Brain graphs (brain connectivity networks) play an important role in modeling the complex structure of the human brain. Furthermore, brain graph learning based on graph neural networks (GNNs) has recently attracted growing interest. Although existing methods have made great progress in brain disorder prediction and pathogenic analysis, there are two key problems: (1) They rarely utilize the pathogenic reason of brain disorders, that is, salient brain regions always lead to abnormal connections between brain regions, to extract critical brain graph information for disorder analysis; (2) Since most of the available brain graph data is limited, how can we improve the performance of brain graph learning models on insufficient training data? Thus, in this paper, we learn brain graph representations for disorder prediction and analyze disorder-specific brain regions and connections from the subgraph perspective. Besides, we introduce the cross-domain brain graph learning framework to alleviate the problem of poor model performance on limited data. To consider the pathogenic reason by brain subgraphs, we first propose the node entropy of brain graphs based on brain graph properties to extract important nodes. We then introduce subgraph information bottleneck to refine the critical subgraph from the rough subgraph generated by these important nodes, recognizing important connections related to disorders. To achieve a better model performance on limited data, we design a cross-domain brain graph learning framework to improve the subgraph extraction model by the meta-learning method. The subgraph extraction model is pre-trained on a large source training dataset and then quickly adapted to target task dataset. Besides, a simple yet effective feature alignment module is applied to mitigate the negative transfer problem for cross-domain datasets. Extensive experimental results, including disorder prediction and pathogenic analysis on real-world neuroimaging data, demonstrate the effectiveness of our method.

To protect both local gradients and estimated parameters in distributed learning, this paper introduces a masked diffusion (MD) strategy, leading to two algorithms: the MD stochastic gradient (MD-SG) and the MD primal-dual stochastic gradient (MPD-SG). The two algorithms distinguish themselves from existing privacy diffusion methods by incorporating two mechanisms: non-zero mean protection noise and a random matrix step-size. The first mechanism ensures the confidentiality of the transmitted values, while the second protects the gradient information. We analyze the mean-square stability and privacy of the proposed methods under standard assumptions. The results indicate that the MPD-SG algorithm, with a sufficiently small parameter γ, can achieve better steady-state performance than the MD-SG algorithm in heterogeneous data scenarios. Finally, simulations illustrate the effectiveness of the proposed algorithms and support the theoretical analysis.

In this article, we consider the data privacy issue of distributed learning over adaptive networks under zero-mean protection noise. First, using a nonzero-mean protection noise, a new privacy-preserving diffusion adaptive least-mean-squares algorithm is devised, named NZPD-LMS. Different from the existing differential privacy noise, the nonzero-mean protection noise is designed with two noises with zero-mean and nonzero-mean, allowing the zero-mean noise to retain differential privacy properties, and the nonzero-mean noise to prevent the use of a sliding average over time to obtain transmission values. Then, based on mean-square analysis, we evaluate stability conditions and steady-state error bounds for the NZPD-LMS algorithm, as well as how each algorithmic parameter affects steady-state error. Finally, several simulations are conducted to illustrate the theoretical findings and effectiveness of the proposed approach.

The censored regression (CR)-based normalized subband adaptive algorithm (CR-NSAF) model has been recently introduced for processing signals with censored data. However, the effectiveness of this algorithm declines when dealing with noisy input signals in impulsive noise environments. To resolve this challenge, we propose a robust bias-compensated CR-NSAF algorithm (RBC-CRNSAF). This algorithm alleviates the negative impacts of the CR system and improves robustness by employing a logarithmic cost function approach. It also minimizes estimation bias from input noise by incorporating new compensation terms into the weights update function. Additionally, we analyze the computational complexity, convergence characteristics, and stability conditions of the algorithm. Finally, computer simulations indicate that RBC-CRNSAF considerably outperforms other similar algorithms in impulsive noise environments, validating its enhanced performance.

Recently, graph neural networks (GNNs) have demonstrated outstanding performance in fundamental tasks such as node classification and link prediction, as well as in specialized domains like recommendation systems, fraud detection, and drug discovery. However, their vulnerability to adversarial attacks raises concerns about their reliability in security-critical areas. To address this issue, researchers are exploring various defense methods, including specific attack countermeasures and certifiable robustness approaches. Nevertheless, these strategies are often effective only against limited attack scenarios, and prevailing certification methods prove inadequate when confronted with injection attacks. In this paper, we propose a method named CERT_UIA to enhance the robustness of GNN models against worst-case attacks, specifically targeting the scenario of Universal node Injection Attacks (UIA), thereby filling a gap in the existing literature on certified robustness in this context. Our approach involves a two-stage attack process that replaces the transformations of the topology and feature spaces with equivalent unified feature transformations, unifying the optimization of worst-case perturbations into a single feature space. Furthermore, we empirically evaluate our method on several benchmark datasets and compare it with existing certified methods.

For the correlated input, the Volterra kernel-based least mean-square (LMS) algorithm in the time-domain exhibits a slow learning rate caused by the large eigenvalue spread of the input covariance matrix. To tackle such an issue, this paper develops a novel frequency-domain Volterra kernel-based filter, resulting in the periodic update constrained frequency-domain second-order Volterra normalized LMS (named as P-CFDSOV-NLMS1) algorithm. Subsequently, by using one- and two-dimensional discrete Fourier transforms (DFTs) simultaneously, another frequency-domain implementation and corresponding P-CFDSOV-NLMS2 algorithm are constructed. In contrast, the P-CFDSOV-NLMS1 scheme only requires one-dimensional DFT operations and takes advantage of the joint information between the block input vectors. Then, the mean and mean-square convergence behaviors of the P-CFDSOV-NLMS1 algorithm are investigated. Furthermore, the designed frequency-domain method is extended to three different widely complex-valued Volterra kernel-based models. Finally, computer simulations reveal that the suggested algorithms outperform the previously reported frequency-domain techniques in terms of convergence speed and tracking ability.

This paper considers the scenario of noisy inputs and compressive diffusion (for reducing communication load) with noisy links over sensor networks. We first study the implementation of diffusion bias-compensated Bayesian adaptation (DBCBA) for noisy inputs, which outperforms the existing solution. Next, an average-estimate step is applied to lessen the impact of link noise in the full diffusion case, yielding a diffusion average-estimate bias-compensated Bayesian adaptation (DABCBA) algorithm. A Bayes-based adaptation construction step is then presented to reconstruct the compressed diffusion information in the presence of link noise, resulting in a compressive DBCBA (CDBCBA) algorithm whose mean and mean-square behaviors are analyzed and the closed-form expression of the steady-state mean-square deviation is derived. In addition, estimators are devised for the input and output noise variances. The excellent performance of our algorithms is demonstrated via numerical examples while the theoretical calculation aligns closely with the simulation results.

Graph pooling technique as the essential component of graph neural networks has gotten increasing attention recently and it aims to learn graph-level representations for the whole graph. Besides, graph pooling is important in graph classification and graph generation tasks. However, current graph pooling methods mainly coarsen a sequence of small-sized graphs to capture hierarchical structures, potentially resulting in the deterioration of the global structure of the original graph and influencing the quality of graph representations. Furthermore, these methods artificially select the number of graph pooling layers for different graph datasets rather than considering each graph individually. In reality, the structure and size differences among graphs necessitate a specific number of graph pooling layers for each graph. In this work, we propose reinforced pooling graph neural networks via adaptive hybrid graph coarsening networks. Specifically, we design a hybrid graph coarsening strategy to coarsen redundant structures of the original graph while retaining the global structure. In addition, we introduce multi-agent reinforcement learning to adaptively perform the graph coarsening process to extract the most representative coarsened graph for each graph, enhancing the quality of graph-level representations. Finally, we design graph-level contrast to improve the preservation of global information in graph-level representations. Extensive experiments with rich baselines on six benchmark datasets show the effectiveness of ReiPool1.

Pedestrian trajectory prediction is a critical technology in the evolution of self-driving cars toward complete artificial intelligence. Over recent years, focusing on the trajectories of pedestrians to model their social interactions has surged with great interest in more accurate trajectory predictions. However, existing methods for modeling pedestrian social interactions rely on pre-defined rules, struggling to capture non-explicit social interactions. In this work, we propose a novel framework named DTGAN, which extends the application of Generative Adversarial Networks (GANs) to graph sequence data, with the primary objective of automatically capturing implicit social interactions and achieving precise predictions of pedestrian trajectory. DTGAN innovatively incorporates random weights within each graph to eliminate the need for pre-defined interaction rules. We further enhance the performance of DTGAN by exploring diverse task loss functions during adversarial training, which yields improvements of 16.7% and 39.3% on metrics ADE and FDE, respectively. The effectiveness and accuracy of our framework are verified on two public datasets. The experimental results show that our proposed DTGAN achieves superior performance and is well able to understand pedestrians' intentions.

To improve the learning performance of the conventional diffusion least mean square (DLMS) algorithms, this article proposes Bayesian-learning-based DLMS (BL-DLMS) algorithms. First, the proposed BL-DLMS algorithms are inferred from a Gaussian state-space model-based Bayesian learning perspective. By performing Bayesian inference in the given Gaussian state-space model, a variable step-size and an estimation of the uncertainty of information of interest at each node are obtained for the proposed BL-DLMS algorithms. Next, a control method at each node is designed to improve the tracking performance of the proposed BL-DLMS algorithms in the sudden change scenario. Then, a lower bound on the variable step-size of each node of the proposed BL-DLMS algorithms is derived to maintain the optimal steady-state performance in the nonstationary scenario (unknown parameter vector of interest is time-varying). Afterward, the mean stability and the transient and steady-state mean square performance of the proposed BL-DLMS algorithms are analyzed in the nonstationary scenario. In addition, two Bayesian-learning-based diffusion bias-compensated LMS algorithms are proposed to handle the noisy inputs. Finally, the superior learning performance of the proposed learning algorithms is verified by numerical simulations, and the simulated results are in good agreement with the theoretical results.

Affine projection (AP) algorithm has been widely used in many applications because of the fast convergence ability for colored inputs. To reduce high steady-state errors resulting from weight-noise correlations, this letter presents an interval-extraction mechanism for AP algorithm, named IEAP. In the procedure, we recommend using an interval between each data point of the output vector in the AP update. Finally, by means of theoretical mean square deviations analysis and computer simulations, the interval-extraction method is demonstrated to be effective.

To address the conflict caused by the fixed sampled period in the multi-sampled multiband-structured subband adaptive filter (MS-MSAF), the adaptive convex combination of two MS-MSAFs is proposed in this paper, in which the individual filters independently run with different sampled periods. Moreover, the mean behavior of the convex-combined two MS-MSAF algorithm is also studied. In addition, the convex-combined two MS-MSAF algorithm with periodic feedback is also developed to further enhance the convergence performance. Finally, the validity of the proposed adaptive filtering algorithms together with their theoretical analyses is supported by computer simulations.

In this paper, a robust diffusion average-estimate normalized least mean square (NLMS) algorithm is proposed to tackle the impulsive noise in adjacent node communication links over distributed networks. Compared with the diffusion NLMS algorithm, the key point of the new algorithm is that it introduces two additional steps: robust detection and average estimation, thus greatly reducing the negative effects of the impulsive link noise. In addition, the mean stability of the proposed robust diffusion average-estimate NLMS algorithm is analyzed. Finally, Monte-Carlo simulation results demonstrate the effectiveness of the proposed robust diffusion algorithm.

The affine combination of two complex-valued least-mean-squares filters (aff-CLMS) addresses the trade-off between fast convergence rate and small steady-state misadjustment error. However, a rigorous analysis of the aff-CLMS algorithm for second-order non-circular inputs is still under investigation. To this end, the focus in this letter is on the full mean-square analysis of the aff-CLMS algorithm, in which the transient analyses of the mixing parameter, as well as the standard and complementary weight-error covariance matrices, are completed. In addition, we derive the closed-form solutions of the steady-state weight-error power and its complementary version of the aff-CLMS. Finally, the effectiveness of the theoretical analysis is supported by computer simulations.

This paper introduces two combined-sample multiband-structured subband adaptive filters (MSAFs). In the design, an adaptive convex combination scheme of two self-reliant multi-sampled MSAF (MS-MSAF) with different sampled periods is firstly developed, which leads to the so-called CTMS-MSAF algorithm. Secondly, based on an adaptive filter, the combined-sample MS-MSAF (CMS-MSAF) algorithm is proposed via designing a time-varying sampled period, which possesses lower computational complexity than the former. Then, the convergence behaviors of the CTMS-MSAF and CMS-MSAF algorithms are investigated using standard mean-square deviation analysis. Finally, the simulation study in the system identification and acoustic echo cancellation applications shows that at the same steady-state error, the CMS-MSAF method provides a faster convergence rate than the improved convex combination of two MSAFs, combined-step-size MSAF and CTMS-MSAF algorithms.

In this paper, an investigation is launched into the compressive diffusion strategy in the presence of noisy communication links so as to develop the compressive diffusion double normalized least mean square (NLMS) algorithm. Based on the single update global weight-error model, an analytical formulation of the transient and steady-state results is made for the compressive diffusion double NLMS algorithm. These analytical results are instrumental to making a better understanding of the mean- square performance of the compressive diffusion strategy against link noises. Lastly, simulation study is carried out to validate the performance of the developed compressive diffusion double NLMS algorithm over adaptive networks subject to link noises.

Sensor networks are an indispensable part of the Internet of Things (IoT), where sensors perform data acquisition and information processing tasks to obtain the parameters of interest so that IoT-based monitoring, diagnosis and other systems respond quickly to the changing conditions, instantaneous faults, etc. Distributed estimation algorithms are usually employed to estimate the parameters of interest in these IoT-based applications. However, when sensor networks have highly correlated input signals and nonstationary behavior in which the parameters of interest are time-varying, conventional distributed estimation algorithms suffer from severely degraded learning performance due to the large eigenvalue spread in the covariance matrix of the input signals and the random perturbation of the parameters of interest. To address these problems, this paper proposes two diffusion Bayesian subband adaptive filter (DBSAF) algorithms from a Bayesian learning perspective. As the highly-correlated input signal is whitened in a multiband structure and an estimate of the uncertainty in the parameters of interest is obtained by performing Bayesian inference, the proposed DBSAF algorithms are able to achieve better learning performance in comparison with the competing diffusion algorithms. The transient and steady-state mean square error performance of the proposed DBSAF algorithms are analyzed, and are verified by numerical simulations. A lower bound on the time-varying step-size is derived to maintain the optimal steady-state performance in nonstationary scenarios. A new method for the estimation of the noise variance is also proposed. Numerical simulations demonstrate the excellent learning performance of the proposed algorithms in comparison with benchmark algorithms.

This study develops a pseudo-energy-conservation relation to analyze the complementary mean-square performance of a complex-valued normalized least mean-square (CNLMS) algorithm. Based on this relation, we derive a recursion describing the transient complementary mean-square deviation (CMSD) behavior of the CNLMS. Closed-form expressions to predict the steady-state CMSD and complementary excess mean-square error conjugate (CEMSEc) are obtained. Because this method inherits the advantages of the energy-conservation method, our results do not restrict the distribution of input signals. Numerical simulations validate our theoretical analysis results.

In this paper, a subband adaptive filtering algorithm is developed over functional link neural network (FLNN) in order to overcome the issue of slow convergence of FLNNs for colored input signals. The basic idea is to introduce a delayless multi-sampled multiband-structured subband FLNN (DMSFLNN). In the proposed DMSFLNN, the principle of minimum disturbance is adopted in every subband with a view to improving the learning capacity of FLNNs. An investigation is made into the mean property of the subband adaptive filtering algorithm, thus establishing a stability condition of the DMSFLNN. Finally, Monte-Carlo simulation study is undertaken to verify the effectiveness of the proposed subband adaptive filtering algorithm.

For the sparse system estimation problem, the l0norm constraint normalized least mean square (l0-NLMS) can offer improved convergence performance than the standard normalized least mean square (NLMS) algorithm. However, in the l0-NLMS algorithm, both choices of the step-size and zero-attractor parameters involve the conflicting requirement of fast convergence rate and low steady-state error. In this paper, we propose the joint adaptive step-size and zero-attractor l0-NLMS (JASZ-lo-NLMS) algorithm to address this issue. The proposed algorithm can simultaneously estimate the optimal step-size and zero-attractor derived by minimizing the mean-square deviation (MSD) at each iteration. Simulations are conducted to demonstrate the efficiency of the proposed algorithm in different signal-to-noise ratio (SNR) and sparse channel environments.

In this paper, the problem of distributed estimation over adaptive networks is studied. A new diffusion normalized least mean-square (DifNLMS) algorithm is developed to tackle the considered problem. The main idea of the developed variable multi-step-size DifNLMS (VMSSDifNLMS) algorithm is to assign an individual time-varying step-size for each delivered signal in the weight adaptation step. As such, the developed algorithm is able to achieve a good tradeoff between fast convergence rate and low misadjustment. Numerical simulations are presented to show that the VMSSDifNLMS algorithm outperforms the conventional DifNLMS, VSSDifLMS, and DifLMS with optimal adaptive combination in terms of both convergence rate and steady-state error.

Recently, an adaptive exponential trigonometric functional link neural network (AETFLN) architecture has been introduced to enhance the nonlinear processing capability of the trigonometric functional link neural network (TFLN). However, it suffers from slow convergence speed, heavy computational burden, and poor robustness to noise in nonlinear acoustic echo cancellation, especially in the double-talk scenario. To reduce its computational complexity and improve its robustness against impulsive noise, this paper develops a recursive adaptive sparse exponential TFLN (RASETFLN). Based on sparse representations of functional links, the robust proportionate adaptive algorithm is deduced from the robust cost function over the RASETFLN in impulsive noise environments. Theoretical analysis shows that the proposed RASETFLN is stable under certain conditions. Finally, computer simulations illustrate that the proposed RASETFLN achieves much improved performance over the AETFLN in several nonlinear scenarios in terms of convergence rate, steady-state error, and robustness against noise.

In this paper, the average mean square deviation (MSD) analysis of the normalized least mean square (NLMS) and least mean square (LMS) algorithms is carried out for cyclostationary input signals. It is shown that the NLMS algorithm has good transient response, while the steady-state MSD of the LMS algorithm does not depend on the periodic input power. In addition, the theoretical results reveals that for cyclostationary input signals, under small step-size conditions, the LMS algorithm can offer smaller steady-state average MSD than the NLMS algorithm at the same convergence rate. That is to say, the NLMS algorithm will suffer from large steady-state MSD for cyclostationary input signals. The theoretical results are validated by computer simulations.

In this paper, we present a robust variable step-size decorrelation normalized least-mean-square (RVSSDNLMS) algorithm. A new constrained minimization problem is developed by minimizing the l2norm of the a decorrelated posteriori error signal with a constraint on the filter coefficients in the l2norm sense. Solving this minimization problem gives birth to the efficient RVSSDNLMS algorithm. The convergence performance and computational complexity of RVSSDNLMS algorithm are analyzed. Finally, simulations show that the proposed RVSSDNLMS considerably outperforms the normalized least-mean-square (NLMS), robust variable step-size NLMS, and pseudoaffine projection algorithms in terms of convergence rate and steady-state error in Gaussian noise and impulsive noise environments.

The step-size in well-known variable step-size least mean square (VSSLMS) is updated as μn+1= αμn+ γen2with , γ > 0, and μn+1is set to μminor μmaxwhen it falls below or above these lower and upper bounds, respectively. It provides fast convergence at early stages of adaptation while ensuring small steady-state misalignment. This paper considers the steady-state performance of the VSSLMS in non-Gaussian noise environments. The contribution of the paper to the VSSLMS is threefold; (1) when γ ≪ 1 - α, the VSSLMS has low steady-state misalignment. (2) when α ≪ 1, the VSSLMS achieves different steady-state misalignments for different noise distributions. (3) In theory, there are different optimal values α for different noise distributions, i.e., 0.17 (Gaussian distribution), 0.21 (Student distribution), 0.38 (Laplace distribution), 0 (Binary and Uniform distributions). Analytical results are compared with simulations and are shown to agree well.