The rising data demands of generative AI models, such as large language models (LLMs), underscore the value of utilizing edge device data in mobile computing, where federated learning (FL) provides a privacy-preserving approach via decentralized model training. To address data heterogeneity across edge devices, federated multi-view learning (FedMVL) has been proposed to improve global model performance by capturing consistency and complementarity among diverse data views. However, existing methods often assume ideal conditions and neglect data uncertainty in mobile edge devices environments. To overcome these challenges, we propose Federated Reliable Multi-view Classification (FedRMVL), a vertical FedMVL framework incorporates Subjective Logic for lightweight uncertainty quantification at local edge devices and applies the Dempster-Shafer combination rule for adaptive and reliable multi-view opinion fusion at the server. Additionally, a partial parameter-sharing strategy is introduced to address feature dimension heterogeneity during federated optimization. The effectiveness and robustness of FedRMVL are validated through theoretical analysis and extensive experiments on real-world datasets.

Federated learning is essential for enabling collaborative model training across decentralized data sources while preserving data privacy and security. This approach mitigates the risks associated with centralized data collection and addresses concerns related to data ownership and compliance. Despite significant advancements in federated learning algorithms that address communication bottlenecks and enhance privacy protection, existing works overlook the impact of differences in data feature dimensions, resulting in global models that disproportionately depend on participants with large feature dimensions. Additionally, current single-view federated learning methods fail to account for the unique characteristics of multi-view data, leading to suboptimal performance in processing such data. To address these issues, we propose a Self-expressive Hypergraph Based Federated Multi-view Learning method (FedMSGL). The proposed method leverages self-expressive character in the local training to learn uniform dimension subspace with latent sample relation. At the central side, an adaptive fusion technique is employed to generate the global model, while constructing a hypergraph from the learned global and view-specific subspace to capture intricate interconnections across views. Experiments on multi-view datasets with different feature dimensions validated the effectiveness of the proposed method.

The Cognitive Internet of Things (CIoT) represents an advanced paradigm that equips IoT devices with cognitive abilities, enabling them to perceive, communicate, learn, reason, and adapt intelligently. This forms a key enabler for next-generation industrial systems. However, the limited local computing resources of CIoT devices make it challenging to perform complex computational tasks. To address this limitation, we propose a CIoT architecture supported by Digital Twin (DT), where the DT serves as a one-to-one virtual replica of the CIoT device, functioning as a “brain” for virtual simulation, data analysis, and intelligent decision-making. We deploy the DT in the drones, which act as aerial computing servers, providing a flexible, scalable, and cost-effective solution, particularly in areas with limited infrastructure. However, selecting reliable drones and designing appropriate incentive mechanisms remain challenging. To address these issues, we propose a hierarchical game-theoretic framework. First, we develop a reputation evaluation model based on the Theory of Planned Behavior (TPB) and the subjective logic model, followed by a coalition game approach to select reliable drones. Under conditions of information asymmetry, we then design a contract theory-based incentive mechanism to encourage drone participation in DT task execution. The Age of Information (AoI) metric is used to ensure the freshness of DT tasks. Numerical results demonstrate the effectiveness of the proposed hierarchical game-theoretic framework and reputation evaluation scheme.

Hashing is essential for approximate nearest neighbor search by mapping high-dimensional data to compact binary codes. The balance between similarity preservation and code diversity is a key challenge. Existing projection-based methods often struggle with fitting binary codes to continuous space due to space heterogeneity. To address this, we propose a novel Cluster Guided Truncated Hashing (CGTH) method that uses latent cluster information to guide the binary learning process. By leveraging data clusters as anchor points and applying a truncated coding strategy, our method effectively maintains local similarity and code diversity. Experiments on benchmark datasets demonstrate that CGTH outperforms existing methods, achieving superior search performance.

Graph-based semi-supervised learning (GSSL) is a quite important technology due to its effectiveness in practice. Existing GSSL works often treat the given labels equally and ignore the unbalance importance of labels. In some inaccurate systems, the collected labels usually contain noise (noisy labels) and the methods treating labels equally suffer from the label noise. In this article, we propose a novel label-weighted learning method on graph for semi-supervised classification under label noise, which allows considering the contribution differences of labels. In particular, the label dependency of data is revealed by graph constraints. With the help of this label dependency, the proposed method develops the strategy of adaptive label weight, where label weights are assigned to labels adaptively. Accordingly, an efficient algorithm is developed to solve the proposed optimization objective, where each subproblem has a closed-form solution. Experimental results on a synthetic dataset and several real-world datasets show the advantage of the proposed method, compared to the state-of-the-art methods.

Incomplete multi-view clustering (IMC) has received considerable attention due to its flexibility in fusing the multi-view information when the view samples are partly missing. However, existing methods seldom consider the affection of the missing samples to the contributions of the views. In this paper, we propose a novel graph fusion based IMC model (SAGF_IMC) to handle this problem. Instead of directly weighting the whole view, SAGF_IMC learns the sample-level auto weight, which allows considering both the contributions of different views and the affection of the missing samples. An effective iterative algorithm is developed, together with its convergence analysis. Experiments are provided to demonstrate that SAGF_IMC is superior to the related state-of-the-art methods by using several real-world datasets.

Direct-optimization-based dictionary learning has attracted increasing attention for improving computational efficiency. However, the existing direct optimization scheme can only be applied to limited dictionary learning problems, and it remains an open problem to prove that the whole sequence obtained by the algorithm converges to a critical point of the objective function. In this article, we propose a novel direct-optimization-based dictionary learning algorithm using the minimax concave penalty (MCP) as a sparsity regularizer that can enforce strong sparsity and obtain accurate estimation. For solving the corresponding optimization problem, we first decompose the nonconvex MCP into two convex components. Then, we employ the difference of the convex functions algorithm and the nonconvex proximal-splitting algorithm to process the resulting subproblems. Thus, the direct optimization approach can be extended to a broader class of dictionary learning problems, even if the sparsity regularizer is nonconvex. In addition, the convergence guarantee for the proposed algorithm can be theoretically proven. Our numerical simulations demonstrate that the proposed algorithm has good convergence performances in different cases and robust dictionary-recovery capabilities. When applied to sparse approximations, the proposed approach can obtain sparser and less error estimation than the different sparsity regularizers in existing methods. In addition, the proposed algorithm has robustness in image denoising and key-frame extraction.

Convolutional transform learning (CTL), learning filters by minimizing the data fidelity loss function in an unsupervised way, is becoming very pervasive, resulting from keeping the best of both worlds: the benefit of unsupervised learning and the success of the convolutional neural network. There have been growing interests in developing efficient CTL algorithms. However, developing a convergent and accelerated CTL algorithm with accurate representations simultaneously with proper sparsity is an open problem. This article presents a new CTL framework with a log regularizer that can not only obtain accurate representations but also yield strong sparsity. To efficiently address our nonconvex composite optimization, we propose to employ the proximal difference of the convex algorithm (PDCA) which relies on decomposing the nonconvex regularizer into the difference of two convex parts and then optimizes the convex subproblems. Furthermore, we introduce the extrapolation technology to accelerate the algorithm, leading to a fast and efficient CTL algorithm. In particular, we provide a rigorous convergence analysis for the proposed algorithm under the accelerated PDCA. The experimental results demonstrate that the proposed algorithm can converge more stably to desirable solutions with lower approximation error and simultaneously with stronger sparsity and, thus, learn filters efficiently. Meanwhile, the convergence speed is faster than the existing CTL algorithms.

Multiview data processing has attracted sustained attention as it can provide more information for clustering. To integrate this information, one often utilizes the non-negative matrix factorization (NMF) scheme which can reduce the data from different views into the subspace with the same dimension. Motivated by the clustering performance being affected by the distribution of the data in the learned subspace, a tri-factorization-based NMF model with an embedding matrix is proposed in this article. This model tends to generate decompositions with uniform distribution, such that the learned representations are more discriminative. As a result, the obtained consensus matrix can be a better representative of the multiview data in the subspace, leading to higher clustering performance. Also, a new lemma is proposed to provide the formulas about the partial derivation of the trace function with respect to an inner matrix, together with its theoretical proof. Based on this lemma, a gradient-based algorithm is developed to solve the proposed model, and its convergence and computational complexity are analyzed. Experiments on six real-world datasets are performed to show the advantages of the proposed algorithm, with comparison to the existing baseline methods.

How to learn dimension-reduced representations of image data for clustering has been attracting much attention. Motivated by that the clustering accuracy is affected by both the prior-known label information of some of the images and the sparsity feature of the representations, we propose a non-negative matrix factorization (NMF) method with dual constraints in this paper. In our model, one constraint is used to keep the label feature and the other constraint is utilized to enhance the sparsity of the representations. Notably that these two constraints are embedded naturally into the traditional NMF model, refraining from the usage of the balance parameters which are hard to choose. Meantime, for solving the proposed model, the alternative iteration scheme is employed, and an efficient algorithm based on convex optimization is designed to conduct each iteration operation. It is proved that this algorithm achieves a nonlinear convergence rate, much faster than existing methods with linear rate. Simulation results demonstrate the advantages of the proposed method.

The introduction of edge computing into blockchain-enabled Internet of Things (IoT) for offloading computational tasks is attracting increasing attention. Computing resource trading unavoidably happens in edge-assisted IoT. However, efficient computing resource trading cannot be achieved because of the “cold start” and “long return” problems. To address these challenges, we propose to use a credit-based payment for fast computing resource trading in edge-assisted blockchain-enabled IoT; therefore, the IoT nodes can finish fast payment and frequent trading by borrowing resource coins from other IoT nodes based on their credit values. In our resource-coin loan problem, we propose an iterative double-auction-based algorithm, where a broker is introduced to solve the loan allocation problem and to determine the size of the loan each lender would provide to each borrower. Furthermore, the broker enforces specific loan pricing rules to induce the borrowers and lenders to bid truthfully. Then, the hidden privacy information could be extracted to achieve the optimal resource-coin allocation and loan pricing. The proposed algorithm can maximize the economic benefits while protecting privacy. Simulations showed that the proposed algorithm can maximize social welfare. In addition, we compared the proposed algorithm with the credit-bank-based method in terms of the satisfaction function and payments. The experimental results demonstrated that the proposed algorithm was individually rational, truthful, and budget-balanced.

Optimal computing resource allocation for edge-cloud-assisted Internet of things (IoT) in blockchain network is attracting increasing attention. Auction is a classical algorithm which guarantees that the computing resources are allocated to the buyers of the computing resource. However, the traditional auction algorithm only guarantees the revenue gains for the sellers of the computing resource. How to guarantee the seller and the buyer of the computing resource when both are willing to trade and moreover, bid truthfully, is still an open problem in computing resource trading for edge-cloud-assisted IoT. In this paper, we introduce a broker with sparse information to manage and adjust the trading market. We then propose an iterative double-sided auction scheme for computing resource trading, where the broker solves an allocation problem to determine how much computing resource is traded and designs a specific price rule to induce the buyers and sellers of the computing resource to submit bids in a truthful way. Thus, hidden information can be extracted gradually to obtain optimal computing resource allocation and trading prices. Hence, the proposed algorithm can achieve the maximum social welfare meanwhile protecting the privacies of the buyers and the sellers. Our theoretical analysis and simulations demonstrate that the proposed algorithm is efficient, i.e., it achieves the maximum social welfare. In addition, the proposed algorithm can provide effective trading strategies for the buyers and sellers of the computing resource, leading to the proposed algorithm satisfying incentive compatibility, individual rationality, and budget balance.

Nonnegative matrix factorization (NMF) is an emerging tool for meaningful low-rank matrix representation. In NMF, explicit constraints are usually required, such that NMF generates desired products (or factorizations), especially when the products have significant sparseness features. It is known that the ability of NMF in learning sparse representation can be improved by embedding a smoothness factor between the products. Motivated by this result, we propose an adaptive nonsmooth NMF (Ans-NMF) method in this paper. In our method, the embedded factor is obtained by using a data-related approach, so it matches well with the underlying products, implying a superior faithfulness of the representations. Besides, due to the usage of an adaptive selection scheme to this factor, the sparseness of the products can be separately constrained, leading to wider applicability and interpretability. Furthermore, since the adaptive selection scheme is processed through solving a series of typical linear programming problems, it can be easily implemented. Simulations using computer-generated data and real-world data show the advantages of the proposed Ans-NMF method over the state-of-the-art methods.

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

A novel image encryption scheme based on compressed sensing and blind source separation is proposed in this work, where there is no statistical requirement to plaintexts. In the proposed method, for encryption, the plaintexts and keys are mixed with each other using a underdetermined matrix first, and then compressed under a project matrix. As a result, it forms a difficult underdetermined blind source separation (UBSS) problem without statistical features of sources. Regarding the decryption, given the keys, a new model will be constructed, which is solvable under compressed sensing (CS) frame. Due to the usage of CS technology, the plaintexts are compressed into the data with smaller size when they are encrypted. Meanwhile, they can be decrypted from parts of the received data packets and thus allows to lose some packets. This is beneficial for the proposed encryption method to suit practical communication systems. Simulations are given to illustrate the availability and the superiority of our method.

This paper presents a projection pursuit (PP) based method for blind separation of nonnegative sources. First, the available observation matrix is mapped to construct a new mixing model, in which the inaccessible source matrix is normalized to be column-sum-to-1. Then, the PP method is proposed to solve this new model, where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions, which leads to the recovery of the sources. The proposed method is much faster than Chan's method, which has similar assumptions to ours, due to the usage of optimal projection. It is also more advantageous in separating cross-correlated sources than the independence- and uncorrelation-based methods, as it does not employ any statistical information of the sources. Furthermore, the new method does not require the mixing matrix to be nonnegative. Simulation results demonstrate the superior performance of our method.

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Nonnegative matrix factorization (NMF) is a widely used method for blind spectral unmixing (SU), which aims at obtaining the endmembers and corresponding fractional abundances, knowing only the collected mixing spectral data. It is noted that the abundance may be sparse (i.e., the endmembers may be with sparse distributions) and sparse NMF tends to lead to a unique result, so it is intuitive and meaningful to constrain NMF with sparseness for solving SU. However, due to the abundance sum-to-one constraint in SU, the traditional sparseness measured by L0/L1-norm is not an effective constraint any more. A novel measure (termed as S-measure) of sparseness using higher order norms of the signal vector is proposed in this paper. It features the physical significance. By using the S-measure constraint (SMC), a gradient-based sparse NMF algorithm (termed as NMF-SMC) is proposed for solving the SU problem, where the learning rate is adaptively selected, and the endmembers and abundances are simultaneously estimated. In the proposed NMF-SMC, there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior. Yet, it does not require the preprocessing of dimension reduction in which some useful information may be lost. Experiments based on synthetic mixtures and real-world images collected by AVIRIS and HYDICE sensors are performed to evaluate the validity of the proposed method.

Nonnegative matrix factorization (NMF) with minimum-volume-constraint (MVC) is exploited in this paper. Our results show that MVC can actually improve the sparseness of the results of NMF. This sparseness is L(0)-norm oriented and can give desirable results even in very weak sparseness situations, thereby leading to the significantly enhanced ability of learning parts of NMF. The close relation between NMF, sparse NMF, and the MVC_NMF is discussed first. Then two algorithms are proposed to solve the MVC_NMF model. One is called quadratic programming_MVC_NMF (QP_MVC_NMF) which is based on quadratic programming and the other is called negative glow_MVC_NMF (NG_MVC_NMF) because it uses multiplicative updates incorporating natural gradient ingeniously. The QP_MVC_NMF algorithm is quite efficient for small-scale problems and the NG_MVC_NMF algorithm is more suitable for large-scale problems. Simulations show the efficiency and validity of the proposed methods in applications of blind source separation and human face images analysis.

In blind source separation, many methods have been proposed to estimate the mixing matrix by exploiting sparsity. However, they often need to know the source number a priori, which is very inconvenient in practice. In this paper, a new method, namely nonlinear projection and column masking (NPCM), is proposed to estimate the mixing matrix. A major advantage of NPCM is that it does not need any knowledge of the source number. In NPCM, the objective function is based on a nonlinear projection and its maxima just correspond to the columns of the mixing matrix. Thus a column can be estimated first by locating a maximum and then deflated by a masking operation. This procedure is repeated until the evaluation of the objective function decreases to zero dramatically. Thus the mixing matrix and the number of sources are estimated simultaneously. Because the masking procedure may result in some small and useless local maxima, particle swarm optimization (PSO) is introduced to optimize the objective function. Feasibility and efficiency of PSO are also discussed. Comparative experimental results show the efficiency of NPCM, especially in the cases where the number of sources is unknown and the sources are relatively less sparse.

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

Blind source separation (BSS) has been widely discussed in many real applications. Recently, under the assumption that both of the sources and the mixing matrix are nonnegative, Wang develop an amazing BSS method by using volume maximization. However, the algorithm that they have proposed can guarantee the nonnegativities of the sources only, but cannot obtain a nonnegative mixing matrix necessarily. In this letter, by introducing additional constraints, a method for fully nonnegative constrained iterative volume maximization (FNCIVM) is proposed. The result is with more interpretation, while the algorithm is based on solving a single linear programming problem. Numerical experiments with synthetic signals and real-world images are performed, which show the effectiveness of the proposed method.

This letter discusses blind separability based on temporal predictability (Stone, 2001 ; Xie, He, & Fu, 2005 ). Our results show that the sources are separable using the temporal predictability method if and only if they have different temporal structures (i.e., autocorrelations). Consequently, the applicability and limitations of the temporal predictability method are clarified. In addition, instead of using generalized eigendecomposition, we suggest using joint approximate diagonalization algorithms to improve the robustness of the method. A new criterion is presented to evaluate the separation results. Numerical simulations are performed to demonstrate the validity of the theoretical results.

To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.