Many optimization tasks involve streaming data with unknown concept drifts, posing a significant challenge as Streaming Data-Driven Optimization (SDDO). Existing methods, while leveraging surrogate model approximation and historical knowledge transfer, are often under restrictive assumptions such as fixed drift intervals and fully environmental observability, limiting their adaptability to diverse dynamic environments. We propose TRACE, a TRAnsferable Concept-drift Estimator that effectively detects distributional changes in streaming data with varying time scales. TRACE leverages a principled tokenization strategy to extract statistical features from data streams and models drift patterns using attention-based sequence learning, enabling accurate detection on unseen datasets and highlighting the transferability of learned drift patterns. Further, we showcase TRACE's plug-and-play nature by integrating it into a streaming optimizer, facilitating adaptive optimization under unknown drifts. Comprehensive experimental results on diverse benchmarks demonstrate the superior generalization, robustness, and effectiveness of our approach in SDDO scenarios.

Incomplete multi-view clustering is a prominent research area in multimedia. Among various techniques, self-representation-based approaches have gained attention for effectively capturing global data structures. However, most methods assume different views share a common self-representation matrix, overlooking view-specific characteristics and cross-view complementarity. To address this limitation, we propose a novel incomplete multi-view clustering model, Joint Shared and Private Self-representation Learning (JSPSL), which decomposes the self-representation matrices into shared and private components with mutually exclusive constraints. JSPSL unifies missing view completion and self-representation learning within a single framework, enabling mutual reinforcement. We apply ADMM to efficiently solve our model. Extensive experiments demonstrate that JSPSL consistently outperforms state-of-the-art algorithms.

Accomplishing a plug-and-play steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI) remains a critical challenge, due to the unsatisfying performance of calibration-free decoding algorithms.A current method called online adaptive canonical correlation analysis (OACCA) has proved efficient in enhancing calibration-free performance by self-adaptation merely with online data.However, OACCA only concerns the adaptation of spatial filters and excludes other useful adaptive procedures like individual template estimation, hindering fully exploitable model decoding and adaptation. This study proposes a new online adaptation framework termed online adaptive extended correlation analysis (OAECA) to augment the calibration-free online adaptation loop. OAECA first recalls and cleans the online trials for reliable data learning, then tunes individual templates and spatial filters for complete model updating, and finally adopts extended feature matching to improve target recognition. The simulation results on two public SSVEP datasets revealed that OAECA significantly outperformed OACCA for almost all 105 subjects, and both offline and online experiments further confirmed the effectiveness of OAECA. Particularly, OAECA achieved the highest average information transfer rate (ITR) of 202.17 bits/min in the online experiment, significantly exceeding the state-of-the-art OACCA of 177.02 bits/min. This study enhanced the calibration-free performance through comprehensive online adaptation, hopefully advancing SSVEP-based BCIs toward practical plug-and-play real-world applications.

Incomplete Multi-View Clustering (IMVC) addresses the challenge of missing data by leveraging available information and effectively mining cross-view relationships. While contrastive learning has recently been introduced into IMVC for discriminative representation learning, existing methods typically adopt pairwise contrastive strategies with view-specific reconstruction and heuristic fusion schemes. These approaches are generally suboptimal when facing high missing-view ratios and struggle to capture latent cross-view dependencies. To overcome these limitations, we propose ConsensNet, a unified consensus-centric framework for IMVC. This is achieved through a unified architecture that integrates contrastive cross-view alignment, consensus prediction, and attention-aware fusion. By aligning all available views into a shared semantic space, ConsensNet effectively captures latent cross-view dependencies without requiring high-quality view completion. Moreover, the attention-aware fusion mechanism dynamically assigns weights to each view based on its relevance to the consensus, thereby reducing the impact of noisy or weakly correlated views. Extensive experiments on multiple datasets demonstrate that ConsensNet consistently outperforms state-of-the-art IMVC methods, particularly under high missing-view scenarios, highlighting its robustness and practical significance.

Objective: Because of the non-stationary nature of electroencephalogram (EEG) signals, traditional non-invasive brain-computer interfaces (BCIs) usually only produce discrete commands, limiting their ability to control external devices continuously. This study proposes a novel BCI control strategy mapping multiple discrete commands to continuous motion, enabling real-time manipulation of a drone in four degrees of freedom (DOF).Methods: Our strategy used the fast steady state visual evoked potential (SSVEP) encoding and decoding method to convert user intentions into the drone’s flight status in near real-time. Simultaneously, the drone’s live video was embedded into the SSVEP stimuli, providing users with a first-person perspective control experience.Results: In drone control experiments, participants successfully maneuvered the drone through complex path-following tasks in simulated and physical scenarios. The mean flight trajectory bias ratio was measured as 0.81, with a mean flight smoothness of -3.31 (measured by spectral arc length) and mean Fitts’s throughput of 9.18 bits/min. Notably, the brain-to-hand ratio (BHR) for all metrics approached 1, indicating that our non-invasive control system achieved comparable performance to manual control systems.Conclusion: These results suggest the effectiveness of our proposed BCI control strategy that maps discrete commands to continuous motion and extends the capabilities of non-invasive BCIs in continuous control scenarios.Significance: This study significantly advances the applications of BCI and propels human-machine interaction towards a more direct realm.

Recently, Low-Rank Matrix (LRM)-based feature extraction methods have drawn increasing attention since they can extract robust features when the data are corrupted. However, these algorithms require a matrix-to-vector transformation to tackle Two-Dimensional (2D) images, through which the spatial structure residing in 2D images is ignored. To solve this problem, we propose a Low-Rank Tensor-based 2D Projection learning model (LRT-2DP) to extract features directly from 2D images as well as to reduce dimensionality. In essence, LRT-2DP embraces the global self-expressiveness property to denoise the corrupted data, from which a 2D projection basis is learned for robust feature extraction. The proposed LRT-2DP can be efficiently optimized with an alternative optimization scheme. Extensive experiments on image feature extraction have demonstrated the superiority of LRT-2DP compared to state-of-the-arts.

Subspace learning has been widely applied for joint feature extraction and dimensionality reduction, demonstrating significant efficacy. Numerous subspace learning methods with diverse assumptions regarding the criteria for the target subspaces have been developed to obtain compact and interpretable data representations. However, when applied to image data, existing methods fail to fully exploit the inherent correlations within the image set. This paper proposes a Robust Discriminative t-Linear Subspace Learning model (RDtSL) to tackle this issue using t-product. The model mainly has four strengths: 1) Taking advantage of t-product, RDtSL learns the projection basis directly from the image set while fully exploiting its internal correlations; 2) Based on its energy preservation module, RDtSL retains the primary energy of samples in the learned subspace, maintaining satisfactory performance even with low subspace dimensions; 3) Class-distinctive features are effectively preserved in the learned representations due to the incorporation of the classification module; 4) Relying on its graph embedding module, RDtSL learns an affinity graph of samples adaptively to enrich the data representations with locality and similarity information. The harmonious balance maintained between the three proposed modules helps RDtSL learn discriminative and informative data representations. We also develop an iterative algorithm to solve RDtSL. Extensive experiments on benchmark databases demonstrate the superiority of the proposed model.

Current multi-view subspace clustering methods typically consist of a within-view module, which explores inherent characteristics using the self-expressive coefficient matrix, and a cross-view module, which promotes consensus among all views toward similar strengths. However, the self-expressive coefficients are directly influenced by the characteristics and distributions of input features, and coefficient matrices with varying strengths may indicate the same clustering structure. Therefore, directly regularizing the coefficient matrices towards a common matrix is unnecessary and may even diminish the clustering performance. We find that it is the relative data relationship, rather than the absolute similarity, that plays a pivotal role in clustering. Building on this realization, we propose a relative comparison measure that enables a more contextual understanding of the data relationship. Subsequently, we develop a Relative Comparison-based Consensus Learning (RCCL) model for multi-view subspace clustering, which encourages the relative data similarities to be consistent across different views. Our RCCL model advances in identifying the underlying data relationship, avoiding unnecessary constraints on absolute consistency, and thereby delving into the fundamental nature of multi-view consensus. We introduce an elegant transformation operator for relative comparison and solve RCCL under the framework of alternating direction method of multipliers. Extensive experiments unequivocally demonstrated the superiority of RCCL.

In real scenarios, graph-based multiview clustering has clearly shown popularity owing to the high efficiency in fusing the information from multiple views. Practically, the multiview graphs offer both consistent and inconsistent cues as they usually come from heterogeneous sources. Previous methods illustrated the importance of leveraging the multiview consistency and inconsistency for accurate modeling. However, when fusing the graphs, the inconsistent parts are generally ignored and hence the valued view-specific attributes are lost. To solve this problem, we propose an accurate complementarity learning (ACL) model for graph-based multiview clustering. ACL clearly distinguishes the consistent, complementary, and noise and corruption terms from the initial multiview graphs. In contrast to existing models that overlooked the complementary information, we argue that the view-specific characteristics extracted from the complementary terms are beneficial for affinity learning. In addition, ACL exploits only the positive parts of the complementary information for preserving the evidence on the positive sample relationship, and ignores the negative cues to avoid the vanishing of effective affinity strengths. This way, the learned affinity matrix is able to properly balance the consistent and complementary information. To solve the ACL model, we introduce an efficient alternating optimization algorithm with a varying penalty parameter. Experiments on synthetic and real-world databases clearly demonstrated the superiority of ACL.

The field of visual search has gained significant attention recently, particularly in the context of web search engines and e-commerce product search platforms. However, the abundance of web images presents a challenge for modern image retrieval systems, as they need to find both relevant and diverse images that maximize users’ satisfaction. In response to this challenge, we propose a non-dominated visual diversity re-ranking (NDVDR) method based on the concept of Pareto optimality. To begin with, we employ a fast binary hashing method as a coarse-grained retrieval procedure. This allows us to efficiently obtain a subset of candidate images for subsequent re-ranking. Fed with this initial retrieved image results, the NDVDR performs a fine-grained re-ranking procedure for boosting both relevance and visual diversity among the top-ranked images. Recognizing the inherent conflict nature between the objectives of relevance and diversity, the re-ranking procedure is simulated as the analytical stage of a multi-criteria decision-making process, seeking the optimal tradeoff between the two conflicting objectives within the initial retrieved images. In particular, a non-dominated sorting mechanism is devised that produces Pareto non-dominated hierarchies among images based on the Pareto dominance relation. Additionally, two novel measures are introduced for the effective characterization of the relevance and diversity scores among different images. We conduct experiments on three popular real-world image datasets and compare our re-ranking method with several state-of-the-art image search re-ranking methods. The experimental results validate that our re-ranking approach guarantees retrieval accuracy while simultaneously boosting diversity among the top-ranked images.

Natural image matting has garnered increasing attention in various computer vision applications. The matting problem aims to find the optimal foreground/background (F/B) color pair for each unknown pixel and thus obtain an alpha matte indicating the opacity of the foreground object. This problem is typically modeled as a large-scale pixel pair combinatorial optimization (PPCO) problem. Heuristic optimization is widely employed to tackle the PPCO problem owing to its gradient-free property and promising search ability. However, traditional heuristic methods often encode F/B solutions to a one-dimensional (1D) representation and then evolve the solutions in a 1D manner. This 1D representation destroys the intrinsic two-dimensional (2D) structure of images, where the significant spatial correlations among pixels are ignored. Moreover, the 1D representation also brings operation inefficiency. To address the above issues, this article develops a spatial-aware tensorial evolutionary image matting (TEIM) method. Specifically, the matting problem is modeled as a 2D Spatial-PPCO (S-PPCO) problem, and a global tensorial evolutionary optimizer is proposed to tackle the S-PPCO problem. The entire population is represented as a whole by a third-order tensor, in which individuals are classified into two types: F and B individuals for denoting the 2D F/B solutions, respectively. The evolution process, consisting of three tensorial evolutionary operators, is implemented based on pure tensor computation for efficiently seeking F/B solutions. The local spatial smoothness of images is also integrated into the evaluation process for obtaining a high-quality alpha matte. Experimental results compared with state-of-the-art methods validate the effectiveness of TEIM.

Travel time estimation is a crucial task in practical transportation applications, while providing the reliability of estimation is important in many working scenarios. Most existing studies do not consider the dynamics of traffic status for different road segments in real time, thus yielding unsatisfactory results. To address the problem, we propose to formulate the traffic network as a temporal attributed graph and perform node representation learning on it. The learned representation is capable of jointly exploiting the dynamic traffic conditions and the topology of the road network, which is then fed into a route-based spatio-temporal dependence learning module to estimate the travel time. By incorporating a distribution loss function, our proposed model is able to predict the distribution of travel time. In the meantime, we design an auxiliary local task of predicting the congestion status of each road segment, which further enhances the generalization performance of the representation learning. Extensive experiments on real-world large-scale datasets demonstrated the superiority of our method compared with the state-of-the-arts.

One essential issue in surrogate-assisted evolutionary algorithms (SAEAs) is how to evaluate solutions and find candidates for evolution, without resorting to the calculation of the computational-expensive real objective function. While most studies use regression models as surrogate models for SAEAs, some recent work propose to use classification models for single-objective expensive optimization, as classification models are more stable and much easier to train with limited available data. However, for multi-objective expensive optimization problems, it is more challenging to classify the solutions into different levels according to their quality, and thus the use of classification-based surrogate models for multi-objective SAEAs has not been explored in-depth. To this end, in this paper we propose a classification-assisted level-based learning swarm optimizer for expensive multi-objective optimization. First, a preference relationship among individuals taking both Pareto dominance and crowding distance into account is defined to divide the whole population into different quality levels. Then, a classification model is trained as the surrogate. In addition, a selection strategy is devised in decision space to acquire solutions on the sparse part on the Pareto front. Experimental results validate the superiority and efficiency of the proposed algorithm on benchmark test functions.

Estimating the time of arrival is a crucial task in intelligent transportation systems. Although considerable efforts have been made to solve this problem, most of them decompose a trajectory into several segments and then compute the travel time by integrating the attributes from all segments. The segment view, though being able to depict the local traffic conditions straightforwardly, is insufficient to embody the intrinsic structure of trajectories on the road network. To overcome the limitation, this study proposes multi-view trajectory representation that comprehensively interprets a trajectory from the segment-, link-, and intersection-views. To fulfill the purpose, we design a hierarchical self-attention network (HierETA) that accurately models the local traffic conditions and the underlying trajectory structure. Specifically, a segment encoder is developed to capture the spatio-temporal dependencies at a fine granularity, within which an adaptive self-attention module is designed to boost performance. Further, a joint link-intersection encoder is developed to characterize the natural trajectory structure consisting of alternatively arranged links and intersections. Afterward, a hierarchy-aware attention decoder is designed to realize a tradeoff between the multi-view spatio-temporal features. The hierarchical encoders and the attentive decoder are simultaneously learned to achieve an overall optimality. Experiments on two large-scale practical datasets show the superiority of HierETA over the state-of-the-arts.

Graph and subspace clustering methods have become the mainstream of multi-view clustering due to their promising performance. However, (1) since graph clustering methods learn graphs directly from the raw data, when the raw data is distorted by noise and outliers, their performance may seriously decrease; (2) subspace clustering methods use a “two-step” strategy to learn the representation and affinity matrix independently, and thus may fail to explore their high correlation. To address these issues, we propose a novel multi-view clustering method via learning aLow-RankTensorGraph (LRTG). Different from subspace clustering methods, LRTG simultaneously learns the representation and affinity matrix in a single step to preserve their correlation. We apply Tucker decomposition and$l_{2,1}$-norm to the LRTG model to alleviate noise and outliers for learning a “clean” representation. LRTG then learns the affinity matrix from this “clean” representation. Additionally, an adaptive neighbor scheme is proposed to find the$K$largest entries of the affinity matrix to form a flexible graph for clustering. An effective optimization algorithm is designed to solve the LRTG model based on the alternating direction method of multipliers. Extensive experiments on different clustering tasks demonstrate the effectiveness and superiority of LRTG over seventeen state-of-the-art clustering methods.

This paper addresses the multi-view subspace clustering problem and proposes the self-paced enhanced low-rank tensor kernelized multi-view subspace clustering (SETKMC) method, which is based on two motivations: (1) singular values of the representations and multiple instances should be treated differently. The reasons are that larger singular values of the representations usually quantify the major information and should be less penalized; samples with different degrees of noise may have various reliability for clustering. (2) many existing methods may cause the degraded performance when multi-view features reside in different nonlinear subspaces. This is because they usually assumed that multiple features lie within the union of several linear subspaces. SETKMC integrates the nonconvex tensor norm, self-paced learning, and kernel trick into a unified model for multi-view subspace clustering. The nonconvex tensor norm imposes different weights on different singular values. The self-paced learning gradually involves instances from more reliable to less reliable ones while the kernel trick aims to handle the multi-view data in nonlinear subspaces. One iterative algorithm is proposed based on the alternating direction method of multipliers. Extensive results on seven real-world datasets show the effectiveness of the proposed SETKMC compared to fifteen state-of-the-art multi-view clustering methods.

Multiview clustering as an important unsupervised method has been gathering a great deal of attention. However, most multiview clustering methods exploit theself-representation propertyto capture the relationship among data, resulting in high computation cost in calculating the self-representation coefficients. In addition, they usually employ different regularizers to learn the representation tensor or matrix from which a transition probability matrix is constructed in a separate step, such as the one proposed by Wuet al.. Thus, an optimal transition probability matrix cannot be guaranteed. To solve these issues, we propose a unified model for multiview spectral clustering by directly learning an adaptive transition probability matrix (MCA2M), rather than an individual representation matrix of each view. Different from the one proposed by Wuet al., MCA2M utilizes the one-step strategy to directly learn the transition probability matrix under the robust principal component analysis framework. Unlike existing methods using the absolute symmetrization operation to guarantee the nonnegativity and symmetry of the affinity matrix, the transition probability matrix learned from MCA2M is nonnegative and symmetric without any postprocessing. An alternating optimization algorithm is designed based on the efficient alternating direction method of multipliers. Extensive experiments on several real-world databases demonstrate that the proposed method outperforms the state-of-the-art methods.

As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.

In multi-view subspace clustering, the low-rankness of the stacked self-representation tensor is widely accepted to capture the high-order cross-view correlation. However, using the nuclear norm as a convex surrogate of the rank function, the self-representation tensor exhibits strong connectivity with dense coefficients. When noise exists in the data, the generated affinity matrix may be unreliable for subspace clustering as it retains the connections across inter-cluster samples due to the lack of sparsity. Since both the connectivity and sparsity of the self-representation coefficients are curial for subspace clustering, we propose a Reliable Multi-View Affinity Learning (RMVAL) method so as to optimize both properties in a single model. Specifically, RMVAL employs the low-rank tensor constraint to yield a well-connected yet dense solution, and purifies the densely connected self-representation tensor by preserving only the connections in local neighborhoods using the$l_1$-norm regularization. This way, the strong connections on the self-representation tensor are retained and the trivial coefficients corresponding to the inter-cluster connections are suppressed, leading to a “clean” self-representation tensor and also a reliable affinity matrix. We propose an efficient algorithm to solve RMVAL using the alternating direction method of multipliers. Extensive experiments on benchmark databases have demonstrated the superiority of RMVAL.

To learn the self-representation matrices/tensor that encodes the intrinsic structure of the data, existing multiview self-representation models consider only the multiview features and, thus, impose equal membership preference across samples. However, this is inappropriate in real scenarios since the prior knowledge, e.g., explicit labels, semantic similarities, and weak-domain cues, can provide useful insights into the underlying relationship of samples. Based on this observation, this article proposes a prior knowledge regularized multiview self-representation (P-MVSR) model, in which the prior knowledge, multiview features, and high-order cross-view correlation are jointly considered to obtain an accurate self-representation tensor. The general concept of "prior knowledge" is defined as the complement of multiview features, and the core of P-MVSR is to take advantage of the membership preference, which is derived from the prior knowledge, to purify and refine the discovered membership of the data. Moreover, P-MVSR adopts the same optimization procedure to handle different prior knowledge and, thus, provides a unified framework for weakly supervised clustering and semisupervised classification. Extensive experiments on real-world databases demonstrate the effectiveness of the proposed P-MVSR model.

Recent years have witnessed the success of deep learning in many fields. Commonly, the deep neural networks are trained by gradient-based methods, which is however ineffective in some cases when the optimization landscapes contain many local optima. In this study, we propose a novel optimization approach that combines neuroevolution with gradient-based method, which possesses the advantages of global search and fast convergence. The main challenge is the high expense of network training, especially when the network structure becomes deeper. This motivates us to utilize the concept of transfer learning which borrows knowledge from a source domain to enhance the learning ability in a target domain. Unfortunately, the design of transfer learning strategies for specific scenarios usually requires external expert knowledge. We therefore propose an adaptive transfer system (ATS) based on dataset similarity, which adaptively adjusts the transferring and retraining modules according to the similarity of the source and target tasks. Empirical studies on image classification problems demonstrate the effectiveness of the proposed algorithm. We are the first attempt to show that the neuroevolution can be successfully applied to deep transfer learning.

Low-rank matrix approximation (LRMA)-based methods have made a great success for grayscale image processing. When handling color images, LRMA either restores each color channel independently using the monochromatic model or processes the concatenation of three color channels using the concatenation model. However, these two schemes may not make full use of the high correlation among RGB channels. To address this issue, we propose a novel low-rank quaternion approximation (LRQA) model. It contains two major components: first, instead of modeling a color image pixel as a scalar in conventional sparse representation and LRMA-based methods, the color image is encoded as a pure quaternion matrix, such that the cross-channel correlation of color channels can be well exploited; second, LRQA imposes the low-rank constraint on the constructed quaternion matrix. To better estimate the singular values of the underlying low-rank quaternion matrix from its noisy observation, a general model for LRQA is proposed based on several nonconvex functions. Extensive evaluations for color image denoising and inpainting tasks verify that LRQA achieves better performance over several state-of-the-art sparse representation and LRMA-based methods in terms of both quantitative metrics and visual quality.

Linear discriminant analysis has been incorporated with various representations and measurements for dimension reduction and feature extraction. In this paper, we propose two-dimensional quaternion sparse discriminant analysis (2D-QSDA) that meets the requirements of representing RGB and RGB-D images. 2D-QSDA advances in three aspects: 1) including sparse regularization, 2D-QSDA relies only on the important variables, and thus shows good generalization ability to the out-of-sample data which are unseen during the training phase; 2) benefited from quaternion representation, 2D-QSDA well preserves the high order correlation among different image channels and provides a unified approach to extract features from RGB and RGB-D images; 3) the spatial structure of the input images is retained via the matrix-based processing. We tackle the constrained trace ratio problem of 2D-QSDA by solving a corresponding constrained trace difference problem, which is then transformed into a quaternion sparse regression (QSR) model. Afterward, we reformulate the QSR model to an equivalent complex form to avoid the processing of the complicated structure of quaternions. A nested iterative algorithm is designed to learn the solution of 2D-QSDA in the complex space and then we convert this solution back to the quaternion domain. To improve the separability of 2D-QSDA, we further propose 2D-QSDAw using the weighted pairwise between-class distances. Extensive experiments on RGB and RGB-D databases demonstrate the effectiveness of 2D-QSDA and 2D-QSDAw compared with peer competitors.

Multi-view clustering refers to the task of partitioning numerous unlabeled multimedia data into several distinct clusters using multiple features. In this paper, we propose a novel nonlinear method called joint learning multi-view clustering (JLMVC) to jointly learn kernel representation tensor and affinity matrix. The proposed JLMVC has three advantages: (1) unlike existing low-rank representation-based multi-view clustering methods that learn the representation tensor and affinity matrix in two separate steps, JLMVC jointly learns them both; (2) using the “kernel trick,” JLMVC can handle nonlinear data structures for various real applications; and (3) different from most existing methods that treat representations of all views equally, JLMVC automatically learns a reasonable weight for each view. Based on the alternating direction method of multipliers, an effective algorithm is designed to solve the proposed model. Extensive experiments on eight multimedia datasets demonstrate the superiority of the proposed JLMVC over state-of-the-art methods.

Low-rank tensor representation-based multi-view clustering has become an efficient method for data clustering due to the robustness to noise and the preservation of the high order correlation. However, existing algorithms may suffer from two common problems: (1) the local view-specific geometrical structures and the various importance of features in different views are neglected; (2) the low-rank representation tensor and the affinity matrix are learned separately. To address these issues, we propose a novel framework to learn the Graph regularized Low-rank Tensor representation and the Affinity matrix (GLTA) in a unified manner. Besides, the manifold regularization is exploited to preserve the view-specific geometrical structures, and the various importance of different features is automatically calculated when constructing the final affinity matrix. An efficient algorithm is designed to solve GLTA using the augmented Lagrangian multiplier. Extensive experiments on six real datasets demonstrate the superiority of GLTA over the state-of-the-arts.

Recent studies have shown the effectiveness of using depth information in salient object detection. However, the most commonly seen images so far are still RGB images that do not contain the depth data. Meanwhile, the human brain can extract the geometric model of a scene from an RGB-only image and hence provides a 3D perception of the scene. Inspired by this observation, we propose a new concept named RGB-'D' saliency detection, which derives pseudo depth from the RGB images and then performs 3D saliency detection. The pseudo depth can be utilized as image features, prior knowledge, an additional image channel, or independent depth-induced models to boost the performance of traditional RGB saliency models. As an illustration, we develop a new salient object detection algorithm that uses the pseudo depth to derive a depth-driven background prior and a depth contrast feature. Extensive experiments on several standard databases validate the promising performance of the proposed algorithm. In addition, we also adapt two supervised RGB saliency models to our RGB-'D' saliency framework for performance enhancement. The results further demonstrate the generalization ability of the proposed RGB-'D' saliency framework.

Benefited from quaternion representation that is able to encode the cross-channel correlation of color images, quaternion principle component analysis (QPCA) was proposed to extract features from color images while reducing the feature dimension. A quaternion covariance matrix (QCM) of input samples was constructed, and its eigenvectors were derived to find the solution of QPCA. However, eigen-decomposition leads to the fixed solution for the same input. This solution is susceptible to outliers and cannot be further optimized. To solve this problem, this paper proposes a novel quaternion ridge regression (QRR) model for two-dimensional QPCA (2D-QPCA). We mathematically prove that this QRR model is equivalent to the QCM model of 2D-QPCA. The QRR model is a general framework and is flexible to combine 2D-QPCA with other technologies or constraints to adapt different requirements of real-world applications. Including sparsity constraints, we then propose a quaternion sparse regression model for 2D-QSPCA to improve its robustness for classification. An alternating minimization algorithm is developed to iteratively learn the solution of 2D-QSPCA in the equivalent complex domain. In addition, 2D-QPCA and 2D-QSPCA can preserve the spatial structure of color images and have a low computation cost. Experiments on several challenging databases demonstrate that 2D-QPCA and 2D-QSPCA are effective in color face recognition, and 2D-QSPCA outperforms the state of the arts.

Motivated by the facts that, (1), the spatial structure of images and the correlation among color channels are important for color face recognition, and (2), natural face images may be occluded, in this work, we propose two-dimensional quaternion sparse principle component analysis (2DQSPCA) to extract features for color face recognition. 2DQSPCA inherently takes the advantage of 2DPCA in preserving the structure of two-dimensional data, as well as the strength of quaternion-s in representing color images holistically. Benefited from the sparsity constraints, 2DQSPCA is robust for occlusions. Experiments demonstrate the superior performance of 2DQSP-CA on color face recognition, especially with occlusions.

To reduce feature dimensions while obtaining robust classification, in this paper, we propose quaternion sparse discriminant analysis (QSDA) for color face recognition. QSDA is formulated as a quaternion sparse regression-type model. It employs the quaternion algebra to provide an elegant and holistic way to represent color face images. The succeeding operations are directly applied to two-dimensional quaternion matrices, and hence QSDA is computationally efficient and well preserves the spatial structure of color face images. Benefited from sparsity constraints, QSDA is robust for classification. An alternating minimization algorithm is designed to solve QSDA. Experimental results demonstrate the effectiveness of QSDA for color face recognition, especially for partially occluded color face images.

Superpixel segmentation targets at grouping pixels in an image into atomic regions whose boundaries align well with the natural object boundaries. This paper first proposes a new feature representation for superpixel segmentation that holistically embraces color, contour, texture, and spatial features. Then, we introduce a clustering-based discriminability measure to iteratively evaluate the importance of different features. Integrating the feature representation and the discriminability measure, we propose a novel content-adaptive superpixel (CAS) segmentation algorithm. CAS is able to automatically and iteratively adjust the weights of different features to fit various properties of image instances. Experiments on several challenging datasets demonstrate that the proposed CAS outperforms the state-of-the-art methods and has a low computational cost.

Superpixel segmentation targets at grouping pixels in an image into atomic regions that align well with the natural object boundaries. In this paper, we propose a novel superpixel segmentation method based on an iterative and adaptive clustering algorithm that embraces color, contour, texture, and spatial features together. The algorithm adjusts the weights of different features automatically in a content-aware way, so as to fit the requirements of various image instances. More specifically, in each iteration, the weights in the aggregation function are adjusted according to the discriminabilities of features in the current working scenario. This way, the algorithm not only possesses improved robustness but also relieves the burden of setting the parameters manually. Experimental verification shows that the algorithm outperforms existing peer algorithms in terms of commonly used evaluation metrics, while using a low computational cost.

Salient object detection aims to correctly highlight the most salient object(s) in an image. Combining fine-grained contrast prior with rough-grained object consistency, this paper proposes a Focusness Guided Salient object detection (FGS) algorithm. To obtain clean and precise contrast map, FGS uses the focusness prior to guide the contrast map. Combing different saliency priors, FGS utilizes a unified least-square framework to generate the final optimal salient map. Experiments demonstrate the proposed method outperforms the state-of-the-arts.