Weight Update Equation Research Articles

Enhancing hyperspectral remote sensing image classification using robust learning technique

Advanced sensor tech integrates into diverse applications, including remote sensing, robotics, and IoT. Combining artificial intelligence (AI) with sensors enhances their capabilities, creating smart sensors, revolutionizing remote sensing and Internet of Things (IoT). This synergy forms a potent technology in the field. This study carries out a comprehensive analysis of the progress made in Hyperspectral sensors and AI-based classification techniques that are employed in remote sensing fields that utilize hyperspectral images. The classification of images obtained from Hyperspectral Sensors (HSS) has emerged as a prominent research subject within the domain of remote sensing. HSS offer a wealth of information across numerous spectral bands, supporting diverse applications such as land cover classification, environmental monitoring, agricultural assessment, change detection, and more. However, the abundance of data present in HSS also poses the challenge called the curse of dimensionality. The reduction of data dimensionality is crucial before applying any machine learning model to achieve optimal results. The present study introduces a new hybrid strategy combining the Back-Propagation algorithm with a variable adaptive momentum (BPVAM) and principal component analysis (PCA) for the purpose of classifying hyperspectral images. PCA is first applied to obtain an optimal set of discriminative features by eliminating highly correlated and redundant features. These features are then fed into the BPVAM model for classification. The addition of the momentum term in the weight update equation of the backpropagation algorithm helped achieve faster convergence with high accuracy. The proposed model was subjected to evaluation through experiments conducted on two benchmark datasets. These results indicated that the hybrid model based on BPVAM with PCA is an efficient technique for HSS classification.

A Cerebellum-Inspired Prediction and Correction Model for Motion Control of a Musculoskeletal Robot

It is an important issue that how to regulate the existing control models of musculoskeletal robots to improve the ability of motion learning and generalization. In this paper, based on the motion modulation function of the cerebellum, a cerebellum-inspired prediction and correction model is proposed to carry out feedforward regulation of the original controller. Firstly, drawing on the reservoir computing mechanism of the cerebellar granular layer, the cerebellum prediction model is established by using the echo state network. Incremental learning for the network is achieved using the replay method, which is able to process control signals with different distributions. The cerebellum prediction network can accurately predict the motion results of the robot under the action of the time-series control signals. Secondly, referring to the neural pathways of the cerebellum, the cerebellum correction model is constructed. The network learning rules are designed by drawing on the long-term potentiation and depression processes of cerebellar synaptic plasticity. The characteristics of the parameters in the network weight update equations are further analyzed. And the hyperparameter update rules of the correction network weights are proposed. To simulate the function of the cerebellum involved in the limb ballistic movement, the adaptive adjustment method for cerebellum correction duration is proposed. The cerebellum correction network can accurately modulate the original control signals by using the motion prediction results. In experiments, a musculoskeletal robot is used to verify the movement effects under the control of the cerebellum model. The results show that the cerebellum-inspired model can effectively improve the motion accuracy and learning efficiency of the musculoskeletal robot, and enhance the motion generalization ability and system robustness of the robot.

A new and effective nonparametric variable step-size normalized least-mean-square algorithm and its performance analysis

This paper presents a new and effective nonparametric variable step-size normalized least-mean-square (VSS-NLMS) algorithm which provides excellent performance in various signal-to-noise ratio (SNR) scenarios. The step-size update expressions are based on steady-state step-size which derives from the filter weight update equations. Specifically, the step-size adjustment rules employ the square root of the estimated error power and the system noise power to enhance the effectiveness of the proposed algorithm. Detailed transient-state and steady-state analyses are presented for the Gaussian white input signal and suggest that the steady-state performance of the proposed algorithm is independent of the smoothing parameter (used in the step-size update expressions). In addition, performance comparisons between the proposed algorithm and other well-known VSS-NLMS algorithms show the improvements of the proposed algorithm. Furthermore, theoretical analyses and simulated behaviors of the proposed algorithm are in good agreement for both transient-state and steady-state. Through simulation results, the irrelevance between the steady-state performance and the smoothing parameter is verified.

Diffusion Bayesian Decorrelation Algorithms Over Networks

The convergence rate of the diffusion normalized least mean squares (NLMS) algorithm can be speeded up by decorrelation of signals. However, the diffusion decorrelation NLMS algorithm confronts the conflicting requirements of fast convergence rate and small steady-state error. To address the issue, this paper proposes a family of diffusion Bayesian decorrelation least mean squares (DBDLMS) algorithms based on decorrelated observation models. Firstly, the weight update equations of the proposed DBDLMS algorithms are obtained by performing Bayesian inference over the decorrelated observation models, with variable step-sizes emerging naturally to help address the conflicting requirement. Secondly, the update equations of the decorrelation coefficient vectors are inferred from the Bayesian perspective, with the variable step-sizes emerging again. Subsequently, the performance analysis of the proposed DBDLMS algorithms is carried out. Moreover, a simple and effective approach is derived to estimate the free parameters for the proposed DBDLMS algorithms. Finally, the learning performance of the proposed algorithms are verified by Monte Carlo simulations.

Hybrid prediction strategy to predict agricultural information

The crop yield prediction (CYP) has a high significance in agriculture. Early crop yield predictions assist the farmers, decision-makers in making timely decisions during the actual growing season. In many developing countries such as India, the process of crop yield prediction is done manually, based on surveys and field visits which are time-consuming, expensive and prone to human error. To overcome these drawbacks, we propose a hybrid prediction strategy which can be applied to predict agricultural information such as crop yield and air temperature with a critical focus on crop yield prediction. The weighted principal component analysis (w-PCA) is used as the feature extraction strategy to extract the relevant features. A hybrid prediction strategy integrating artificial neural network (ANN) with modified-particle swarm optimization (m-PSO) is proposed. Initial parameters of ANN are selected using m-PSO with modified inertia weight and velocity update equations. This hybridized ANN then performs prediction on the selected features. This proposed prediction model which we call as hybrid-ANN (H-ANN) comprises of w-PCA as feature extractor, m-PSO for selecting initial weights and biases of ANN. Experiments were performed on eight real world and two benchmark agriculture data sets for crop yield and air temperature prediction. Results show that the proposed prediction model (H-ANN) performed with improvements in the range of 2 to 30%, 0.2 to 4% and 0.12 to 3% with respect to R-squared (R2), root mean square error (RMSE) and mean absolute error (MAE) respectively when compared to other prediction models such as ANN, ANN trained using GA (GA-ANN), ANN trained using standard PSO (SPSO-ANN), multiple linear regression (MLR), support vector regression (SVR) and ensemble of bagged regression trees (ET) on benchmark and real-world agricultural datasets.

Design of quaternion-valued second-order Volterra adaptive filters for nonlinear 3-D and 4-D signals

In this paper, the quaternion-valued second-order Volterra adaptive filters (QSOVAFs) are designed for the processing of nonlinear three-dimensional (3-D) and four-dimensional (4-D) signals. In the proposed frameworks, the structure of the strictly nonlinear (SNL), semi-widely nonlinear (SWNL), and widely nonlinear (WNL) QSOVAFs are primarily constructed in the quaternion domain. Then, their loss functions defined by the instantaneous error signals are minimized in the quaternion domain by using the recent generalized Hamilton-real (GHR) calculus. Thus, novel weight update equations are obtained for training the proposed SNL-QSOVAF, SWNL-QSOVAF, and WNL-QSOVAF. Furthermore, the stability bounds for each quaternion-valued kernel functions of them are derived from the convergence in the mean analysis. The comprehensive simulations on the nonlinear system identification and one-step-ahead prediction experiments support that the proposed SWNL-QSOVAF and WNL-QSOVAF can be effectively used in the processing of nonlinear noncircular quaternion signals, whereas that their SNL version can produce optimal results for nonlinear circular quaternion signals.

Externally Recurrent Neural Network based identification of dynamic systems using Lyapunov stability analysis

This paper proposes an Externally Recurrent Neural Network (ERNN) for approximating the unknown dynamics of complex nonlinear systems and time series prediction. The proposed model utilizes the present as well as delayed values of the system outputs as well as of the external input. The weight update equations are tested for their boundedness by applying the Lyapunov stability method. Further, the error convergence proof is also given. The proposed model is put to test by considering various nonlinear examples and its performance is also compared with other state of the art methods. The results obtained in the present study indicate that the method is efficient and has provided accurate results.

Robust adaptive learning approach to self-organizing maps

The Self-Organizing Map (SOM) has attracted much research in diverse fields of study, where it has been successfully applied to a wide range of artificial intelligence applications. In this paper, a new intelligent adaptive learning SOM, in contrast with the conventional SOM algorithm, is presented. The proposed SOM overcomes the disadvantages of the conventional SOM by deriving a new variable learning rate that can adaptively achieve the optimal weights and obtain the winner neurons with a shorter learning process time. To quantify the performance, the proposed SOM was compared with various unsupervised algorithms to examine how well the network weight update equation adapts and reaches the optimum weights with fewer iterations. Extensive experiments were conducted using eight different databases from the UCI and KEEL repositories. The proposed SOM algorithm was further compared with the conventional SOM, GF-SOM, PLSOM, and PLSOM2 algorithms. The proposed SOM algorithm showed superiority in terms of the convergence rate, Quantization Error (QE), Topology Error (TE) preserving map, and accuracy during the classification process.

Performance of soft limiters in the LMS algorithm for cyclostationary white Gaussian inputs

Abstract The analysis of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation were obtained for a stationary white Gaussian data model in [28] for system identification. Here the input signal is modeled by a cyclostationary white Gaussian random process with periodically time-varying power. The system parameters vary according to a random-walk. Using the previous analysis results, nonlinear recursions are presented for the transient and steady-state weight first and second moments that include the effect of the soft limiters. Monte Carlo simulations of the algorithms provide strong support for the theory.

Stochastic analysis of soft limiters in the LMS algorithm for stationary white Gaussian inputs—A unified theory

The effects of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation are investigated for a stationary white Gaussian data model for system identification. Nonlinear recursions are derived for the transient and steady-state weight first and second moments that include the effect of soft limiters on both the input and the error driving the algorithm. By varying a single parameter of the soft limiter, a general theory is presented that is applicable to LMS, soft limiting of the input, error or both and sign–sign LMS.

Feedback for reinforcement learning based brain–machine interfaces using confidence metrics

Objective. For brain–machine interfaces (BMI) to be used in activities of daily living by paralyzed individuals, the BMI should be as autonomous as possible. One of the challenges is how the feedback is extracted and utilized in the BMI. Our long-term goal is to create autonomous BMIs that can utilize an evaluative feedback from the brain to update the decoding algorithm and use it intelligently in order to adapt the decoder. In this study, we show how to extract the necessary evaluative feedback from a biologically realistic (synthetic) source, use both the quantity and the quality of the feedback, and how that feedback information can be incorporated into a reinforcement learning (RL) controller architecture to maximize its performance. Approach. Motivated by the perception–action–reward cycle (PARC) in the brain which links reward for cognitive decision making and goal-directed behavior, we used a reward-based RL architecture named Actor–Critic RL as the model. Instead of using an error signal towards building an autonomous BMI, we envision to use a reward signal from the nucleus accumbens (NAcc) which plays a key role in the linking of reward to motor behaviors. To deal with the complexity and non-stationarity of biological reward signals, we used a confidence metric which was used to indicate the degree of feedback accuracy. This confidence was added to the Actor’s weight update equation in the RL controller architecture. If the confidence was high (>0.2), the BMI decoder used this feedback to update its parameters. However, when the confidence was low, the BMI decoder ignored the feedback and did not update its parameters. The range between high confidence and low confidence was termed as the ‘ambiguous’ region. When the feedback was within this region, the BMI decoder updated its weight at a lower rate than when fully confident, which was decided by the confidence. We used two biologically realistic models to generate synthetic data for MI (Izhikevich model) and NAcc (Humphries model) to validate proposed controller architecture. Main results. In this work, we show how the overall performance of the BMI was improved by using a threshold close to the decision boundary to reject erroneous feedback. Additionally, we show the stability of the system improved when the feedback was used with a threshold. Significance: The result of this study is a step towards making BMIs autonomous. While our method is not fully autonomous, the results demonstrate that extensive training times necessary at the beginning of each BMI session can be significantly decreased. In our approach, decoder training time was only limited to 10 trials in the first BMI session. Subsequent sessions used previous session weights to initialize the decoder. We also present a method where the use of a threshold can be applied to any decoder with a feedback signal that is less than perfect so that erroneous feedback can be avoided and the stability of the system can be increased.

Lyapunov stability-based control and identification of nonlinear dynamical systems using adaptive dynamic programming

This paper presents a novel control and identification scheme based on adaptive dynamic programming for nonlinear dynamical systems. The aim of control in this paper is to make output of the plant to follow the desired reference trajectory. The dynamics of plants are assumed to be unknown, and to tackle the problem of unknown plant’s dynamics, parameter variations and disturbance signal effects, a separate neural network-based identification model is set up which will work in parallel to the plant and the control scheme. Weights update equations of all neural networks present in the proposed scheme are derived using both gradient descent (GD) and Lyapunov stability (LS) criterion methods. Stability proof of LS-based algorithm is also given. Weight update equations derived using LS criterion ensure the global stability of the system, whereas those obtained through GD principle do not. Further, adaptive learning rate is employed in weight update equation instead of constant one in order to have fast learning of weight vectors. Also, LS- and GD-based weight update equations are also tested against parameter variation and disturbance signal. Three nonlinear dynamical systems (of different complexity) including the forced rigid pendulum trajectory control are used in this paper on which the proposed scheme is applied. The results obtained with LS method are found more accurate than those obtained with the GD-based method.

Improving the Performance of the PNLMS Algorithm Using Norm Regularization

The proportionate normalized least mean square (PNLMS) algorithm and its variants are by far the most popular adaptive filters that are used to identify sparse systems. The convergence speed of the PNLMS algorithm, though very high initially, however, slows down at a later stage, even becoming worse than sparsity agnostic adaptive filters like the NLMS. In this paper, we address this problem by introducing a carefully constructed $l_1$ norm (of the coefficients) penalty in the PNLMS cost function which favors sparsity. This results in certain zero attracting terms in the PNLMS weight update equation which help in the shrinkage of the coefficients, especially the inactive taps, thereby arresting the slowing down of convergence and also producing lesser steady state excess mean square error (EMSE). A rigorous convergence analysis of the proposed algorithm is presented that expresses the steady state mean square deviation of both the active and the inactive taps in terms of a zero attracting coefficient of the algorithm. The analysis reveals that further reduction of the EMSE is possible by deploying a variable step size (VSS) simultaneously with a variable zero attracting coefficient in the weight update process. Simulation results confirm superior performance of the proposed VSS zero attracting PNLMS algorithm over existing algorithms, especially in terms of having both higher convergence speed and lesser steady state EMSE simultaneously.

The Data‐Reusing MCC‐Based Algorithm and Its Performance Analysis

Maximum correntropy criterion (MCC) provides a robust optimality criterion for non-Gaussian signal processing. In this paper, the weight update equation of the conventional MCC-based adaptive filtering algorithm is modified by reusing the past K input vectors, forming a class of data-reusing MCC-based algorithm, called DRMCC algorithm. Comparing with the conventional MCCbased algorithm, the DR-MCC algorithm provides a much better convergence performance when the input data is correlated. The mean-square stability bound of the DRMCC algorithm has been studied theoretically. For both Gaussian noise case and non-Gaussian noise case, the expressions for the steady-state Excess mean square error (EMSE) of DR-MCC algorithm have been derived. The relationship between the data-reusing order and the steadystate EMSEs is also analyzed. Simulation results are in agreement with the theoretical analysis.

A robust adaptive hybrid feedback cancellation scheme for hearing aids in the presence of outliers

It has been demonstrated that the Filtered-x Wilcoxon LMS (FxWLMS) based adaptive filter mitigates the effect of the outliers acquired by the microphone signal of hearing aids by minimizing the Wilcoxon norm and hence shows better cancellation performance than the existing Filtered-x LMS (FxLMS) algorithm. The prediction error method based adaptive feedback canceller (PEMAFC) reduces the bias present in the estimate of the feedback path due to the continuous adaptive filtering (CAF). However, the impulse response of the measured feedback path is close to zero for the first many samples due to the delay introduced by ADC converters and then contains few significant values, which results in slow convergence rate when an adaptive filter is used to model the same. To overcome this limitation, we propose a proportionate normalized WLMS (PNWLMS) algorithm based PEMAFC (P-PNWLMS) for feedback cancellation in hearing aid in the presence of outliers. Further, with an objective to improve the convergence rate and performance accuracy simultaneously, this paper proposes a novel convex PNWLMS (CPNWLMS) algorithm which incorporates convex combination of PNWLMS and WLMS algorithms. The weight update equations are derived for PEMAFC trained by PNWLMS (P-PNWLMS) and CPNWLMS (P-CPNWLMS) algorithms respectively. The results of the simulation study show improved performance of the proposed CPNWLMS based adaptive filter over its component filters.

An optimal variable step-size affine projection algorithm for the modified filtered-x active noise control

This paper introduces an optimal variable step-size affine projection algorithm for the modified filtered-x active noise control systems. First, the recursion form of the error covariance from the tap weight update equation is constructed, not ignoring the dependency between the estimation error and the secondary noise signal. Such consideration has not been concerned previously for the analysis of the modified filtered-x affine projection algorithm. Second, a recursion form of the mean square deviation is derived from that of the error covariance. From the recursion form, an optimal step size is decided to get the fastest convergence rate. Both the recursion forms of the mean square deviation and the optimal step size require scalar additions and multiplications that do not contribute to the overall complexity seriously. The simulation results on the active noise control environments show both fast convergence rate and low steady-state error.

Variable matrix-type step-size affine projection algorithm with orthogonalized input vectors

In this paper, we propose a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram–Schmidt process to implement the weight update equation of the APA using the sum of normalized least mean squares (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation, which is equivalent to adopting the step size in the form of a diagonal matrix in the APA. We adopt a variable step-size scheme, in which the individual step sizes are determined to minimize the mean square deviation of the APA in order to achieve the fastest convergence on every iteration. Furthermore, because of the weight vector updated successively only along each innovative one among the reused inputs and effect of the regularization absorbed into the derived step size, the algorithm works well even for badly excited input signals. Experimental results show that our proposed algorithm has almost optimal performance in terms of convergence rate and steady-state estimation error, and these results are remarkable especially for badly excited input signals.

Neural Network Based STLF Model to Study the Seasonal Impact of Weather and Exogenous Variables

Load forecasting is very essential for efficient and reliable operation of the power system. Uncertainties of weather behavior significantly affect the prediction accuracy, which increases the operational cost. In this study, neural network (NN) based 168 hours ahead short term load forecast (STLF) model is proposed to study seasonal impact of calendar year. The affect of the model inputs such as, weather variables, calendar events and type of a day on load demand is considered to enhance the forecast accuracy. The weight update equations of gradient descent algorithm are derived and Mean Absolute Percentage Error (MAPE) is used as performance index. The performance of NN is measured in terms of confidence interval, which is based on training, testing, validation and cumulative impact of these phases. The simulations result shows that the forecast accuracy is affected by seasonal variation of input data.

Bayesian approach of nearfield acoustic reconstruction with particle filters

This paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the Bayesian approach of parameter estimation. In particular, the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method (ESM). A state-space model is formulated in light of the ESM. The parameters to estimate are amplitudes and locations of the equivalent sources. The parameters constitute the state vector which follows a first-order Markov process with the transition matrix being the identity for every frequency-domain data frame. Filtered estimates of the state vector obtained are assigned weights adaptively. The implementation of recursive Bayesian filters involves a sequential Monte Carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function (PMF) which evolves with iteration. The weight update equation governs the evolution of this PMF and depends primarily on the likelihood function and the prior distribution. It is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation.

다중 클래스 아다부스트를 이용한 엘리베이터 내 군집 밀도 추정

본 논문에서는 다중 클래스 아다부스트 기반의 분류기를 이용하여 엘리베이터 내 군집 밀도를 추정하는 방법을 제안한다. SOM을 사용하는 기존의 방법은 재현성이 떨어지며 충분한 성능을 내지 못한다. 제안한 방법은 GLDM(Grey-Level Dependency Matrix)과 GGDM(Grey-Gradient Dependency Matrix)의 텍스처 특징과 다중 클래스 아다부스트 기반의 분류기를 통해 실내 군집 밀도를 추정한다. 다중 클래스를 분류하기 위해 기존의 아다부스트 알고리즘에서 웨이트 업데이트 식을 변형하여 더 높은 성능의 약한 분류기를 생성하도록 하였다. 군집 밀도는 인원수에 따라 0명, 1~2명, 3~4명, 5명 이상 등 네 가지 클래스로 구분하였다. 엘리베이터 내 영상을 이용한 모의 실험 결과 제안된 방법은 기존의 방법보다 약 20% 정도의 검출률 향상을 나타내었다. In this paper, an crowd density in elevator estimation method based on multi-class Adaboost classifier is proposed. The SOM (Self-Organizing Map) based conventional methods have shown insufficient performance in practical scenarios and have weakness for low reproducibility. The proposed method estimates the crowd density using multi-class Adaboost classifier with texture features, namely, GLDM(Grey-Level Dependency Matrix) or GGDM(Grey-Gradient Dependency Matrix). In order to classify into multi-label, weak classifier which have better performance is generated by modifying a weight update equation of general Adaboost algorithm. The crowd density is classified into four categories depending on the number of persons in the crowd, which can be 0 person, 1-2 people, 3-4 people, and 5 or more people. The experimental results under indoor environment show the proposed method improves detection rate by about 20% compared to that of the conventional method.