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As an emerging decentralized machine learning technique, federated learning organizes collaborative training and preserves the privacy and security of participants. However, untrustworthy devices, typically Byzantine attackers, pose a significant challenge to federated learning since they can upload malicious parameters to corrupt the global model. To defend against such attacks, we propose a novel robust aggregation method-maximum correntropy aggregation (MCA), which applies the maximum correntropy criterion (MCC) to derive a central value from parameters. Different from the previous use of MCC for denoising, we utilize it as a similarity metric to measure parameter distribution and aggregate a robust center. Correntropy in MCC, with all even-order moments of the parameter, contains high-order statistical properties, which allows for a comprehensive capture of parameter characteristics, thus helping to prevent interference from attackers. Meanwhile, correntropy extracts information from the parameters themselves, without requiring the proportion of malicious attackers. Through the fixed-point iteration, we solve the optimization objective, demonstrating the linear convergence of the iteration formula. Theoretical analysis reveals the robustness aggregation property of MCA and the error bound between MCA and the global optimal solution, with linear convergence to the optimal solution neighborhood. By performing independent identically distribution (IID) and non-IID experiments on three different datasets, we show that MCA exhibits significant robustness under mainstream attacks, whereas other methods cannot withstand all of them.

A novel model called error loss network (ELN) is proposed to build an error loss function for supervised learning. The ELN is similar in structure to a radial basis function (RBF) neural network, but its input is an error sample and output is a loss corresponding to that error sample. That means the nonlinear input-output mapper of the ELN creates an error loss function. The proposed ELN provides a unified model for a large class of error loss functions, which includes some information-theoretic learning (ITL) loss functions as special cases. The activation function, weight parameters, and network size of the ELN can be predetermined or learned from the error samples. On this basis, we propose a new machine learning paradigm where the learning process is divided into two stages: first, learning a loss function using an ELN; second, using the learned loss function to continue to perform the learning. Experimental results are presented to demonstrate the desirable performance of the new method.

Due to its high computational complexity, graph-based methods have limited applicability in large-scale multiview clustering tasks. To address this issue, many accelerated algorithms, especially anchor graph-based methods and indicator learning-based methods, have been developed and made a great success. Nevertheless, since the restrictions of the optimization strategy, these accelerated methods still need to approximate the discrete graph-cutting problem to a continuous spectral embedding problem and utilize different discretization strategies to obtain discrete sample categories. To avoid the loss of effectiveness and efficiency caused by the approximation and discretization, we establish a discrete fast multiview anchor graph clustering (FMAGC) model that first constructs an anchor graph of each view and then generates a discrete cluster indicator matrix by solving the discrete multiview graph-cutting problem directly. Since the gradient descent-based method makes it hard to solve this discrete model, we propose a fast coordinate descent-based optimization strategy with linear complexity to solve it without approximating it as a continuous one. Extensive experiments on widely used normal and large-scale multiview datasets show that FMAGC can improve clustering effectiveness and efficiency compared to other state-of-the-art baselines.

This article proposes a novel low-rank matrix factorization model for semisupervised image clustering. In order to alleviate the negative effect of outliers, the maximum correntropy criterion (MCC) is incorporated as a metric to build the model. To utilize the label information to improve the clustering results, a constraint graph learning framework is proposed to adaptively learn the local structure of the data by considering the label information. Furthermore, an iterative algorithm based on Fenchel conjugate (FC) and block coordinate update (BCU) is proposed to solve the model. The convergence properties of the proposed algorithm are analyzed, which shows that the algorithm exhibits both objective sequential convergence and iterate sequential convergence. Experiments are conducted on six real-world image datasets, and the proposed algorithm is compared with eight state-of-the-art methods. The results show that the proposed method can achieve better performance in most situations in terms of clustering accuracy and mutual information.

Brain-inspired computing technique presents a promising approach to prompt the rapid development of artificial general intelligence (AGI). As one of the most critical aspects, spiking neural networks (SNNs) have demonstrated superiority for AGI, such as low power consumption. Effective training of SNNs with high generalization ability, high robustness, and low power consumption simultaneously is a significantly challenging problem for the development and success of applications of spike-based machine intelligence. In this research, we present a novel and flexible learning framework termed high-order spike-based information bottleneck (HOSIB) leveraging the surrogate gradient technique. The presented HOSIB framework, including second-order and third-order formation, i.e., second-order information bottleneck (SOIB) and third-order information bottleneck (TOIB), comprehensively explores the common latent architecture and the spike-based intrinsic information and discards the superfluous information in the data, which improves the generalization capability and robustness of SNN models. Specifically, HOSIB relies on the information bottleneck (IB) principle to prompt the sparse spike-based information representation and flexibly balance its exploitation and loss. Extensive classification experiments are conducted to empirically show the promising generalization ability of HOSIB. Furthermore, we apply the SOIB and TOIB algorithms in deep spiking convolutional networks to demonstrate their improvement in robustness with various categories of noise. The experimental results prove the HOSIB framework, especially TOIB, can achieve better generalization ability, robustness and power efficiency in comparison with the current representative studies.

One of the hottest topics in unsupervised learning is how to efficiently and effectively cluster large amounts of unlabeled data. To address this issue, we propose an orthogonal conceptual factorization (OCF) model to increase clustering effectiveness by restricting the degree of freedom of matrix factorization. In addition, for the OCF model, a fast optimization algorithm containing only a few low-dimensional matrix operations is given to improve clustering efficiency, as opposed to the traditional CF optimization algorithm, which involves dense matrix multiplications. To further improve the clustering efficiency while suppressing the influence of the noises and outliers distributed in real-world data, an efficient correntropy-based clustering algorithm (ECCA) is proposed in this article. Compared with OCF, an anchor graph is constructed and then OCF is performed on the anchor graph instead of directly performing OCF on the original data, which can not only further improve the clustering efficiency but also inherit the advantages of the high performance of spectral clustering. In particular, the introduction of the anchor graph makes ECCA less sensitive to changes in data dimensions and still maintains high efficiency at higher data dimensions. Meanwhile, for various complex noises and outliers in real-world data, correntropy is introduced into ECCA to measure the similarity between the matrix before and after decomposition, which can greatly improve the clustering effectiveness and robustness. Subsequently, a novel and efficient half-quadratic optimization algorithm was proposed to quickly optimize the ECCA model. Finally, extensive experiments on different real-world datasets and noisy datasets show that ECCA can archive promising effectiveness and robustness while achieving tens to thousands of times the efficiency compared with other state-of-the-art baselines.

Multichannel electroencephalogram (EEG) is an array signal that represents brain neural networks and can be applied to characterize information propagation patterns for different emotional states. To reveal these inherent spatial graph features and increase the stability of emotion recognition, we propose an effective emotion recognition model that performs multicategory emotion recognition with multiple emotion-related spatial network topology patterns (MESNPs) by learning discriminative graph topologies in EEG brain networks. To evaluate the performance of our proposed MESNP model, we conducted single-subject and multisubject four-class classification experiments on two public datasets, MAHNOB-HCI and DEAP. Compared with existing feature extraction methods, the MESNP model significantly enhances the multiclass emotional classification performance in the single-subject and multisubject conditions. To evaluate the online version of the proposed MESNP model, we designed an online emotion monitoring system. We recruited 14 participants to conduct the online emotion decoding experiments. The average online experimental accuracy of the 14 participants was 84.56%, indicating that our model can be applied in affective brain-computer interface (aBCI) systems. The offline and online experimental results demonstrate that the proposed MESNP model effectively captures discriminative graph topology patterns and significantly improves emotion classification performance. Moreover, the proposed MESNP model provides a new scheme for extracting features from strongly coupled array signals.

The minimum error entropy (MEE) criterion is a powerful approach for non-Gaussian signal processing and robust machine learning. However, the instantiation of MEE on robust classification is a rather vacancy in the literature. The original MEE purely focuses on minimizing Renyi's quadratic entropy of the prediction errors, which could exhibit inferior capability in noisy classification tasks. To this end, we analyze the optimal error distribution with adverse outliers and introduce a specific codebook for restriction, which optimizes the error distribution toward the optimal case. Half-quadratic-based optimization and convergence analysis of the proposed learning criterion, called restricted MEE (RMEE), are provided. The experimental results considering logistic regression and extreme learning machine on synthetic data and UCI datasets, respectively, are presented to demonstrate the superior robustness of RMEE. Furthermore, we evaluate RMEE on a noisy electroencephalogram dataset, so as to strengthen its practical impact.

Perturbation has a positive effect, as it contributes to the stability of neural systems through adaptation and robustness. For example, deep reinforcement learning generally engages in exploratory behavior by injecting noise into the action space and network parameters. It can consistently increase the agent's exploration ability and lead to richer sets of behaviors. Evolutionary strategies also apply parameter perturbations, which makes network architecture robust and diverse. Our main concern is whether the notion of synaptic perturbation introduced in a spiking neural network (SNN) is biologically relevant or if novel frameworks and components are desired to account for the perturbation properties of artificial neural systems. In this work, we first review part of the locality-sensitive hashing (LSH) of similarity search, the FLY algorithm, as recently published in Science, and propose an improved architecture, time-shifted spiking LSH (TS-SLSH), with the consideration of temporal perturbations of the firing moments of spike pulses. Experiment results show promising performance of the proposed method and demonstrate its generality to various spiking neuron models. Therefore, we expect temporal perturbation to play an active role in SNN performance.

Deep hashing methods have shown their superiority to traditional ones. However, they usually require a large amount of labeled training data for achieving high retrieval accuracies. We propose a novel transductive semisupervised deep hashing (TSSDH) method which is effective to train deep convolutional neural network (DCNN) models with both labeled and unlabeled training samples. TSSDH method consists of the following four main ingredients. First, we extend the traditional transductive learning (TL) principle to make it applicable to DCNN-based deep hashing. Second, we introduce confidence levels for unlabeled samples to reduce adverse effects from uncertain samples. Third, we employ a Gaussian likelihood loss for hash code learning to sufficiently penalize large Hamming distances for similar sample pairs. Fourth, we design the large-margin feature (LMF) regularization to make the learned features satisfy that the distances of similar sample pairs are minimized and the distances of dissimilar sample pairs are larger than a predefined margin. Comprehensive experiments show that the TSSDH method can produce superior image retrieval accuracies compared to the representative semisupervised deep hashing methods under the same number of labeled training samples.

Kernel-based extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has achieved outstanding performance in addressing various regression and classification problems. Compared with the basic ELM, KELM has a better generalization ability owing to no needs of the number of hidden nodes given beforehand and random projection mechanism. Since KELM is derived under the minimum mean square error (MMSE) criterion for the Gaussian assumption of noise, its performance may deteriorate under the non-Gaussian cases, seriously. To improve the robustness of KELM, this article proposes a mixture correntropy-based KELM (MC-KELM), which adopts the recently proposed maximum mixture correntropy criterion as the optimization criterion, instead of using the MMSE criterion. In addition, an online sequential version of MC-KELM (MCOS-KELM) is developed to deal with the case that the data arrive sequentially (one-by-one or chunk-by-chunk). Experimental results on regression and classification data sets are reported to validate the performance superiorities of the new methods.

As an effective and efficient discriminative learning method, broad learning system (BLS) has received increasing attention due to its outstanding performance in various regression and classification problems. However, the standard BLS is derived under the minimum mean square error (MMSE) criterion, which is, of course, not always a good choice due to its sensitivity to outliers. To enhance the robustness of BLS, we propose in this work to adopt the maximum correntropy criterion (MCC) to train the output weights, obtaining a correntropy-based BLS (C-BLS). Due to the inherent superiorities of MCC, the proposed C-BLS is expected to achieve excellent robustness to outliers while maintaining the original performance of the standard BLS in the Gaussian or noise-free environment. In addition, three alternative incremental learning algorithms, derived from a weighted regularized least-squares solution rather than pseudoinverse formula, for C-BLS are developed. With the incremental learning algorithms, the system can be updated quickly without the entire retraining process from the beginning when some new samples arrive or the network deems to be expanded. Experiments on various regression and classification data sets are reported to demonstrate the desirable performance of the new methods.

Concept factorization (CF) has shown its great advantage for both clustering and data representation and is particularly useful for image representation. Compared with nonnegative matrix factorization (NMF), CF can be applied to data containing negative values. However, the performance of CF method and its extensions will degenerate a lot due to the negative effects of outliers, and CF is an unsupervised method that cannot incorporate label information. In this article, we propose a novel CF method, with a novel model built based on the maximum correntropy criterion (MCC). In order to capture the local geometry information of data, our method integrates the robust adaptive embedding and CF into a unified framework. The label information is utilized in the adaptive learning process. Furthermore, an iterative strategy based on the accelerated block coordinate update is proposed. The convergence property of the proposed method is analyzed to ensure that the algorithm converges to a reliable solution. The experimental results on four real-world image data sets show that the new method can almost always filter out the negative effects of the outliers and outperform several state-of-the-art image representation methods.

The distributions of input data are very important for learning machines, such as the convex universal learning machines (CULMs). The CULMs are a family of universal learning machines with convex optimization. However, the computational complexity is a crucial problem in CULMs, because the dimension of the nonlinear mapping layer (the hidden layer) of the CULMs is usually rather large in complex system modeling. In this article, we propose an efficient quantization method called Probability density Rank-based Quantization (PRQ) to decrease the computational complexity of CULMs. The PRQ ranks the data according to the estimated probability densities and then selects a subset whose elements are equally spaced in the ranked data sequence. We apply the PRQ to kernel ridge regression (KRR) and random Fourier feature recursive least squares (RFF-RLS), which are two typical algorithms of CULMs. The proposed method not only keeps the similarity of data distribution between the code book and data set but also reduces the computational cost by using the kd-tree. Meanwhile, for a given data set, the method yields deterministic quantization results, and it can also exclude the outliers and avoid too many borders in the code book. This brings great convenience to practical applications of the CULMs. The proposed PRQ is evaluated on several real-world benchmark data sets. Experimental results show satisfactory performance of PRQ compared with some state-of-the-art methods.

The extreme learning machine (ELM) has attracted much attention over the past decade due to its fast learning speed and convincing generalization performance. However, there still remains a practical issue to be approached when applying the ELM: the randomly generated hidden node parameters without tuning can lead to the hidden node outputs being nonuniformly distributed, thus giving rise to poor generalization performance. To address this deficiency, a novel activation function with an affine transformation (AT) on its input is introduced into the ELM, which leads to an improved ELM algorithm that is referred to as an AT-ELM in this paper. The scaling and translation parameters of the AT activation function are computed based on the maximum entropy principle in such a way that the hidden layer outputs approximately obey a uniform distribution. Application of the AT-ELM algorithm in nonlinear function regression shows its robustness to the range scaling of the network inputs. Experiments on nonlinear function regression, real-world data set classification, and benchmark image recognition demonstrate better performance for the AT-ELM compared with the original ELM, the regularized ELM, and the kernel ELM. Recognition results on benchmark image data sets also reveal that the AT-ELM outperforms several other state-of-the-art algorithms in general.

Comparing with traditional learning criteria, such as mean square error, the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyi's entropy estimator, called information potential (IP), is a popular MEE cost in information theoretic learning. The computational complexity of IP is, however, quadratic in terms of sample number due to double summation. This creates the computational bottlenecks, especially for large-scale data sets. To address this problem, in this paper, we propose an efficient quantization approach to reduce the computational burden of IP, which decreases the complexity from O(N 2 ) to O(MN) with M << N . The new learning criterion is called the quantized MEE (QMEE). Some basic properties of QMEE are presented. Illustrative examples with linear-in-parameter models are provided to verify the excellent performance of QMEE.

This paper investigates the online recorded data-based composite neural control of uncertain strict-feedback systems using the backstepping framework. In each step of the virtual control design, neural network (NN) is employed for uncertainty approximation. In previous works, most designs are directly toward system stability ignoring the fact how the NN is working as an approximator. In this paper, to enhance the learning ability, a novel prediction error signal is constructed to provide additional correction information for NN weight update using online recorded data. In this way, the neural approximation precision is highly improved, and the convergence speed can be faster. Furthermore, the sliding mode differentiator is employed to approximate the derivative of the virtual control signal, and thus, the complex analysis of the backstepping design can be avoided. The closed-loop stability is rigorously established, and the boundedness of the tracking error can be guaranteed. Through simulation of hypersonic flight dynamics, the proposed approach exhibits better tracking performance.

The minimum error entropy (MEE) is an important and highly effective optimization criterion in information theoretic learning (ITL). For regression problems, MEE aims at minimizing the entropy of the prediction error such that the estimated model preserves the information of the data generating system as much as possible. In many real world applications, the MEE estimator can outperform significantly the well-known minimum mean square error (MMSE) estimator and show strong robustness to noises especially when data are contaminated by non-Gaussian (multimodal, heavy tailed, discrete valued, and so on) noises. In this brief, we present some theoretical results on the robustness of MEE. For a one-parameter linear errors-in-variables (EIV) model and under some conditions, we derive a region that contains the MEE solution, which suggests that the MEE estimate can be very close to the true value of the unknown parameter even in presence of arbitrarily large outliers in both input and output variables. Theoretical prediction is verified by an illustrative example.

Based on the knowledge that input data distribution is important for learning, a data density-dependent quantization scheme (DQS) is proposed for sparse input data representation. The usefulness of the representation scheme is demonstrated by using it as a data preprocessing unit attached to the well-known least squares support vector machine (LS-SVM) for application on big data sets. Essentially, the proposed DQS adopts a single shrinkage threshold to obtain a simple quantization scheme, which adapts its outputs to input data density. With this quantization scheme, a large data set is quantized to a small subset where considerable sample size reduction is generally obtained. In particular, the sample size reduction can save significant computational cost when using the quantized subset for feature approximation via the Nyström method. Based on the quantized subset, the approximated features are incorporated into LS-SVM to develop a data density-dependent quantized LS-SVM (DQLS-SVM), where an analytic solution is obtained in the primal solution space. The developed DQLS-SVM is evaluated on synthetic and benchmark data with particular emphasis on large data sets. Extensive experimental results show that the learning machine incorporating DQS attains not only high computational efficiency but also good generalization performance.

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

In a recent paper, we developed a novel quantized kernel least mean square algorithm, in which the input space is quantized (partitioned into smaller regions) and the network size is upper bounded by the quantization codebook size (number of the regions). In this paper, we propose the quantized kernel least squares regression, and derive the optimal solution. By incorporating a simple online vector quantization method, we derive a recursive algorithm to update the solution, namely the quantized kernel recursive least squares algorithm. The good performance of the new algorithm is demonstrated by Monte Carlo simulations.

In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.