Domain adaptive retrieval aims to transfer knowledge from a labeled source domain to an unlabeled target domain, enabling effective retrieval while mitigating domain discrepancies. However, existing methods encounter several fundamental limitations: 1) neglecting class-level semantic alignment and excessively pursuing pair-wise sample alignment; 2) lacking either pseudo-label reliability consideration or geometric guidance for assessing label correctness; 3) directly quantizing original features affected by domain shift, undermining the quality of learned hash codes. In view of these limitations, we propose Prototype-based Semantic Consistency Alignment (PSCA), a two-stage framework for effective domain adaptive retrieval. In the first stage, a set of orthogonal prototypes directly establishes class-level semantic connections, maximizing inter-class separability while gathering intra-class samples. During the prototype learning, geometric proximity provides a reliability indicator for semantic consistency alignment through adaptive weighting of pseudo-label confidences. The resulting membership matrix and prototypes facilitate feature reconstruction, ensuring quantization on reconstructed rather than original features, thereby improving subsequent hash coding quality and seamlessly connecting both stages. In the second stage, domain-specific quantization functions process the reconstructed features under mutual approximation constraints, generating unified binary hash codes across domains. Extensive experiments validate PSCA's superior performance across multiple datasets.

In recent years, numerous hashing techniques have been developed to boost efficient cross-modal retrieval. Once a retrieval model is deployed, the hash code length is fixed to achieve optimal performance. To address different retrieval scenarios while maintaining retrieval accuracy, a common approach is to redesign and retrain the original model with different hash code length. However, this retraining process can increase the training load and may lead to worse results. To tackle these challenges, we present Regenerated Cross-Modal Hashing (RCMH), a novel cross-modal hashing framework designed to improve the quality of existing hash codes and convert them to arbitrary lengths with high efficiency. First, we clip or pad the existing hash codes to initialize them with the target length, under the supervision of the similarity matrix generated by the augmented label information. Second, we introduce a linear-nonlinear competitive reconstruction approach to reduce the semantic gaps and further capture the deeper relationships from linear image features and nonlinear text features. In this way, each pair of samples is compared and selected to obtain reconstructed binary codes that can preserve the modality-specific properties. Finally, to reduce the training costs caused by iterations of variables, the regenerate hashing term is utilized to regenerate final hash codes with the reconstructed binary codes while preserving the information from the existing hash codes without iterative optimization. Notably, RCMH can be integrated with existing state-of-the-art (SOTA) methods with robustness, helping them to adjust the hash code length and achieve better retrieval performance.

This article addresses the predefined-time optimal motion control problem of an autonomous surface vehicle (ASV) with disturbances under dynamic self-triggered frameworks via reinforcement learning (RL). Initially, to eliminate the influence of disturbance on the ASV, a predefined-time second-order integral sliding mode control (SOISM) strategy is formulated by establishing a novel integral sliding mode (ISM) function and a terminal sliding mode function. Subsequently, a predefined-time approximate optimal motion (AOM) control strategy is further developed to ensure the ASV maintains a stable state. Furthermore, a single critic network is used to obtain an approximate solution of the Hamilton-Jacobi-Bellman (HJB) equation. The above two strategies are established under the dynamic self-triggered framework, which relies on the current information to predict the next updating time, effectively reducing the computational and communication burden while avoiding the continuous monitoring of the ASV state. In the theoretical analysis, the main challenges lie in the design of Lyapunov functions and triggered conditions to ensure the stability of the sliding mode dynamics and the disturbed ASV. By applying the Lyapunov stability principle and designing two novel Lyapunov functions and triggered conditions that both contain dynamic variables, we demonstrate that the developed control strategies can ensure the stability within the specified time frame. Ultimately, simulation results verify the efficacy of the proposed motion control approach.

The task of predicting product quality in injection molding aims to forecast quality based on the manufacturing process parameters. Previous works have gravitated toward constructing ANFIS model integrated with heuristic algorithms to relocate the model to the optimal position. However, this constrains the model's own capacity for learning by relying on the heuristic algorithm and depends on time-consuming and costly industrial data. To address these issues, we pro pose an Evolution-ANFIS (EANFIS) framework incorporating the KL-Divergence diffusion model, Self-Evolutionary Search (SES), Neuron Evolutionary Iteration (NEI) and Space Pre Optimization (SPO) modules. Our method is divided into two parts: data generation and model learning. The KL-Divergence diffusion model aligns the distribution between pseudo-sample and original-sample to complete the first stage. The latter stage utilizes multiple ANFIS sub-models and enables these models to autonomously learn deep representations through diverse strategies. Specifically, SES facilitates deep-level feature extraction by employing arc-length strategy to steer sub-models toward optimal feature representations. Furthermore, NEI and SPO are proposed to prevent learning bias, which assists each sub model in escaping suboptimal dilemmas and focuses on learning fine-grained feature mapping. Extensive experiments validate the superiority of our EANFIS approach, even outperforming certain machine learning counterparts. The code is available at https://github.com/hejk/EANFIS.

Zero-shot anomaly detection (ZSAD) is a challenging task that aims to detect anomalies in images without any prior knowledge of the anomaly classes. This task is especially difficult because anomalies are rare, diverse, and often manifest differently across domains, making it hard for models to generalize when training data is scarce or unavailable. Recently, vision-language models (VLMs), such as CLIP, have shown great potential in ZSAD, but they often struggle to adapt to unseen domains due to the lack of domain-aware knowledge. To address these challenges, we propose the Domain Adaptation CLIP (DACLIP), a novel approach that adapts domain-aware knowledge to the VLM. Specifically, DACLIP leverages a Domain-Aware Knowledge Adaptation (DAKA) strategy to enhance CLIP for ZSAD across different domains. The DAKA strategy comprises multiple experts that specialize in target domains, enabling the model to dynamically select and combine specialized experts tailored to anomaly characteristics, thus improving its ability to generalize and detect a wide range of anomalies. Furthermore, we introduce learnable domain-aware prompts that are jointly learned by and injected into both the CLIP encoders (visual and text) and the DAKA modules. This dual-pathway learning enables the model to capture domain-specific features at multiple levels of the architecture, allowing for more effective adaptation to new domains and anomaly types. We evaluate our approach on several benchmark datasets spanning industrial and medical domains. Extensive experiments demonstrate that DACLIP consistently outperforms state-of-the-art methods in ZSAD, achieving significant improvements in both image-level and pixel-level anomaly detection tasks.

Reconstruction-based methods have achieved excellent performance in anomaly detection. Diffusion models are considered highly suitable for anomaly detection tasks due to their strong ability in reconstruction. Nevertheless, diffusion-based models require the reconstruction of noise features, which may lack the capacity for fine-grained feature reconstruction and fail to provide adequate semantic information for reconstruction guidance. To solve the aforementioned problems, this paper proposes a Fine-Grained Enhancement Convolutional Diffusion Transformer Anomaly Detection (FECDTAD) framework for multi-class anomaly detection. The core model of the proposed framework is the Fine-Grained Enhancement Convolutional Denoising Transformer (FECDT), which employs the diffusion transformer paradigm. To enhance fine-grained reconstruction in the diffusion process, the FECDTAD adopts a series of feature information fusion strategies. Specifically, to enhance both fine-grained perception and global understanding, the FECDT model employs a simple feature fusion module to integrate shallow-level and deep-level features extracted from a pre-trained vision transformer. To enhance the capacity for fine-grained feature reconstruction, the FECDT integrates local and global information via a CNN-Transformer architecture. Moreover, to provide guidance for the reconstruction of anomalous areas, semantic information is propagated into the FECDT through a Cross-Attention module. Experimental results demonstrate that the proposed method is effective and can surpass the state-of-the-art methods.

Partial Multi-Label Learning (PML) deals with a practical scenario where each instance is associated with a set of candidate labels, among which only a subset corresponds to the ground-truth labels while the others are unrelated. Existing PML methods typically employ label association recovery as a structural disambiguation strategy to identify credible labels. However, these methods attempt to recover associations directly from candidate labels, which leads to unreliable disambiguation due to the distorted label structures. To this end, this paper proposes a novel PML method via dual label association recovery (PML-DLAR).The essential strategy is to first eliminate the spurious correlations in label space before recovering dual label associations. Specifically, a biorthogonal transformation is employed to decouple the instance-level and label-level association structures affected by noisy labels. Subsequently, reliable instance-level associations are reconstructed through global geometric structure alignment between feature and pseudo-label spaces. Finally, class specific feature representations are constructed through class prototypes to guide label-level semantic association recovery in label space. Comprehensive experiments validate the superior performance of PML-DLAR over state-of-the-art methods.

Recent text-to-image (T2I) diffusion models have demonstrated remarkable capabilities in visual synthesis, yet their performance heavily relies on the quality of input prompts. However, optimizing discrete prompts remains challenging because the discrete nature of tokens prevents the direct application of the gradient descent method and the vast search space of possible token combinations. As a result, existing approaches either suffer from quantization errors when employing continuous optimization techniques or be- come trapped in local optima due to coordinate-wise greedy search. In this paper, we propose STEPS, a novel Sequential probability Tensor Estimation approach for hard Prompt Search. Our method reformulates discrete prompt optimization as a sequential probability tensor estimation problem, leveraging the inherent low-rank characteristics to address the curse of dimensionality. To further improve the computational efficiency, we develop a memory-bounded sampling approach that shrinks the prompt space without the iteration step dependency while preserving sequential optimization dynamics. Extensive experiments on various public datasets demonstrate that our method consistently outperforms existing approaches in T2I generation, cross-model prompt transferability, and harmful prompt optimization, validating the effectiveness of the proposed framework.

Class-Incremental Learning (CIL) has gained considerable attention due to its capacity to accommodate new classes during learning. Replay-based methods demonstrate state-of-the-art performance in CIL but suffer from high memory consumption to save a set of old exemplars for revisiting. To address this challenge, many memory-efficient replay methods have been developed by exploiting image compression techniques. However, the gains are often bittersweet when pixel-level compression methods are used. Here, we present a simple yet efficient approach that employs tensor decomposition to address these limitations. This method fully exploits the low intrinsic dimensionality and pixel correlation of images to achieve high compression efficiency while preserving sufficient discriminative information, significantly enhancing performance. We also introduce a hybrid exemplar selection strategy to improve the representativeness and diversity of stored exemplars. Extensive experiments across datasets with varying resolutions consistently demonstrate that our approach substantially boosts the performance of baseline methods, showcasing strong generalization and robustness.

Tensor regression is a powerful tool for analyzing complex multi-dimensional data in fields such as neuroimaging and spatiotemporal analysis, but its effectiveness is often hindered by insufficient sample sizes. To overcome this limitation, we adopt a transfer learning strategy that leverages knowledge from related source tasks to improve performance in data-scarce target tasks. This approach, however, introduces additional challenges including model shifts, covariate shifts, and decentralized data management. We propose the Low-Rank Tensor Transitions (LoRT) framework, which incorporates a novel fusion regularizer and a two-step refinement to enable robust adaptation while preserving low-tubal-rank structure. To support decentralized scenarios, we extend LoRT to D-LoRT, a distributed variant that maintains statistical efficiency with minimal communication overhead. Theoretical analysis and experiments on tensor regression tasks, including compressed sensing and completion, validate the robustness and versatility of the proposed methods. These findings indicate the potential of LoRT as a robust method for tensor regression in settings with limited data and complex distributional structures.

As the length of input text increases, the key-value (KV) cache in LLMs imposes prohibitive GPU memory costs and limits long-context inference on resource constrained devices. Existing approaches, such as KV quantization and pruning, reduce memory usage but suffer from numerical precision loss or suboptimal retention of key-value pairs. In this work, Low Rank Query and Key attention (LRQK) is introduced, a two-stage framework that jointly decomposes full-precision query and key matrices into compact rank-\(r\) factors during the prefill stage, and then employs these low-dimensional projections to compute proxy attention scores in \(\mathcal{O}(lr)\) time at each decode step. By selecting only the top-\(k\) tokens and a small fixed set of recent tokens, LRQK employs a mixed GPU-CPU cache with a hit-and-miss mechanism where only missing full-precision KV pairs are transferred, thereby preserving exact attention outputs while reducing CPU-GPU data movement. Extensive experiments on the RULER and LongBench benchmarks with LLaMA-3-8B and Qwen2.5-7B demonstrate that LRQK matches or surpasses leading sparse-attention methods in long context settings, while delivering significant memory savings with minimal accuracy loss. Our code is available at \url{https://github.com/tenghuilee/LRQK}.

Label prototype learning has emerged as an effective paradigm in Partial Multi-Label Learning (PML), providing a distinctive framework for modeling structured representations of label semantics while naturally filtering noise through prototype-based label confidence estimation. However, existing prototype-based methods face a critical limitation: class prototypes are the biased estimates due to noisy candidate labels, particularly when positive samples are scarce. To this end, we first propose a mutually class prototype alignment strategy bypassing noise interference by introducing two different transformation matrices, which makes the class prototypes learned by the fuzzy clustering and candidate label set mutually alignment for correcting themselves. Such alignment is also passed on to the fuzzy memberships label in turn. In addition, to eliminate noise interference in the candidate label set during the classifier learning, we use the learned permutation matrix to transform the fuzzy memberships label for learning a label reliability indicator matrix accompanied by the candidate label set. This makes the label reliability indicator matrix absolutely prevent the occurrence of numerical values located in non-label and simultaneously eliminate the introduction of incorrect label as much as possible. The resulting indicator matrix guides a robust multi-label classifier training process, jointly optimizing label confidence and classifier parameters. Extensive experiments demonstrate that our proposed model exhibits significant performance advantages over state-of-the-art PML approaches.

Despite the growing success of transform-based tensor models such as the t-product, their underlying geometric principles remain poorly understood. Classical differential geometry, built on real-valued function spaces, is not well suited to capture the algebraic and spectral structure induced by transform-based tensor operations. In this work, we take an initial step toward a geometric framework for tensors equipped with tube-wise multiplication via orthogonal transforms. We introduce the notion of smooth t-manifolds, defined as topological spaces locally modeled on structured tensor modules over a commutative t-scalar ring. This formulation enables transform-consistent definitions of geometric objects, including metrics, gradients, Laplacians, and geodesics, thereby bridging discrete and continuous tensor settings within a unified algebraic-geometric perspective. On this basis, we develop a statistical procedure for testing whether tensor data lie near a low-dimensional t-manifold, and provide nonasymptotic guarantees for manifold fitting under noise. We further establish approximation bounds for tensor neural networks that learn smooth functions over t-manifolds, with generalization rates determined by intrinsic geometric complexity. This framework offers a theoretical foundation for geometry-aware learning in structured tensor spaces and supports the development of models that align with transform-based tensor representations.

Unsupervised learning provides efficient analytical tools for data-centric Internet of Things (IoT) applications. Nonnegative matrix factorization (NMF) is a fundamental tool in unsupervised machine learning, offering interpretable and part-based feature representations. While NMF is provably robust to bounded additive perturbations, the emergence of adversarial attacks highlights the need to reassess the certified robustness under strategically crafted perturbations. In this work, we propose a novel attack method that more effectively disrupts NMF factorization than existing adversarial methods by incorporating two key strategies: i) imposing low-rank constraints to guide perturbations toward principal subspaces; and ii) relaxing nonnegativity constraints on perturbations to inject negative components that effectively alter original feature additivity. We present analyses including ablation studies, convergence performance, and computational complexity. Extensive experiments on benchmark datasets show that the proposed method effectively attacks both vanilla NMF and existing adversarial NMF variants by disrupting the factorization and degrading performance in downstream tasks such as feature extraction and clustering.

Large language models have demonstrated predictable scaling behaviors with respect to model parameters and training data. This study investigates whether a similar scaling relationship exist for vision-language models with respect to the number of vision tokens. A mathematical framework is developed to characterize a relationship between vision token number and the expected divergence of distance between vision-referencing sequences. The theoretical analysis reveals two distinct scaling regimes: sublinear scaling for less vision tokens and linear scaling for more vision tokens. This aligns with model performance relationships of the form \(S(n) \approx c / n^{\alpha(n)}\), where the scaling exponent relates to the correlation structure between vision token representations. Empirical validations across multiple vision-language benchmarks show that model performance matches the prediction from scaling relationship. The findings contribute to understanding vision token scaling in transformers through a theoretical framework that complements empirical observations.

Recently, tensor singular value decomposition (t-SVD)-based methods were proposed to solve the low-rank tensor completion (LRTC) problem, which has achieved unprecedented success on image and video inpainting tasks. The t-SVD is limited to process third-order tensors. When faced with higher-order tensors, it reshapes them into third-order tensors, leading to the destruction of interdimensional correlations. To address this limitation, this letter introduces a tproductinduced Tucker decomposition (tTucker) model that replaces the mode product in Tucker decomposition with t-product, which jointly extends the ideas of t-SVD and high-order SVD. This letter defines the rank of the tTucker decomposition and presents an LRTC model that minimizes the induced Schatten-p norm. An efficient alternating direction multiplier method (ADMM) algorithm is developed to optimize the proposed LRTC model, and its effectiveness is demonstrated through experiments conducted on both synthetic and real data sets, showcasing excellent performance.

While tensor ring (TR) decomposition methods have been extensively studied, the determination of TR-ranks remains a challenging problem, with existing methods being typically sensitive to the determination of the starting rank (i.e., the first rank to be optimized). Moreover, current methods often fail to adaptively determine TR-ranks in the presence of noisy and incomplete data, and exhibit computational inefficiencies when handling high-dimensional data. To address these issues, we propose an odd-dimensional unfolding method for the effective determination of TR-ranks. This is achieved by leveraging the symmetry of the TR model and the bound rank relationship in TR decomposition. In addition, we employ the singular value thresholding algorithm to facilitate the adaptive determination of TR-ranks and use randomized sketching techniques to enhance the efficiency and scalability of the method. Extensive experimental results in rank identification, data denoising, and completion demonstrate the potential of our method for a broad range of applications.

In this paper, the model-free dynamic event-driven safe (MFDEDS) control of unknown nonaffine systems with state and input constraints is investigated via adaptive dynamic programming. To begin with, by introducing a dynamic compensator and performing system transformation, the safe control problem with state and input constraints is transformed into an optimal regulation problem of an unconstrained system. Afterwards, an integral reinforcement learning algorithm is applied to the unconstrained system to derive an optimal safe control policy independent of the original system model, which achieves model-free approximate optimal control for the original system. To conserve computing and communication resources, a novel game-based dynamic event-driven mechanism is established, which models the control policy and the event-driven error as players in a zero-sum game, with the aim of obtaining the worst event-driven error to maximize the triggering interval. Furthermore, an approximate solution to the Hamilton-Jacobi-Bellman equation is derived by constructing a single-critic learning structure, which results in an approximate optimal safe control policy. Theoretical analysis demonstrates that the proposed MFDEDS control scheme ensures the closed-loop system is asymptotically stable. Ultimately, the efficacy of the developed approach is corroborated through two simulation examples.

Satellite on-orbit remote sensing image intelligent interpretation relies on on-orbit devices with extremely limited computational resources, utilizing advanced neural networks designed through lightweight methodologies to achieve fast and accurate interpretation of on-orbit remote sensing images. Nevertheless, the current design of lightweight neural networks exhibits three salient issues: firstly, the prevailing “one-size-fits-all" network lightweight design pattern is notably inefficient; secondly, there is a deficiency in analysing the impact of lightweight operations on network performance; thirdly, the mutual influence among various lightweight operations is overlooked. To address these issues, firstly, we propose a neural network lightweightability measurement model and its computational method by investigating the effects of various lightweight operations; secondly, we propose a neural network general lightweight design framework (GLD) tailored for satellite on-orbit remote sensing images intelligent interpretation. Specifically, GLD, based on a meta-leaning approach, integrates knowledge distillation (KD), pruning and quantization, three general lightweight technologies, into a framework. It dynamically assesses the distillability, prunability and quantifiability of neural networks, and uses this assessment and uses this as supervision to dynamically jointly optimizes KD, pruning and quantization, making it applicable to various mainstream neural networks; furthermore, we explore the mutual influence among lightweight operations based on GLD; finally, through ablation experiments and comparative experiments, we further verify the effectiveness and superiority of GLD.

The recently proposed tensor tubal rank has been witnessed to obtain extraordinary success in real-world tensor data completion. However, existing works usually fix the transform orientation along the third mode and may fail to turn multidimensional low-tubal-rank structure into account. To alleviate these bottlenecks, we introduce two unfolding induced tensor nuclear norms (TNNs) for the tensor completion (TC) problem, which naturally extends tensor tubal rank to high-order data. Specifically, we show how multidimensional low-tubal-rank structure can be captured by utilizing a novel balanced unfolding strategy, upon which two TNNs, namely, overlapped TNN (OTNN) and latent TNN (LTNN), are developed. We also show the immediate relationship between the tubal rank of unfolding tensor and the existing tensor network (TN) rank, e.g., CANDECOMP/PARAFAC (CP) rank, Tucker rank, and tensor ring (TR) rank, to demonstrate its efficiency and practicality. Two efficient TC models are then proposed with theoretical guarantees by analyzing a unified nonasymptotic upper bound. To solve optimization problems, we develop two alternating direction methods of multipliers (ADMM) based algorithms. The proposed models have been demonstrated to exhibit superior performance based on experimental findings involving synthetic and real-world tensors, including facial images, light field images, and video sequences.

Conventional Outlier Robust Tensor Decomposition (ORTD) approaches generally represent sparse outlier corruption within a specific mode. However, such an assumption, which may hold for matrices, proves inadequate when applied to high-order tensors. In the tensor domain, the outliers are prone to be corrupted in multiple modes simultaneously. Addressing this limitation, this study proposes a novel ORTD approach by recovering low-rank tensors contaminated by outliers spanning multiple modes. In particular, we conceptualize outliers within high-order tensors as latent tensor group sparsity by decomposing the corrupted tensor into a sum of multiple latent components, where each latent component is exclusive to outliers within a particular direction. Thus, it can effectively mitigate the outlier corruptions prevalent in high-order tensors across multiple modes. To theoretically guarantee recovery performance, we rigorously analyze a non-asymptotic upper bound of the estimation error for the proposed ORTD approach. In the optimization process, we develop an efficient alternate direction method of multipliers (ADMM) algorithm. Empirical validation of the approach's efficacy is undertaken through comprehensive experimentation.

Deep Multi-view Clustering (DMVC) stands out as a widely adopted technique aiming at enhanced clustering performance by leveraging diverse data sources. However, the critical issue of vulnerability to adversarial attacks is unexplored due to the lack of well-defined attack objectives. To fill this crucial gap, this paper is the first work to investigate the possibility of adversarial attacks on DMVC models. Specifically, we introduce an adversarial attack with Generative Adversarial Networks (GANs) with the aim to maximally change the complementarity and consistency of multiple views, thus leading to wrong clustering. Building upon this adversarial context, in the realm of defense, we propose a novel Adversarially Robust Deep Multi-View Clustering by leveraging adversarial training. Based on the analysis from an information-theoretic perspective, we design an Attack Mitigator that provides a foundation to guarantee the adversarial robustness of our DMVC models. Experiments conducted on multi-view datasets confirmed that our attack framework effectively reduces the clustering performance of the target model. Furthermore, our proposed adversarially robust method is also demonstrated to be an effective defense against such attacks. This work is a pioneer in exploring adversarial threats and advancing both theoretical understanding and practical strategies for robust multi-view clustering. Code is available at https://github.com/libertyhhn/AR-DMVC.

Tensor networks are efficient for extremely high-dimensional representation, but their model selection, known as tensor network structure search (TN-SS), is a challenging problem. Although several works have targeted TN-SS, most existing algorithms are manually crafted heuristics with poor performance, suffering from the curse of dimensionality and local convergence. In this work, we jump out of the box, studying how to harness large language models (LLMs) to automatically discover new TN-SS algorithms, replacing the involvement of human experts. By observing how human experts innovate in research, we model their common workflow and propose an automatic algorithm discovery framework called tnGPS. The proposed framework is an elaborate prompting pipeline that instruct LLMs to generate new TN-SS algorithms through iterative refinement and enhancement. The experimental results demonstrate that the algorithms discovered by tnGPS exhibit superior performance in benchmarks compared to the current state-of-the-art methods. Our code is available at https://github.com/ChaoLiAtRIKEN/tngps.

In multi-output regression, we identify a previously neglected challenge that arises from the inability of training distribution to cover all combinations of input features, leading to combinatorial distribution shift (CDS). To the best of our knowledge, this is the first work to formally define and address this problem. We tackle it through a novel tensor decomposition perspective, proposing the Functional t-Singular Value Decomposition (Ft-SVD) theorem which extends the classical tensor SVD to infinite and continuous feature domains, providing a natural tool for representing and analyzing multi-output functions. Within the Ft-SVD framework, we formulate the multi-output regression problem under CDS as a low-rank tensor estimation problem under the missing not at random (MNAR) setting, and introduce a series of assumptions about the true functions, training and testing distributions, and spectral properties of the ground-truth embeddings, making the problem more tractable. To address the challenges posed by CDS in multi-output regression, we develop a tailored Double-Stage Empirical Risk Minimization (ERM-DS) algorithm that leverages the spectral properties of the embeddings and uses specific hypothesis classes in each frequency component to better capture the varying spectral decay patterns. We provide rigorous theoretical analyses that establish performance guarantees for the ERM-DS algorithm. This work lays a preliminary theoretical foundation for multi-output regression under CDS.

The positioning accuracy determines the scope of the application of an unmanned aerial vehicle (UAV). In view of the existing UAV cooperative localization methods that normally require prior information and the assistance of external systems, such as the global positioning system (GPS), this study aims to adopt range radios to measure the time-of-arrival (TOA) information among UAVs and then perform clock synchronization and cooperative localization based on ranging measurements. We propose a framework to jointly estimate the clock error and relative distance, adjust the onboard clock, and perform relative positioning. To achieve autonomous clock synchronization and ranging, a practical approach based on peer-to-peer pseudorange measurements is proposed in this study. We modeled the synchronous two-way ranging (STWR) process using a discretetime state-space model, according to which a linear parameter estimation method and clock steering method are presented. Finally, a closed loop consisting of STWR, parameter estimation, and clock tuning is constructed to improve the ranging accuracy, which leads to improved localization accuracy. Simulation results show that the proposed approach outperforms existing methods and can achieve sub-nanosecond-level time synchronization and meter-level cooperative localization.

Recently, fusing low-resolution hyperspectral images (LR-HSIs) with high-resolution multispectral images (HR-MSIs) to obtain high-resolution HSI (HR-HSI) has become an emerging study. In this letter, Bayesian nonlocal canonical polyadic (CP) factorization (BNCPF) is proposed for fusing LR-HSI with HR-MSI, which applies CP factorization on the nonlocal tensors of HR-HSI. Compared with the vanilla scheme of applying CP factorization on HR-HSI, the nonlocal tensors reveal balanced low-rank properties along different modes, and thus CP factorization can better capture their intrinsic low-rankness. To avoid the immense CP-ranks selection on the nonlocal tensors, we develop a sparse Bayesian framework for automatic rank determination. For parameters estimation, we adopt the alternating direction method of multipliers (ADMMs) for the maximum a posteriori (MAP) estimator optimization. Experimental results verify the superiority and rank-robustness of the proposed method.

The deep-learning-based detection of planetary craters provides significant assistance for in-orbit vehicles in space exploration. However, most object detection researches to date tended to focus on the single-source data collected by mono-type sensors, and their performances were severely hindered by the disability of using diverse source data from various sensors. For effectually using distinct sources in resource-limited vehicles, we present a compact framework to learn unified representation from elevation and visual sources basing on tensor decomposition. In particular, the vital elevation is extracted to obtain the deficient information in visuals. Furthermore, for accommodating limited computing resource, a compound tensor decomposition layer is proposed based on the special structure of decomposition, which extracts the source-specific and source-independent information, and at the same time crafts unified representation for terrains. Comprehensive comparisons with recent methods demonstrate the effective representation learning of the proposed method on different planetary terrains and in insufficient data learning setting, revealing its potential for real-world applications.

Hashing-based techniques present appealing solutions for cross-modal retrieval due to its low storage requirements and excellent query efficiency. The majority of cross-modal hashing methods typically adopt equal-length encoding scheme to represent multimodal data and achieve cross-modal similarity search. However, such scheme can be regarded as a relatively strict limitation, because it sacrifices the flexible representation of multimodal data in reality and cannot always guarantee the optimal retrieval performance. To address the challenge, this paper focuses on encoding heterogeneous data with varying hash lengths. To achieve this purpose, we propose a flexible cross-modal hashing approach, named Two-stage Asymmetric Similarity Preserving Hashing, TASPH for short, which can be applied to both unequal-length and equal-length retrieval scenarios. Specifically, in the first stage, TASPH designs a novel discrete asymmetric strategy to learn the modality-specific hash codes with varying lengths, enabling a flexible representation of heterogeneous data. Simultaneously, TASPH utilizes two semantic transformation matrices to establish the semantic correlations between varying hash codes. Different from most of the existing approaches that employ relaxation solutions, TASPH satisfies the discrete constraints without any relaxation. In the second stage, the learned semantic transformation matrices are employed to alleviate cross-modal heterogeneity, which guarantees that TASPH can learn more powerful hash functions to improve the discriminative ability of hash codes. Abundant experiments conducted on three benchmark datasets demonstrate encouraging results compared with the state-of-the-art approaches under different retrieval scenarios.

Learning a comprehensive representation from multiview data is crucial in many real-world applications. Multiview representation learning (MRL) based on nonnegative matrix factorization (NMF) has been widely adopted by projecting high-dimensional space into a lower order dimensional space with great interpretability. However, most prior NMF-based MRL techniques are shallow models that ignore hierarchical information. Although deep matrix factorization (DMF)-based methods have been proposed recently, most of them only focus on the consistency of multiple views and have cumbersome clustering steps. To address the above issues, in this article, we propose a novel model termed deep autoencoder-like NMF for MRL (DANMF-MRL), which obtains the representation matrix through the deep encoding stage and decodes it back to the original data. In this way, through a DANMF-based framework, we can simultaneously consider the multiview consistency and complementarity, allowing for a more comprehensive representation. We further propose a one-step DANMF-MRL, which learns the latent representation and final clustering labels matrix in a unified framework. In this approach, the two steps can negotiate with each other to fully exploit the latent clustering structure, avoid previous tedious clustering steps, and achieve optimal clustering performance. Furthermore, two efficient iterative optimization algorithms are developed to solve the proposed models both with theoretical convergence analysis. Extensive experiments on five benchmark datasets demonstrate the superiority of our approaches against other state-of-the-art MRL methods.

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries are noise-free to provide a theoretical guarantee of exact recovery of missing entries, which is quite restrictive in practice. To remedy such drawback, this article proposes a novel noisy tensor completion model, which complements the incompetence of existing works in handling the degeneration of high-order and noisy observations. Specifically, the tensor ring nuclear norm (TRNN) and least-squares estimator are adopted to regularize the underlying tensor and the observed entries, respectively. In addition, a nonasymptotic upper bound of estimation error is provided to depict the statistical performance of the proposed estimator. Two efficient algorithms are developed to solve the optimization problem with convergence guarantee, one of which is specially tailored to handle large-scale tensors by replacing the minimization of TRNN of the original tensor equivalently with that of a much smaller one in a heterogeneous tensor decomposition framework. Experimental results on both synthetic and real-world data demonstrate the effectiveness and efficiency of the proposed model in recovering noisy incomplete tensor data compared with state-of-the-art tensor completion models.

Robust tensor completion (RTC) aims to recover a low-rank tensor from its incomplete observations with outlier corruption. The recently proposed tensor ring (TR) model has demonstrated superiority in solving the RTC problem. However, the methods using the TR model either require a preassigned TR rank or aggressively pursue the minimum TR rank, where the latter often leads to biased solutions in the presence of noise. To tackle these bottlenecks, a Bayesian robust TR decomposition (BRTR) method is proposed to give a more accurate solution for the RTC problem, which can avoid exquisite selection of the TR rank and penalty parameters. A variational Bayesian (VB) algorithm is developed to infer the probability distribution of posteriors. During the learning process, BRTR can prune off zero components of core tensors, resulting in automatic TR rank determination. Extensive experiments show that BRTR can achieve significantly improved performance than other state-of-the-art methods.

Multi-channel learning has gained significant attention in recent applications, where neural networks with t-product layers (t-NNs) have shown promising performance through novel feature mapping in the transformed domain. However, despite the practical success of t-NNs, the theoretical analysis of their generalization remains unexplored. We address this gap by deriving upper bounds on the generalization error of t-NNs in both standard and adversarial settings. Notably, it reveals that t-NNs compressed with exact transformed low-rank parameterization can achieve tighter adversarial generalization bounds compared to non-compressed models. While exact transformed low-rank weights are rare in practice, the analysis demonstrates that through adversarial training with gradient flow, highly over-parameterized t-NNs with the ReLU activation can be implicitly regularized towards a transformed low-rank parameterization under certain conditions. Moreover, this paper establishes sharp adversarial generalization bounds for t-NNs with approximately transformed low-rank weights. Our analysis highlights the potential of transformed low-rank parameterization in enhancing the robust generalization of t-NNs, offering valuable insights for further research and development.

Tensor-ring (TR) decomposition is a powerful tool for exploiting the low-rank property of multiway data and has been demonstrated great potential in a variety of important applications. In this article, non-negative TR (NTR) decomposition and graph-regularized NTR (GNTR) decomposition are proposed. The former equips TR decomposition with the ability to learn the parts-based representation by imposing non-negativity on the core tensors, and the latter additionally introduces a graph regularization to the NTR model to capture manifold geometry information from tensor data. Both of the proposed models extend TR decomposition and can be served as powerful representation learning tools for non-negative multiway data. The optimization algorithms based on an accelerated proximal gradient are derived for NTR and GNTR. We also empirically justified that the proposed methods can provide more interpretable and physically meaningful representations. For example, they are able to extract parts-based components with meaningful color and line patterns from objects. Extensive experimental results demonstrated that the proposed methods have better performance than state-of-the-art tensor-based methods in clustering and classification tasks.

Tensor-ring (TR) decomposition was recently studied and applied for low-rank tensor completion due to its powerful representation ability of high-order tensors. However, most of the existing TR-based methods tend to suffer from deterioration when the selected rank is larger than the true one. To address this issue, this article proposes a new low-rank sparse TR completion method by imposing the Frobenius norm regularization on its latent space. Specifically, we theoretically establish that the proposed method is capable of exploiting the low rankness and Kronecker-basis-representation (KBR)-based sparsity of the target tensor using the Frobenius norm of latent TR-cores. We optimize the proposed TR completion by block coordinate descent (BCD) algorithm and design a modified TR decomposition for the initialization of this algorithm. Extensive experimental results on synthetic data and visual data have demonstrated that the proposed method is able to achieve better results compared to the conventional TR-based completion methods and other state-of-the-art methods and, meanwhile, is quite robust even if the selected TR-rank increases.

Since a large proportion of real-world data is made of different representations or views, learning on data represented with multiple views (e.g., numerous types of features or modalities) has garnered considerable attention recently. Nonnegative matrix factorization (NMF) has been widely adopted for multi-view learning due to its great interpretability. We focus on unsupervised multi-view data representation in this paper and propose a novel framework termed Deep Autoencoder-like NMF (DANMF-MDR), which learns an intact representation by simultaneously exploring multi-view complementary and consistent information. Furthermore, an efficient iterative optimization algorithm is developed to solve the proposed model. Experimental results on three real-world multi-view datasets demonstrate that ours performs better than the SOTA multi-view NMF-based MDR approaches.

Abstract Tensor completion has gained considerable research interest in recent years and has been frequently applied to image restoration. This type of method basically employs the low‐rank nature of images, implicitly requiring that the whole picture is of globally consistent features. As a result, existing tensor completion algorithms often give reasonably good performance if the target image has only random pixel‐level missing. Unfortunately, pixel‐level missing is very rare in practice and it is often wanted to restore an image with irregular hole‐shaped missing, such as removing electricity poles from landscape photos or irrelevant people from tourist photos. This task is extremely difficult for traditional low‐rank based tensor completion methods. To overcome this drawback, a Contour Information regularized Tensor RIng Completion (CITRIC) method is proposed for practical image restoration. Meanwhile, the contour information regularization is used to capture significant local features, whereas the low‐rank tensor ring structure is utilized to capture as much global information as possible. The alternating direction method of multipliers (ADMM) is adopted to optimize the cost function. Extensive experimental results using real‐world images show that CITRIC is more practical than existing methods and can restore real‐world images with irregular hole‐shaped missing.

We make an attempt to understand convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall characteristics of neural networks without being disturbed by the horribly complex architectures. Specifically, we attempt to convert the basic structures of a convolutional neural network (CNN) and their combinations to the form of Volterra convolutions. The results show that most of convolutional neural networks can be approximated in the form of Volterra convolution, where the approximated proxy kernels preserve the characteristics of the original network. Analyzing these proxy kernels may give valuable insight about the original network. Based on this setup, we present methods to approximate the order-zero and order-one proxy kernels, and verify the correctness and effectiveness of our results.

As the volume of real-world data with numerous missing entries continues to grow rapidly, tensor completion has been a powerful tool to enhance such flawed data analysis. While existing methods mainly consider static data, there is a great need to deal with streaming data. In this letter, a multi-aspect streaming tensor ring completion (MASTR) method is proposed, where the low-rank tensor ring (TR) model is exploited to capture subspace information and transfer high-order correlations between multiple sub-tensors. Experimental results on synthetic data, hyperspectral data and video data demonstrate superior recovery performance compared to state-of-the-art methods.

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor recovery tasks. However, due to the large-scale tensor data in real-world applications, existing TRPCA models often suffer from high computational complexity. In this letter, we propose an efficient TRPCA under hybrid model of Tucker and TT. Specifically, in theory we reveal that TT nuclear norm (TTNN) of the original big tensor can be equivalently converted to that of a much smaller tensor via a Tucker compression format, thereby significantly reducing the computational cost of singular value decomposition (SVD). Numerical experiments on both synthetic and real-world tensor data verify the superiority of the proposed model.

Deep multitask learning (MTL) shares beneficial knowledge across participating tasks, alleviating the impacts of extreme learning conditions on their performances such as the data scarcity problem. In practice, participators stemming from different domain sources often have varied complexities and input sizes, for example, in the joint learning of computer vision tasks with RGB and grayscale images. For adapting to these differences, it is appropriate to design networks with proper representational capacities and construct neural layers with corresponding widths. Nevertheless, most of the state-of-the-art methods pay little attention to such situations, and actually fail to handle the disparities. To work with the dissimilitude of tasks' network designs, this article presents a distributed knowledge-sharing framework called tensor ring multitask learning (TRMTL), in which the relationship between knowledge sharing and original weight matrices is cut up. The framework of TRMTL is flexible, which is not only capable of sharing knowledge across heterogenous networks but also able to jointly learn tasks with varied input sizes, significantly improving performances of data-insufficient tasks. Comprehensive experiments on challenging datasets are conducted to empirically validate the effectiveness, efficiency, and flexibility of TRMTL in dealing with the disparities in MTL.

In general, existing cross-domain recognition methods mainly focus on changing the feature representation of data or modifying the classifier parameter and their efficiencies are indicated by the better performance. However, most existing methods do not simultaneously integrate them into a unified optimization objective for further improving the learning efficiency. In this article, we propose a novel cross-domain recognition algorithm framework by integrating both of them. Specifically, we reduce the discrepancies in both the conditional distribution and marginal distribution between different domains in order to learn a new feature representation which pulls the data from different domains closer on the whole. However, the data from different domains but the same class cannot interlace together enough and thus it is not reasonable to mix them for training a single classifier. To this end, we further propose to learn double classifiers on the respective domain and require that they dynamically approximate to each other during learning. This guarantees that we finally learn a suitable classifier from the double classifiers by using the strategy of classifier fusion. The experiments show that the proposed method outperforms over the state-of-the-art methods.

Cross-modal retrieval has attracted considerable attention for searching in large-scale multimedia databases because of its efficiency and effectiveness. As a powerful tool of data analysis, matrix factorization is commonly used to learn hash codes for cross-modal retrieval, but there are still many shortcomings. First, most of these methods only focus on preserving locality of data but they ignore other factors such as preserving reconstruction residual of data during matrix factorization. Second, the energy loss of data is not considered when the data of cross-modal are projected into a common semantic space. Third, the data of cross-modal are directly projected into a unified semantic space which is not reasonable since the data from different modalities have different properties. This article proposes a novel method called average approximate hashing (AAH) to address these problems by: 1) integrating the locality and residual preservation into a graph embedding framework by using the label information; 2) projecting data from different modalities into different semantic spaces and then making the two spaces approximate to each other so that a unified hash code can be obtained; and 3) introducing a principal component analysis (PCA)-like projection matrix into the graph embedding framework to guarantee that the projected data can preserve the main energy of data. AAH obtains the final hash codes by using an average approximate strategy, that is, using the mean of projected data of different modalities as the hash codes. Experiments on standard databases show that the proposed AAH outperforms several state-of-the-art cross-modal hashing methods.

Non-negative Tucker decomposition (NTD) is one of the most popular techniques for tensor data representation. To enhance the representation ability of NTD by multiple intrinsic cues, that is, manifold structure and supervisory information, in this article, we propose a generalized graph regularized NTD (GNTD) framework for tensor data representation. We first develop the unsupervised GNTD (UGNTD) method by constructing the nearest neighbor graph to maintain the intrinsic manifold structure of tensor data. Then, when limited must-link and cannot-link constraints are given, unlike most existing semisupervised learning methods that only use the pregiven supervisory information, we propagate the constraints through the entire dataset and then build a semisupervised graph weight matrix by which we can formulate the semisupervised GNTD (SGNTD). Moreover, we develop a fast and efficient alternating proximal gradient-based algorithm to solve the optimization problem and show its convergence and correctness. The experimental results on unsupervised and semisupervised clustering tasks using four image datasets demonstrate the effectiveness and high efficiency of the proposed methods.

Accurate electroencephalogram (EEG) pattern decoding for specific mental tasks is one of the key steps for the development of brain-computer interface (BCI), which is quite challenging due to the considerably low signal-to-noise ratio of EEG collected at the brain scalp. Machine learning provides a promising technique to optimize EEG patterns toward better decoding accuracy. However, existing algorithms do not effectively explore the underlying data structure capturing the true EEG sample distribution and, hence, can only yield a suboptimal decoding accuracy. To uncover the intrinsic distribution structure of EEG data, we propose a clustering-based multitask feature learning algorithm for improved EEG pattern decoding. Specifically, we perform affinity propagation-based clustering to explore the subclasses (i.e., clusters) in each of the original classes and then assign each subclass a unique label based on a one-versus-all encoding strategy. With the encoded label matrix, we devise a novel multitask learning algorithm by exploiting the subclass relationship to jointly optimize the EEG pattern features from the uncovered subclasses. We then train a linear support vector machine with the optimized features for EEG pattern decoding. Extensive experimental studies are conducted on three EEG data sets to validate the effectiveness of our algorithm in comparison with other state-of-the-art approaches. The improved experimental results demonstrate the outstanding superiority of our algorithm, suggesting its prominent performance for EEG pattern decoding in BCI applications.

Low-rank tensor completion (LRTC) aims to impute the missing entries from partially observed tensor data, among which low-rankness is of vital importance to get satisfactory results. In this letter, we propose a hierarchical low-rank factorization framework for high-order tensors. For the first layer, the low TR rank is exploited, and for the second layer the low-rankness of each TR core is further considered. With the hierarchical model, the low-rankness of the original tensor can be fully utilized and thus achieving better completion performance. Experimental results on synthetic data and on inpainting tasks using various datasets demonstrate the superior performance and efficiency of our proposed method as compared to the state-of-the-art algorithms.

A common approach for synchronizing the agents in a Wireless Sensor Network (WSN) is two-way timing stamps exchange mechanism. In this letter, by analyzing the change of accumulated clock offset within each communication cycle, an improved two-state discrete-time state model is proposed. A step further, two Kalman-filter-based estimators are proposed, by which the clock parameters and propagation delays can be estimated. The simulation results show that the proposed estimators outperform the conventional Kalman Filter (KF), especially with respect to the accumulated clock offset.

Tensor-ring (TR) decomposition has recently attracted considerable attention in solving the low-rank tensor completion (LRTC) problem. However, due to an unbalanced unfolding scheme used during the update of core tensors, the conventional TR-based completion methods usually require a large TR rank to achieve the optimal performance, which leads to high computational cost in practical applications. To overcome this drawback, we propose a new method to exploit the low TR-rank structure in this article. Specifically, we first introduce a balanced unfolding operation called tensor circular unfolding, by which the relationship between TR rank and the ranks of tensor unfoldings is theoretically established. Using this new unfolding operation, we further propose an algorithm to exploit the low TR-rank structure by performing parallel low-rank matrix factorizations to all circularly unfolded matrices. To tackle the problem of nonuniform missing patterns, we apply a row weighting trick to each circularly unfolded matrix, which significantly improves the adaptive ability to various types of missing patterns. The extensive experiments have demonstrated that the proposed algorithm can achieve outstanding performance using a much smaller TR rank compared with the conventional TR-based completion algorithms; meanwhile, the computational cost is reduced substantially.

The low‐rank tensor completion problem, which aims to recover the missing data from partially observable data. However, most of the existing tensor completion algorithms based on Tucker decomposition cannot avoid using singular value decomposition (SVD) operation to calculate the Tucker factors, so they are not suitable for the completion of large‐scale data. To solve this problem, they propose a new faster tensor completion algorithm, which uses the method of random projection to project the unfolding matrix of each mode of the tensor into the low‐dimensional subspace, and then obtain the Tucker factors by the orthogonal decomposition. Their method can effectively avoid the high computational cost of SVD operation. The results of the synthetic data experiments and real data experiments verify the effectiveness and feasibility of their method.

Dictionary learning plays a significant role in the field of machine learning. Existing works mainly focus on learning dictionary from a single domain. In this paper, we propose a novel projective double reconstructions (PDR) based dictionary learning algorithm for cross-domain recognition. Owing the distribution discrepancy between different domains, the label information is hard utilized for improving discriminability of dictionary fully. Thus, we propose a more flexible label consistent term and associate it with each dictionary item, which makes the reconstruction coefficients have more discriminability as much as possible. Due to the intrinsic correlation between cross-domain data, the data should be reconstructed with each other. Based on this consideration, we further propose a projective double reconstructions scheme to guarantee that the learned dictionary has the abilities of data itself reconstruction and data crossreconstruction. This also guarantees that the data from different domains can be boosted mutually for obtaining a good data alignment, making the learned dictionary have more transferability. We integrate the double reconstructions, label consistency constraint and classifier learning into a unified objective and its solution can be obtained by proposed optimization algorithm that is more efficient than the conventional l1 optimization based dictionary learning methods. The experiments show that the proposed PDR not only greatly reduces the time complexity for both training and testing, but also outperforms over the stateof- the-art methods.

Blind source separation (BSS) is a typical unsupervised learning method that extracts latent components from their observations. In the meanwhile, convolutive BSS (CBSS) is particularly challenging as the observations are the mixtures of latent components as well as their delayed versions. CBSS is usually solved in frequency domain since convolutive mixtures in time domain is just instantaneous mixtures in frequency domain, which allows to recover source frequency components independently of each frequency bin by running ordinary BSS, and then concatenate them to form the Fourier transformation of source signals. Because BSS has inherent permutation ambiguity, this category of CBSS methods suffers from a common drawback: it is very difficult to choose the frequency components belonging to a specific source as they are estimated from different frequency bins using BSS. This paper presents a tensor framework that can completely eliminate the permutation ambiguity. By combining each frequency bin with an anchor frequency bin that is chosen arbitrarily in advance, we establish a new virtual BSS model where the corresponding correlation matrices comply with a block tensor decomposition (BTD) model. The essential uniqueness of BTD and the sparse structure of coupled mixing parameters allow the estimation of the mixing matrices free of permutation ambiguity. Extensive simulation results confirmed that the proposed algorithm could achieve higher separation accuracy compared with the state-of-the-art methods.

Nonnegative Tucker Decomposition (NTD) is one of the most popular technique for feature extraction and representation from nonnegative tensor data with preserving internal structure information. From the perspective of geometry, highdimensional data are usually drawn in low-dimensional submanifold of the ambient space. In this paper, we propose a novel Graph reguralized Nonnegative Tucker Decomposition (GNTD) method which is able to extract the low-dimensional parts-based representation and preserve the geometrical information simultaneously from high-dimensional tensor data. We also present an effictive algorithm to solve the proposed GNTD model. Experimental results demonstrate the effectiveness and high efficiency of the proposed GNTD method.

Common spatial pattern (CSP)-based spatial filtering has been most popularly applied to electroencephalogram (EEG) feature extraction for motor imagery (MI) classification in brain-computer interface (BCI) application. The effectiveness of CSP is highly affected by the frequency band and time window of EEG segments. Although numerous algorithms have been designed to optimize the spectral bands of CSP, most of them selected the time window in a heuristic way. This is likely to result in a suboptimal feature extraction since the time period when the brain responses to the mental tasks occurs may not be accurately detected. In this paper, we propose a novel algorithm, namely temporally constrained sparse group spatial pattern (TSGSP), for the simultaneous optimization of filter bands and time window within CSP to further boost classification accuracy of MI EEG. Specifically, spectrum-specific signals are first derived by bandpass filtering from raw EEG data at a set of overlapping filter bands. Each of the spectrum-specific signals is further segmented into multiple subseries using sliding window approach. We then devise a joint sparse optimization of filter bands and time windows with temporal smoothness constraint to extract robust CSP features under a multitask learning framework. A linear support vector machine classifier is trained on the optimized EEG features to accurately identify the MI tasks. An experimental study is implemented on three public EEG datasets (BCI Competition III dataset IIIa, BCI Competition IV datasets IIa, and BCI Competition IV dataset IIb) to validate the effectiveness of TSGSP in comparison to several other competing methods. Superior classification performance (averaged accuracies are 88.5%, 83.3%, and 84.3% for the three datasets, respectively) based on the experimental results confirms that the proposed algorithm is a promising candidate for performance improvement of MI-based BCIs.

High accuracy of electroencephalogram (EEG) classification can hardly be achieved if the signals are contaminated by severe artefacts. One helpless way to avoid such artefacts is usually to directly discard the severely disturbed EEG segments. This study considers a more elegant way that tries to recover the disturbed segments from other undisturbed segments. The possible artefacts in EEG are treated as missing values. A Bayesian tensor factorization (BTF) based method is proposed to implement EEG completion for artefact removal. By specifying a sparsity-inducing hierarchical prior, the underlying low-rank tensor is discovered from incomplete EEG tensor with automatically inferred model parameters. The EEG missing values are effectively predicted with robustness to overfitting. Effectiveness of the BTF algorithm is demonstrated on EEG data recorded from seven subjects in a brain-computer interface paradigm based on event-related potentials.

With the increasing availability of various sensor technologies, we now have access to large amounts of multiblock (also called multiset, multirelational, or multiview) data that need to be jointly analyzed to explore their latent connections. Various component analysis methods have played an increasingly important role for the analysis of such coupled data. In this article, we first provide a brief review of existing matrix-based (two-way) component analysis methods for the joint analysis of such data with a focus on biomedical applications. Then, we discuss their important extensions and generalization to multiblock multiway (tensor) data. We show how constrained multiblock tensor decomposition methods are able to extract similar or statistically dependent common features that are shared by all blocks, by incorporating the multiway nature of data. Special emphasis is given to the flexible common and individual feature analysis of multiblock data with the aim to simultaneously extract common and individual latent components with desired properties and types of diversity. Illustrative examples are given to demonstrate their effectiveness for biomedical data analysis.

Regularization has been one of the most popular approaches to prevent overfitting in electroencephalogram (EEG) classification of brain-computer interfaces (BCIs). The effectiveness of regularization is often highly dependent on the selection of regularization parameters that are typically determined by cross-validation (CV). However, the CV imposes two main limitations on BCIs: 1) a large amount of training data is required from the user and 2) it takes a relatively long time to calibrate the classifier. These limitations substantially deteriorate the system's practicability and may cause a user to be reluctant to use BCIs. In this paper, we introduce a sparse Bayesian method by exploiting Laplace priors, namely, SBLaplace, for EEG classification. A sparse discriminant vector is learned with a Laplace prior in a hierarchical fashion under a Bayesian evidence framework. All required model parameters are automatically estimated from training data without the need of CV. Extensive comparisons are carried out between the SBLaplace algorithm and several other competing methods based on two EEG data sets. The experimental results demonstrate that the SBLaplace algorithm achieves better overall performance than the competing algorithms for EEG classification.

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CANDECOMP/PARAFAC (CP)-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The low-CP-rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Student-t distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without the need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the low-rank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many state-of-the-art algorithms on both synthetic and real-world data sets demonstrate the superiorities of our method from several perspectives.

Real-world data are often acquired as a collection of matrices rather than as a single matrix. Such multiblock data are naturally linked and typically share some common features while at the same time exhibiting their own individual features, reflecting the underlying data generation mechanisms. To exploit the linked nature of data, we propose a new framework for common and individual feature extraction (CIFE) which identifies and separates the common and individual features from the multiblock data. Two efficient algorithms termed common orthogonal basis extraction (COBE) are proposed to extract common basis is shared by all data, independent on whether the number of common components is known beforehand. Feature extraction is then performed on the common and individual subspaces separately, by incorporating dimensionality reduction and blind source separation techniques. Comprehensive experimental results on both the synthetic and real-world data demonstrate significant advantages of the proposed CIFE method in comparison with the state-of-the-art.

Very often data we encounter in practice is a collection of matrices rather than a single matrix. These multi-block data often share some common features, due to the background in which they are measured. In this study we propose a new concept of linked blind source separation (BSS) that aims at discovering and extracting unique and physically meaningful common components from multi-block data, which also contain strong individual components. The validity and potential of the proposed method is justified by simulations.

Nonnegative matrix factorization (NMF) with orthogonality constraints is quite important due to its close relation with the K-means clustering. While existing algorithms for orthogonal NMF impose strict orthogonality constraints, in this letter we propose a penalty method with the aim of performing approximately orthogonal NMF, together with two efficient algorithms respectively based on the Hierarchical Alternating Least Squares (HALS) and the Accelerated Proximate Gradient (APG) approaches. Experimental evidence was provided to show their high efficiency and flexibility by using synthetic and real-world data.

Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of data. However, as the data tensor often has multiple modes and is large scale, the existing NTD algorithms suffer from a very high computational complexity in terms of both storage and computation time, which has been one major obstacle for practical applications of NTD. To overcome these disadvantages, we show how low (multilinear) rank approximation (LRA) of tensors is able to significantly simplify the computation of the gradients of the cost function, upon which a family of efficient first-order NTD algorithms are developed. Besides dramatically reducing the storage complexity and running time, the new algorithms are quite flexible and robust to noise, because any well-established LRA approaches can be applied. We also show how nonnegativity incorporating sparsity substantially improves the uniqueness property and partially alleviates the curse of dimensionality of the Tucker decompositions. Simulation results on synthetic and real-world data justify the validity and high efficiency of the proposed NTD algorithms.

We present a novel framework for tensor valued Gaussian processes (GP) regression, which exploits a covariance function defined on tensor representation of data inputs. In this way, we bring together the powerful GP methods supported by Bayesian inference and higher-order tensor analysis techniques into one framework. This enables us to account for the underlying structure of data within the model, providing a powerful framework for structural data analysis, such as 3D video sequences. To this end, we propose a new kernel function with tensor arguments under the assumption of generative models, in the form of product kernels where a symmetrical Kullback-Leibler divergence measure is exploited to define the covariance function for tensorial data. A fully Bayesian treatment is employed to estimate the hyperparameters and infer the predictive distributions. Simulation results on both the synthetic data and a real world application of estimating the crowd size from 3D videos demonstrate the effectiveness of the proposed framework.

Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-negative canonical polyadic decomposition (NCPD) based on low-rank approximation (LRA) and hierarchical alternating least square (HALS) techniques. We applied NCPD (LRAHALS and benchmark HALS) and CPD to extract multi-domain features of a visual ERP. The features and components extracted by LRAHALS NCPD and HALS NCPD were very similar, but LRAHALS NCPD was 70 times faster than HALS NCPD. Moreover, the desired multi-domain feature of the ERP by NCPD showed a significant group difference (control versus depressed participants) and a difference in emotion processing (fearful versus happy faces). This was more satisfactory than that by CPD, which revealed only a group difference.

Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs). Despite its efficiency, a potential problem is that using pre-constructed sine-cosine waves as the required reference signals in the CCA method often does not result in the optimal recognition accuracy due to their lack of features from the real electro-encephalo-gram (EEG) data. To address this problem, this study proposes a novel method based on multiset canonical correlation analysis (MsetCCA) to optimize the reference signals used in the CCA method for SSVEP frequency recognition. The MsetCCA method learns multiple linear transforms that implement joint spatial filtering to maximize the overall correlation among canonical variates, and hence extracts SSVEP common features from multiple sets of EEG data recorded at the same stimulus frequency. The optimized reference signals are formed by combination of the common features and completely based on training data. Experimental study with EEG data from 10 healthy subjects demonstrates that the MsetCCA method improves the recognition accuracy of SSVEP frequency in comparison with the CCA method and other two competing methods (multiway CCA (MwayCCA) and phase constrained CCA (PCCA)), especially for a small number of channels and a short time window length. The superiority indicates that the proposed MsetCCA method is a new promising candidate for frequency recognition in SSVEP-based BCIs.

Two main issues for event-related potential (ERP) classification in brain-computer interface (BCI) application are curse-of-dimensionality and bias-variance tradeoff, which may deteriorate classification performance, especially with insufficient training samples resulted from limited calibration time. This study introduces an aggregation of sparse linear discriminant analyses (ASLDA) to overcome these problems. In the ASLDA, multiple sparse discriminant vectors are learned from differently l1-regularized least-squares regressions by exploiting the equivalence between LDA and least-squares regression, and are subsequently aggregated to form an ensemble classifier, which could not only implement automatic feature selection for dimensionality reduction to alleviate curse-of-dimensionality, but also decrease the variance to improve generalization capacity for new test samples. Extensive investigation and comparison are carried out among the ASLDA, the ordinary LDA and other competing ERP classification algorithms, based on different three ERP datasets. Experimental results indicate that the ASLDA yields better overall performance for single-trial ERP classification when insufficient training samples are available. This suggests the proposed ASLDA is promising for ERP classification in small sample size scenario to improve the practicability of BCI.

We present a new supervised tensor regression method based on multi-way array decompositions and kernel machines. The main issue in the development of a kernel-based framework for tensorial data is that the kernel functions have to be defined on tensor-valued input, which here is defined based on multi-mode product kernels and probabilistic generative models. This strategy enables taking into account the underlying multilinear structure during the learning process. Based on the defined kernels for tensorial data, we develop a kernel-based tensor partial least squares approach for regression. The effectiveness of our method is demonstrated by a real-world application, i.e., the reconstruction of 3D movement trajectories from electrocorticography signals recorded from a monkey brain.

CANonical polyadic DECOMPosition (CANDECOMP, CPD), also known as PARAllel FACtor analysis (PARAFAC) is widely applied to Nth-order (N ≥ 3) tensor analysis. Existing CPD methods mainly use alternating least squares iterations and hence need to unfold tensors to each of their N modes frequently, which is one major performance bottleneck for large-scale data, especially when the order N is large. To overcome this problem, in this paper, we propose a new CPD method in which the CPD of a high-order tensor (i.e., N > 3) is realized by applying CPD to a mode reduced one (typically, third-order tensor) followed by a Khatri-Rao product projection procedure. This way is not only quite efficient as frequently unfolding to N modes is avoided, but also promising to conquer the bottleneck problem caused by high collinearity of components. We show that, under mild conditions, any Nth-order CPD can be converted to an equivalent third-order one but without destroying essential uniqueness, and theoretically they simply give consistent results. Besides, once the CPD of any unfolded lower order tensor is essentially unique, it is also true for the CPD of the original higher order tensor. Error bounds of truncated CPD are also analyzed in the presence of noise. Simulations show that, compared with state-of-the-art CPD methods, the proposed method is more efficient and is able to escape from local solutions more easily.

A new canonical polyadic (CP) decomposition method is proposed in this letter, where one factor matrix is extracted first by using any standard blind source separation (BSS) method and the remainder components are computed efficiently via sequential singular value decompositions of rank-1 matrices. The new approach provides more interpretable factors and it is extremely efficient for ill-conditioned problems. Especially, it overcomes the bottleneck problems, which often cause very slow convergence speed in CP decompositions. Simulations confirmed the validity and efficiency of the proposed method.

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate N non-stationary sources from M(M <; N) mixtures. First, an improved method is proposed for estimating the mixing matrix, where the negative value of the auto WVD of the sources is fully considered. Then after extracting all the auto-term TF points, the auto WVD value of the sources at every auto-term TF point can be found out exactly with the proposed approach no matter how many active sources there are as long as N ≤ 2M-1. Further discussion about the extraction of auto-term TF points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones.

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) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.

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.

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.