frequency estimation. In the model, the system frequency is considered as an unknown model parameter, and it is simultaneously estimated with other unknown parameters. This resulted in an efficient numerical algorithm for the measurement of power components, which is not sensitive to variations of the system frequency. This is an important achievement, which improves the accuracy of the method during network transients. The new estimator has been improved by the strategy for tuning its forgetting factor according to the system dynamics, and it is tested through computer simulations and by using data records obtained under laboratory conditions. The algorithm was developed for a single-phase system, and the approach might be easily extended to multiphase systems. [ABSTRACT FROM AUTHOR]

Many systems nowadays follow not only physical laws but also manmade rules. These systems are known as discrete-event dynamic systems (DEDSs), where simulation is the only faithful way for performance evaluation. Due to various advantages in practice, designs (or solution candidates) with low descriptive complexity (called simple designs) are usually preferred over complex ones when their performances are close. However, the descriptive complexity (DC) is usually nonlinear and takes discrete value, which makes traditional methods such as linear programming and gradient-based local search not applicable. Existing methods for simulation-based optimization (SBO) do not explore the preference on descriptive complexity and thus cannot solve the problem efficiently. The major contributions of this paper are to point out the importance of considering SBO problems with DC preference, and to develop an adaptive sampling algorithm (ASA) to find the simplest good design. It is shown that ASA terminates within finite iterations and with controllable probability of making mistake. The computational complexity of ASA and its dependence on various parameters are discussed. ASA is then applied to three parameter optimization problems and a node activation policy optimization problem in a wireless sensor network. Numerical results show that ASA is more efficient than blind picking and Levin search in most cases. We hope this work can shed some insight to how to find simple and good designs in general. [ABSTRACT FROM AUTHOR]

The paper proposes two nonlinear system identification methods in order to reduce the compromise between convergence speed and steady-state that occurs when using third order adaptive Volterra filters. Combination of filters and combination of kernels schemes are outlined. Adaptation of the kernels is achieved using a Normalized Least Mean Square algorithm. The tradeoff between speed and stability is emphasized by selecting different step-size parameters for each kernel. Both nonlinear approaches are applied in acoustic Loudspeaker-Enclosure-Microphone setups where several sources of nonlinearities exist: the overdriven amplifier's or small loudspeakers' operated at high volume. A third order polynomial with distinct Linear-to-Nonlinear Ratios is chosen to model these distortions. The evaluation is made in terms of Echo Return Loss Enhancement in experiments conducted for various input signals. Results show that the overall adaptive combinations perform each time better or at least as well as the best component filter. [ABSTRACT FROM AUTHOR]

Using the ℓ1-norm to regularize the least-squares criterion, the batch least-absolute shrinkage and selection operator (Lasso) has well-documented merits for estimating sparse signals of interest emerging in various applications where observations adhere to parsimonious linear regression models. To cope with high complexity, increasing memory requirements, and lack of tracking capability that batch Lasso estimators face when processing observations sequentially, the present paper develops a novel time-weighted Lasso (TWL) approach. Performance analysis reveals that TWL cannot estimate consistently the desired signal support without compromising rate of convergence. This motivates the development of a time- and norm-weighted Lasso (TNWL) scheme with ℓ1-norm weights obtained from the recursive least-squares (RLS) algorithm. The resultant algorithm consistently estimates the support of sparse signals without reducing the convergence rate. To cope with sparsity-aware recursive real-time processing, novel adaptive algorithms are also developed to enable online coordinate descent solvers of TWL and TNWL that provably converge to the true sparse signal in the time-invariant case. Simulated tests compare competing alternatives and corroborate the performance of the novel algorithms in estimating time-invariant signals, and tracking time-varying signals under sparsity constraints. [ABSTRACT FROM AUTHOR]

The PARAFAC decomposition of a higher-order tensor is a powerful multilinear algebra tool that becomes more and more popular in a number of disciplines. Existing PARAFAC algorithms are computationally demanding and operate in batch mode-both serious drawbacks for on-line applications. When the data are serially acquired, or the underlying model changes with time, adaptive PARAFAC algorithms that can track the sought decomposition at low complexity would be highly desirable. This is a challenging task that has not been addressed in the literature, and the topic of this paper. Given an estimate of the PARAFAC decomposition of a tensor at instant t, we propose two adaptive algorithms to update the decomposition at instant t + 1, the new tensor being obtained from the old one after appending' a new slice in the 'time' dimension. The proposed algorithms can yield estimation performance that is very close to that obtained via repeated application of state-of-art batch algorithms, at orders of magnitude lower complexity. The effectiveness of the proposed algorithms is illustrated using a MIMO radar application (tracking of directions of arrival and directions of departure) as an example. [ABSTRACT FROM AUTHOR]

Trading off computational complexity and quality is an important performance constraint for real time application of motion estimation algorithm. Previously, the novel concept of a distance-dependent thresholding search (DTS) was introduced for performance scalable motion estimation in video coding applications. This encompassed the full search as well as other fast searching techniques, such as the three-step search, with different threshold settings providing various quality-of-service levels in terms of processing speed and predicted image quality. The main drawback of the DTS was that the threshold values had to be manually defined. In this paper, the DTS algorithm has been extended to a fast and fully adaptive DTS (FADTS), a key feature of which is the automatic adaptation of the threshold using a desired target and the content from the actual video sequence, to achieve either a guaranteed level of quality or processing complexity. Experimental results confirm the performance of the FADTS algorithm in achieving this objective by demonstrating either comparable or improved search speed over existing fast algorithms including the diamond search, hexagon-based search, and enhanced hexagon-based search, while maintaining similar error performance. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r > 0) dominant generalized. eigen-subspace and a sequential algorithm based on deflation technique for the first v-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first v-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, sequence detection and channel estimation for frequency-selective, intersymbol interference (ISI)-producing channels under Class-A impulsive noise are considered. We introduce a novel suboptimum sequence detection (SSD) scheme and show that although SSD employs a simplified metric, it achieves practically the same performance as maximum-likelihood sequence detection (MLSD). For both SSD and MLSD, a lower bound on the achievable performance is derived, which is similar to the classical matched-filter bound for frequency- selective (fading) channels under Gaussian noise. For channel estimation, we adopt a minimum entropy criterion and derive efficient least-mean-entropy and recursive least-entropy algorithms. For both adaptive algorithms, we analyze the steady-state channel-estimation error variance. Theoretical considerations and simulation results show that in Class-A impulsive noise, the proposed sequence detection and adaptive channel-estimation schemes yield significant performance gains over their respective conventional counterparts (designed for Gaussian noise). Although the novel algorithms require knowledge of the Class-A noise-model parameters, their computational complexity is comparable to that of the corresponding conventional algorithms. [ABSTRACT FROM AUTHOR]

An algorithm for the mean squared error (MSE) minimization, through the bias-to-variance ratio optimization, has been recently proposed and used in the literature. This algorithm is based on the analysis of the intersection of confidence intervals (ICIs). The algorithm does not require explicit knowledge of the estimation bias for a "near to optimal" parameter estimation. This paper presents a detailed analysis of the algorithm performances, including procedures and relations that can be used for a fine adjustment of the algorithm parameters. Reliability of the algorithm is studied for various kinds of estimation noise. Results are confirmed on a simulated example with uniform, Gaussian, and Laplacian noise. An illustration of the algorithm application on a simple filtering example is given. [ABSTRACT FROM AUTHOR]

This paper focuses on the new model for the classification of railhead defects, through images acquired by a rail inspection vehicle. In this regard, we discuss the use of set-membership concept, derived from the adaptive filter theory, into the training procedure of an upper and lower singleton type-2 fuzzy logic system, aiming to reduce computational complexity and to increase the convergence speed. The performance is based on the data set composed of images provided by a Brazilian railway company, which covers the four possible railhead defects (cracking, flaking, head-check and spalling) and the normal condition of the railhead. Additionally, we apply different levels of additive white Gaussian noise in the images in order to challenge the proposed model. Finally, we discuss performance analysis in terms of convergence speed, computational complexity reduction, and classification ratio. The reported results show that the proposal achieved improved convergence speed, slightly higher classification ratio and remarkable computation complexity reduction when we limit the number of epochs for training, which may be required under real-time constraint or low computational resource availability. [ABSTRACT FROM AUTHOR]

An antenna array consists of distributed antenna elements whose outputs are combined in such a way that the parameters of communication system are optimized. A smart antenna is an antenna array system aided by some "smart" algorithms designed to adapt to different signal environments. Through beamforming, smart antennas offer low co-channel interference and large antenna gain to the desired signal, leading to better performance than conventional antenna systems. Since beamforming is performed in software, forming several beams with the same array is possible by simply reusing the array output. The signal received at each antenna element is multiplied by an optimum weight and these products are added to get the desired output signal. The weight vector can be calculated using one of the many adaptive algorithms such as Least Mean Square (LMS) algorithm, Sample Matrix Inversion (SMI) algorithm, Recursive Least Square (RLS) algorithm and their variants. The SMI algorithm has a faster convergence rate since it employs direct inversion of covariance matrix to compute the weights. This paper analyzes how weight vector and beam pattern of the smart antenna system are changing for different angles of arrival of desired signal and also for different number of antenna elements in an antenna array. [ABSTRACT FROM AUTHOR]

This paper presents adaptive bidirectional minimum mean-square error parameter estimation algorithms for fast-fading channels. The time correlation between successive channel gains is exploited to improve the estimation and tracking capabilities of adaptive algorithms and provide robustness against time-varying channels. Bidirectional normalized least mean-square and conjugate gradient algorithms are devised along with adaptive mixing parameters that adjust to the time-varying channel correlation properties. An analysis of the proposed algorithms is provided along with a discussion of their performance advantages. Simulations for an application to interference suppression in multiuser DS-CDMA systems show the advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we introduce an adaptive procedure for the numerical computation of a high‐dimensional integrals on HPC systems with heterogeneous nodes composed of multi‐core CPU and GPU devices. To this aim, we have integrated together two different approaches: a first one is in charge of a fair workload among the threads running on the multi‐core CPU, while a second one is in charge of an efficient execution of the computational kernels on the GPU. We tested the resulting algorithm on several test functions on a system where the nodes are provided with two Intel ten‐core CPU and one NVIDIA GPU device. [ABSTRACT FROM AUTHOR]

The problem of quickest detection of dynamic events in networks is studied. At some unknown time, an event occurs, and a number of nodes in the network are affected by the event, in that they undergo a change in the statistics of their observations. It is assumed that the event is dynamic, in that it can propagate along the edges in the network, and affect more and more nodes with time. The event propagation dynamics is assumed to be unknown. The goal is to design a sequential algorithm that can detect a “significant” event, i.e., when the event has affected no fewer than $\eta $ nodes, as quickly as possible, while controlling the false alarm rate. Fully connected networks are studied first, and the results are then extended to arbitrarily connected networks. The designed algorithms are shown to be adaptive to the unknown propagation dynamics, and their first-order asymptotic optimality is demonstrated as the false alarm rate goes to zero. The algorithms can be implemented with linear computational complexity in the network size at each time step, which is critical for online implementation. Numerical simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Multi-agent reinforcement learning (MARL) has been successfully applied in many fields. In MARL, the policy evaluation problem is one of crucial problems. In order to solve this problem, distributed Temporal-Difference (TD) learning algorithm is one of the most popular methods in a cooperative manner. Despite its empirical success, however, the theory of the adaptive variant of distributed TD learning still remain limited. To fill this gap, we propose an adaptive distributed temporal-difference algorithm (referred to as MS - ADTD) under Markovian sampling over time-varying networks. Furthermore, we rigorously analyze the convergence of MS - ADTD , the theoretical results show that the local estimation can converge linearly to the optimal neighborhood. Meanwhile, the theoretical results are verified by simulation experiments. • This paper proposes a distributed adaptive TD learning algorithm under Markovian sampling. • It theoretically analyzes the non-asymptotic convergence performance of the proposed algorithm. • It verifies the performance of the proposed algorithm by experiments. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive beamforming algorithm is proposed under a linearly and quadratically constrained minimum variance (LQCMV) beamforming framework, based on a dual-domain projection approach that can efficiently implement a quadratic-inequality constraint with a possibly rank-deficient positive semi-definite matrix, and the properties of the proposed algorithm are analyzed. As an application, relaxed zero-forcing (RZF) beamforming is presented which adopts a specific quadratic constraint that bounds the power of residual interference in the beamformer output with the aid of interference-channel side-information available typically in wireless multiple-access systems. The dual-domain projection in this case plays a role in guiding the adaptive algorithm towards a better direction to minimize the interference and noise, leading to considerably faster convergence. The robustness issue against channel mismatch and ill-posedness is also addressed. Numerical examples show that the efficient use of interference side-information brings considerable gains. [ABSTRACT FROM PUBLISHER]

• An adaptive method is proposed for target detection in hyperspectral images. • The robust NLMS adaptive algorithm is used to design the proposed method. • The method tries to use spectral signature library rather than statistical moments. • The method has high performance for high quality hyperspectral images. In this paper, a novel adaptive algorithm for target detection in hyperspectral images (HSIs) is proposed. In a general classification, the proposed method belongs to the category of those methods which are not based on the statistical moments of the observed HSI (e.g. correlation or covariance matrix). The main processing burden of the proposed method is over a known set of spectral signatures. Assuming a linear spectral mixing model, the proposed method takes a set of spectral signatures which one of them relates to the target material and the others relate to the background materials. Based on an adaptive approach, the normalized least mean square (NLMS) adaptive algorithm is engaged to estimate a weight vector which is almost orthogonal to the background materials spectral signature whereas it makes an absolutely non-orthogonal pair with the target material spectral signature. The estimated weight vector is multiplied by the observed HSI to make the final decision. One synthetic and two real hyperspectral images are considered to evaluate the performance of the proposed method. The evaluation results show that the proposed method outperforms its counterparts. [ABSTRACT FROM AUTHOR]

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected in the process of solving equations. Using a fixed basis leads to the so-called basis error since orbitals may not lie entirely within the linear span of the basis. To avoid such an error, multiresolution bases are used in adaptive algorithms so that basis functions are selected from a fixed collection of functions, large enough to approximate solutions within any user-selected accuracy. Our new method achieves adaptivity without using a multiresolution basis. Instead, as part of an iteration to solve nonlinear equations, our algorithm selects the 'best' subset of linearly independent terms of a Gaussian mixture from a collection that is much larger than any possible basis since the locations and shapes of the Gaussian terms are not fixed in advance. Approximating an orbital within a given accuracy, our algorithm yields significantly fewer terms than methods using multiresolution bases. We demonstrate our approach by solving the Hartree-Fock equations for two diatomic molecules, HeH+ and LiH, matching the accuracy previously obtained using multiwavelet bases. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert advice, is remarkably both worst-case optimal and adaptive to the easier stochastic and adversarial with a gap problems. This shows that, in spite of its small, non-adaptive learning rate, Hedge possesses the same optimal regret guarantee in the stochastic case as recently introduced adaptive algorithms. Moreover, our analysis exhibits qualitative differences with other versions of the Hedge algorithm, such as the fixed-horizon variant (with constant learning rate) and the one based on the so-called "doubling trick", both of which fail to adapt to the easier stochastic setting. Finally, we determine the intrinsic limitations of anytime Hedge in the stochastic case, and discuss the improvements provided by more adaptive algorithms. [ABSTRACT FROM AUTHOR]

Abstract In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depends on the number of observations and their innovation. The algorithms described herein use an adaptive step-size to accelerate the learning and can offer an excellent tradeoff between convergence speed and steady state, which allows them to solve nonlinear filtering and estimation problems with a large number of parameters without requiring a large computational cost. The data-selective update scheme also limits the number of operations performed and the size of the dictionary created by the kernel expansion, saving computational resources and dealing with one of the major problems of kernel adaptive algorithms. A statistical analysis is carried out along with a computational complexity analysis of the proposed algorithms. Simulations show that the proposed KNLMS algorithms outperform existing algorithms in examples of nonlinear system identification and prediction of a time series originating from a nonlinear difference equation. [ABSTRACT FROM AUTHOR]

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One of the key issues in decentralized beamforming is the need to phase-align the carriers of all the sensors in a wireless sensor network. Recent work in this area has shown the viability of certain methods that incorporate single-bit feedback from a beacon. This paper analyzes the behavior of the method (showing conditions for convergence in distribution and also giving a concrete way to calculate the final distribution of the convergent ball) and then generalizes the method in three ways. First, by incorporating both negative and positive feedback it is possible to double the convergence rate of the algorithm without adversely effecting the final variance. Second, a way of reducing the amount of energy required (by reducing the number of transmissions needed for convergence) is shown; its convergence and final variance can also be conveniently described. Finally, a wideband analog is proposed that operates in a decentralized manner to align the time delay (rather than the phase) between sensors. [ABSTRACT FROM AUTHOR]

Adaptive wavelet algorithms for solving operator equations have been shown to converge with the best possible rates in linear complexity. For the latter statement, all costs are taken into account, i.e. also the cost of approximating entries from the infinite stiffness matrix with respect to the wavelet basis using suitable quadrature. A difficulty is the construction of a suitable wavelet basis on the generally non-trivially shaped domain on which the equation is posed. In view of this, recently corresponding algorithms have been proposed that require only a wavelet frame instead of a basis. By employing an overlapping decomposition of the domain, where each subdomain is the smooth parametric image of the unit cube, and by lifting a wavelet basis on this cube to each of the subdomains, the union of these collections defines such a frame. A potential bottleneck within this approach is the efficient approximation of entries corresponding to pairs of wavelets from different collections. Indeed, such wavelets are piecewise smooth with respect to mutually non-nested partitions. In this paper, considering partial differential operators and spline wavelets on the subdomains, we propose an easy implementable quadrature scheme to approximate the required entries, which allows the fully discrete adaptive frame algorithm to converge with the optimal rate in linear complexity. [ABSTRACT FROM PUBLISHER]

Conventional modeling and simulation formalisms only give support to the representation of model behavior, providing no constructs for describing changes in model structure. However, some systems are better modeled by self-reconfigurable formalisms. We have developed the Discrete Flow System Specification (DFSS) to exploit dynamic structure, component-based and hierarchical model construction. Due to structural similarity, dynamic self-configuring DFSS models offer a good description of systems, like adaptive algorithms and reconfigurable computer architectures. In this paper, we present the modeling and simulation of a parallel adaptive divide-and-conquer integration algorithm in the C aosT alk modeling and simulation framework, a realization of the DFSS formalism. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive linear-receiver structure based on interpolated finite-impulse response (FIR) filters with adaptive interpolators for direct-sequence code-division multiple-access (DS-CDMA) systems in multipath channels. The interpolated minimum mean-squared error (MMSE) and the interpolated constrained minimum-variance (CMV) solutions are described for a novel scheme, where the interpolator is rendered time-varying in order to mitigate multiple-access interference and multiple-path propagation effects. Based upon the interpolated MMSE and CMV solutions, we present computationally efficient stochastic gradient and exponentially weighted recursive least squares type algorithms for both receiver and interpolator filters in the supervised and blind modes of operation. A convergence analysis of the algorithms and a discussion of the convergence properties of the method are carried out for both modes of operation. Simulation experiments for a downlink scenario show that the proposed structures achieve a superior bit-error-rate convergence and steady-state performance to previously reported reduced-rank receivers at lower complexity. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel sensor deployment algorithm, called the adaptive triangular deployment (ATRI) algorithm, for large-scale unattended mobile sensor networks. The ATRI algorithm aims at maximizing coverage area and minimizing coverage gaps and overlaps by adjusting the deployment layout of nodes close to equilateral triangulation, which is proven to be the optimal layout to provide the maximum no-gap coverage. The algorithm only needs the location information of nearby nodes, thereby avoiding communication cost for exchanging global information. By dividing the transmission range into six sectors, each node adjusts the relative distance to its one-hop neighbors in each sector separately. The distance threshold strategy and the movement state diagram strategy are adopted to avoid the oscillation of nodes. The simulation results show that the ATRI algorithm achieves a much larger coverage area and smaller average moving distance of nodes than existing algorithms. We also show that the ATRI algorithm is applicable to practical environments and tasks such as working in both bounded and unbounded areas and avoiding irregularly shaped obstacles. In addition, the density of nodes can be adjusted adaptively to different requirements of tasks. [ABSTRACT FROM AUTHOR]

The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS has the order of accuracy n̄n = 2[(n + 1)/2], i.e., the global error is of the form O(|h|n̄), where |h| is the maximum step size and [·] denotes the entire part of the expression in brackets. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive algorithm is suggested for the implementation of polynomial based image interpolation techniques such as Bilinear, Bicubic, Cubic Spline and Cubic O-MOMS. This algorithm is based on the minimization of the squared estimation error at each pixel in the interpolated image by adaptively estimating the distance of the pixel to be estimated from its neighbors. The adaptation process at each pixel is performed iteratively to yield the best estimate of this pixel value. This adaptive interpolation algorithm takes into consideration the mathematical model by which a low resolution (LR) image is obtained from a high resolution (HR) image. This adaptive algorithm is compared to traditional polynomial based interpolation techniques and to the warped distance interpolation techniques. The performance of this algorithm is also compared to the performance of other algorithms used in commercial interpolation softwares such as the ACDSee and the Photopro programs. Results show that the suggested adaptive algorithm is superior from the Peak Signal to Noise Ratio (PSNR) point of view to other traditional techniques and it has a higher ability of edge preservation than traditional image techniques. The computational cost of the adaptive algorithm is studied and found to be moderate. [ABSTRACT FROM AUTHOR]

This paper introduces an iterative space–time soft estimator (ISSE) that performs joint channel estimation and soft data detection in time-varying multiple-input multiple-output channels. The ISSE alternates channel estimation, taking explicitly into account the channel variability, and soft data detection. We suggest to implement the latter stage as a decision feedback (DF) structure consisting of two linear minimum mean square error (MMSE) matrix filters with an intercalated threshold detector. DF schemes are known to provide an appealing trade-off between performance and computational complexity. The main contribution of the paper is the channel estimation scheme. We derive a time-varying sequence of linear filters for channel estimation according to the MMSE principle. These filters depend both on the data and the second order statistics of the channel. Hence, we introduce a scalar approximation of the channel autocovariance function that relies on the statistical homogeneity of the multipath scattering. Under this assumption, we also design a globally convergent block-adaptive algorithm to estimate and track the second order statistics of a stationary channel. The robustness of the proposed approach when either the homogeneity or the stationarity hypotheses do not hold is shown through computer simulations. [Copyright &y& Elsevier]

Evoked potentials (EPs) have been widely used to quantify neurological system properties. Changes in EP latency may indicate impending neurological dysfunctions. This paper provides a review and a performance comparison of three classes of latency change estimation algorithms: correlation based, adaptive least mean square (LMS) based, and p-norm based algorithms. Data analysis based on computer simulated data and data from impact acceleration and hypoxia experiments were conducted. This concluded that correlation-based algorithms should only be used when the expected latency change is fixed and the noises are not correlated. While all adaptive LMS type algorithms were capable of tracking and estimating latency changes (fixed or variable) under Gaussian noise conditions, the direct LMS-based algorithm reduced the estimation error power given by traditional filter type LMS algorithms as much as 93%. When periodic interference was present, the frequency selective LMS algorithms outperformed other LMS-based algorithms and reduced of the estimation error power by 89%. Alpha-stable noise processes are better approximations of noises found in various EP analysis applications and adaptive p-norm based algorithms are found to be very robust under such noise conditions, eliminate erroneous abrupt latency changes other algorithms would have produced. [ABSTRACT FROM AUTHOR]