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.

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.

Accurately calculating the electronic structure of strongly correlated chemical systems necessitates a detailed description of both static and dynamical electron correlations, posing a significant challenge in ab initio quantum chemistry. Although the high memory and computational demands generally limit these calculations to relatively modest systems, the advanced computational capabilities of modern GPUs provide new avenues to expand these limits. However, complex control flows inherent to computation notably impair performance on GPUs. Furthermore, the significant disparity in computational load across different branches leads to load imbalance, challenging the large-scale simulations.

High-quality ocean observation is essential for research and applications in ocean exploration and climate change. With moving into the era of big data in recent years, it becomes crucial to process these massive raw observations accurately and efficiently. This paper addressed issues encountered in processing ocean big data within traditional delayed-mode quality control systems, including substantial serial I/O workloads and frequent context switching. A parallel quality control scheme named CODC-pyParaQC was proposed by constructing computing process groups. It retains the advantages of the existed delayed-mode quality control system (e.g. CODC-QC) while improving the efficiency of the quality control procedure, solving the feasibility of a large-scale parallel computation of the quality control scheme and realizing the (near) real-time quality control of massive ocean observation profiles. The results showed that the efficiency of single-node quality control has been improved by about 10 times. Leveraging the computing power of supercomputers and employing multi process groups for cross-node parallel computation, we have developed a fast and efficient (near) real-time quality control procedure. This system processed approximately 22,548,733 temperature profiles from the world ocean database (1940-2023) in about 6.5 hours. Our new quality control scheme can ensure the computing capability necessary for establishing a high-quality ocean observation profile database.

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.

Highly scattering media, such as milk, skin, and clouds, are common in the real world. Rendering participating media is challenging, especially for high-order scattering dominant media, because the light may undergo a large number of scattering events before leaving the surface. Monte Carlo-based methods typically require a long time to produce noise-free results. Based on the observation that low-albedo media contain less noise than high-albedo media, we propose reducing the variance of the rendered results using differentiable regularization. We first render an image with low-albedo participating media together with the gradient with respect to the albedo, and then predict the final rendered image with a low-albedo image and gradient image via a novel prediction function. To achieve high quality, we also consider the gradients of neighboring frames to provide a noise-free gradient image. Ultimately, our method can produce results with much less overall error than equal-time path tracing 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.

Deep neural networks have been shown to be effective for unsupervised monocular visual odometry that can predict the camera’s ego-motion based on an input of monocular video sequence. However, most existing unsupervised monocular methods haven’t fully exploited the extracted information from both local geometric structure and visual appearance of the scenes, resulting in degraded performance. In this paper, a novel geometry-aware network is proposed to predict the camera’s ego-motion by learning representations in both 2D and 3D space. First, to extract geometry-aware features, we design an RGB-PointCloud feature fusion module to capture information from both geometric structure and the visual appearance of the scenes by fusing local geometric features from depth-map-derived point clouds and visual features from RGB images. Furthermore, the fusion module can adaptively allocate different weights to the two types of features to emphasize important regions. Then, we devise a relevant feature filtering module to build consistency between the two views and preserve informative features with high relevance. It can capture the correlation of frame pairs in the feature-embedding space by attention mechanisms. Finally, the obtained features are fed into the pose estimator to recover the 6-DoF poses of the camera. Extensive experiments show that our method achieves promising results among the unsupervised monocular deep learning methods on the KITTI odometry and TUM-RGBD datasets.

With intersection and convergence of multiple disciplines and technologies, more and more researchers are actively exploring interdisciplinary cooperation outside their main research fields. Facing a new research field, researchers often hope to quickly learn what is being studied in this field, which research points are receiving high attention, which researchers are studying these research points, and then consider the possibility of collaborating with core researchers on these research points. In addition, students who are preparing academic further education usually conduct research on mentors and mentors’ research platforms, including academic connections, employment opportunities, etc. In order to satisfy these requirements, we (1) designs a research point state map based on a science map to help researchers and students understand the development state of a new research field; (2) designs a bar-link author-affiliation information graph to help researchers and students clarify academic networks of scholars and find suitable collaborators or mentors; (3) designs citation patten histogram to quickly discover research achievements with high research value, such as the Sleeping Beauty papers, recently hot papers, classic papers and so on. Finally, an interactive analytical system named PubExplorer was implemented with IEEE VIS publication data, and it’s effectiveness is verified through case studies.

Domain adaptive person re-identification (Re-ID) is challenging due to the domain gap between the source and target domains. Existing methods have recently shown great promise by training models with contrastive learning and assigning pseudo labels by clustering, in which a memory bank is utilized to keep features for contrast. However, two main problems lead to sub-optimal generalization ability for existing methods. First, there is no constraint on the updating for memory kept features in existing methods, resulting in inaccurate contrastive learning. Second, the inevitable noisy labels during clustering are usually ignored. To alleviate these problems, we propose a Label Rectifying with Consistent Contrastive-learning (LRCC) framework with two strategies. (1) The consistent contrastive-learning (CC) strategy works with a memory bank which stores the source domain class centroids and all the target domain image features. With the CC strategy, the contrast is conducted across the source and target domains simultaneously. More specifically, we design and maintain consistent clustering during model iteration, thus the classes of memory kept target features are invariable in one epoch. (2) The label rectifying (LR) strategy introduces an auxiliary classifier into the LRCC framework. Thus the pseudo labels are rectified by minimizing the prediction variance between the primary classifier and the auxiliary classifier. To verify the effectiveness of LRCC, we conduct experiments on three public person Re-ID datasets under the domain adaptive setting, DukeMTMC-reID, Market-1501, and MSMT17. The experimental results demonstrate that the proposed LRCC can obtain reliable pseudo labels and achieves state-of-the-art adaptation performance.

Facial action units (AUs) analysis plays an important role in facial expression recognition (FER). Existing deep spectral convolutional networks (DSCNs) have made encouraging performance for FER based on a set of facial local regions and a predefined graph structure. However, these regions do not have close relationships to AUs, and DSCNs cannot model the dynamic spatial dependencies of these regions for estimating different facial expressions. To tackle these issues, we propose a novel double dynamic relationships graph convolutional network (DDRGCN) to learn the strength of the edges in the facial graph by a trainable weighted adjacency matrix. We construct facial graph data by 20 regions of interest (ROIs) guided by different facial AUs. Furthermore, we devise an efficient graph convolutional network in which the inherent dependencies of vertices in the facial graph can be learned automatically during network training. Notably, the proposed model only has 110K parameters and 0.48MB model size, which is significantly less than most existing methods. Experiments on four widely-used FER datasets demonstrate that the proposed dynamic relationships graph network achieves superior results compared to existing light-weight networks, not just in terms of accuracy but also model size and speed.

Low-rank tensor recovery has been widely applied to computer vision and machine learning. Recently, tubal nuclear norm (TNN) based optimization is proposed with superior performance as compared to other tensor nuclear norms. However, one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations. To this end, we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way (K ≥ 3) tensors. We further formulate two robust tensor decomposition models via the proposed norms and develop two algorithms as the solutions. Theoretically, we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error. Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.

Optical coherence tomography angiography (OCTA) is an emerging non-invasive imaging technique for imaging the microvasculature of the eye based on phase variance or amplitude decorrelation derived from repeated OCT images of the same tissue area. Stripe noise occurs during the OCTA acquisition process due to the involuntary movement of the eye. To remove the stripe noise (or 'destriping') effectively, we propose two novel image decomposition models to simultaneously destripe all the OCTA images of the same eye cooperatively: cooperative uniformity destriping (CUD) model and cooperative similarity destriping (CSD) model. Both the models consider stripe noise by low-rank constraint but in different ways: the CUD model assumes that stripe noise is identical across all the layers while the CSD model assumes that the stripe noise at different layers are different and have to be considered in the model. Compared to the CUD model, CSD is a more general solution for real OCTA images. An efficient solution (CSD+) is developed for model CSD to reduce the computational complexity. The models were extensively evaluated against state-of-the-art methods on both synthesized and real OCTA datasets. The experiments demonstrated not only the effectiveness of the CSD and CSD+ models in terms of peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) and CSD+ is twice faster than CSD, but also their beneficiary effect on the vessel segmentation of OCTA images. We expect our models will become a powerful tool for clinical applications.

Tensor completion arouses much attention in signal processing and machine learning. The tensor train (TT) decomposition has shown better performances than the Tucker decomposition in image and video inpainting. In this paper, we propose a novel tensor completion model based on a newly defined latent Schatten TT norm. Then, the statistical performance is analyzed by establishing a non-asymptotic upper bound on the estimation error. Further, a scalable algorithm is developed to efficiently solve the model. Experimental results of color image inpainting demonstrate that the proposed norm has promising performances compared to other variants of Schatten norm.

Due to the superiority in exploiting the ubiquitous "spatial-shifting" property in modern multi-way data, the recently proposed low-tubal-rank model has been successfully applied for tensor recovery in signal processing and computer vision. In this paper, we define the generalized tensor Dantzig selector to recover a low-tubal-rank tensor from noisy linear measurements. Algorithmically, we develop an efficient algorithm based on the ADMM framework. Statistically, we establish non-asymptotic upper bounds on the estimation error for the problems of tensor completion and compressive sensing. Numerical experiments illustrate that our bounds can predict the scaling behavior of the estimation error. Experiments on realword datasets show the effectiveness of the proposed model.

Real multi-way data may suffer from missing entries, noise and outliers simultaneously. The recently proposed tubal nuclear norm (TNN) has shown its superiority in tensor completion. However, statistical analysis of TNN based models is still deficient. This paper aims to robustly recover a polluted incomplete tensor with rigorous statistical guarantee. Specifically, an estimator based on a weighed variant of TNN is proposed to complete a low-tubal-rank tensor corrupted by element sparse errors or slice sparse sample outliers from partial noisy observations. Non-asymptotic upper bounds on the estimation error are established and further proved to be minimax optimal up to a log factor. Sharpness of the upper bounds is verified on synthetic datasets and superiority of the proposed estimator is demonstrated through robust video inpainting.

Salient object detection can identify the most distinctive objects in a scene. In this study, a novel graph‐based approach is proposed to detect a salient object via reliable boundary seeds and saliency refinement. A natural image is firstly mapped to a graph with superpixels as nodes. Saliency information is then diffused over the graph using seeds. For the reason that the boundary nodes may contain salient nodes, it is not appropriate to use all boundary nodes as the background seeds. Therefore, a boundary saliency measurement is proposed to obtain more accurate background seeds. After that, the information of background seeds is diffused by a two‐stage scheme. A background‐based map and a foreground‐based map are generated based on the two‐stage scheme. Furthermore, in order to enhance the detection accuracy, a refinement model is presented to fuse the information of background‐based and foreground‐based maps. Experiments on seven public datasets show the proposed algorithm out‐performs the state‐of‐the‐art salient object detection algorithms.

Low-rank matrix completion aims to recover matrices with missing entries and has attracted considerable attention from machine learning researchers. Most of the existing methods, such as weighted nuclear-norm-minimization-based methods and Qatar Riyal (QR)-decomposition-based methods, cannot provide both convergence accuracy and convergence speed. To investigate a fast and accurate completion method, an iterative QR-decomposition-based method is proposed for computing an approximate singular value decomposition. This method can compute the largest r(r > 0) singular values of a matrix by iterative QR decomposition. Then, under the framework of matrix trifactorization, a method for computing an approximate SVD based on QR decomposition (CSVDQR)-based L2,1-norm minimization method (LNM-QR) is proposed for fast matrix completion. Theoretical analysis shows that this QR-decomposition-based method can obtain the same optimal solution as a nuclear norm minimization method, i.e., the L2,1-norm of a submatrix can converge to its nuclear norm. Consequently, an LNM-QR-based iteratively reweighted L2,1-norm minimization method (IRLNM-QR) is proposed to improve the accuracy of LNM-QR. Theoretical analysis shows that IRLNM-QR is as accurate as an iteratively reweighted nuclear norm minimization method, which is much more accurate than the traditional QR-decomposition-based matrix completion methods. Experimental results obtained on both synthetic and real-world visual data sets show that our methods are much faster and more accurate than the state-of-the-art methods.

In recent years, various graph-based salient object detection methods have been successfully proposed. Since existing methods may miss some object regions with low contrast to background, a novel propagation model via deformed smoothness constraint is proposed to address this problem. By regularizing nodes and their neighbors locally, the deformed smoothness constraint is able to prevent erroneous label propagation. Thus, the object regions with low contrast to background can be emerged. Besides, the deformed smoothness constraint is further utilized in a map refinement model, which can suppress the background noises in label propagation result. Experiments on three public datasets show that the proposed method outperforms eleven state-of-the-art salient object detection methods.

Face alignment is an important issue in many computer vision problems. The key problem is to find the nonlinear mapping from face image or feature to landmark locations. In this paper, we propose a novel cascaded approach with bidirectional Long Short Term Memory (LSTM) neural networks to approximate this nonlinear mapping. The cascaded structure is used to reduce the complexity of this problem and accelerate the algorithm by conducting the coarse-to-fine search. In each cascaded module, features of landmarks are delivered as inputs into the bidirectional LSTM network. The depth of the network guarantees the ability to learn highly complex mapping. The recurrent connections in LSTM explore the relationships of different landmarks and ensure that the shape of the face is maintained. On several challenging public databases, our approach achieves state-of-the-art performances.

Object detection plays a critical role for automatic video analysis in many vision applications. Background subtraction has been the mainstream in the field of moving objects detection. However, most of state‐of‐the‐art techniques of background subtraction operate on each pixel independently ignoring the global features of images. A motion detection method based on subspace update of background is proposed in this study. This method uses a subspace spanned by the principal components of background sequence to characterise the background and integrates the regional continuity of objects to segment the foreground. To deal with changes in the background geometry, a learning factor is introduced into the authors’ model to update the subspace timely. Additionally, to reduce computational complexity, they use two‐dimension principal component analysis (PCA) rather than traditional PCA to obtain the principal components of background. Experiments demonstrate that the update policy is effective and in most cases this proposed method can achieve better results than others compared in this study.

Low-rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision. Most existing methods formulate the task as a low-rank matrix approximation problem. A truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm. The corresponding optimization method, truncated nuclear norm regularization (TNNR), converges better than the nuclear norm minimization-based methods. However, it is not robust to the number of subtracted singular values and requires a large number of iterations to converge. In this paper, a TNNR method based on weighted residual error (TNNR-WRE) for matrix completion and its extension model (ETNNR-WRE) are proposed. TNNR-WRE assigns different weights to the rows of the residual error matrix in an augmented Lagrange function to accelerate the convergence of the TNNR method. The ETNNR-WRE is much more robust to the number of subtracted singular values than the TNNR-WRE, TNNR alternating direction method of multipliers, and TNNR accelerated proximal gradient with Line search methods. Experimental results using both synthetic and real visual data sets show that the proposed TNNR-WRE and ETNNR-WRE methods perform better than TNNR and Iteratively Reweighted Nuclear Norm (IRNN) methods.

In computer vision and pattern recognition applications, there are usually a vast number of unlabelled data whereas the labelled data are very limited. Active learning is a kind of method that selects the most representative or informative examples for labelling and training; thus, the best prediction accuracy can be achieved. A novel active learning algorithm is proposed here based on one‐versus‐one strategy support vector machine (SVM) to solve multi‐class image classification. A new uncertainty measure is proposed based on some binary SVM classifiers and some of the most uncertain examples are selected from SVM output. To ensure that the selected examples are diverse from each other, Gaussian kernel is adopted to measure the similarity between any two examples. From the previous selected examples, a batch of diverse and uncertain examples are selected by the dynamic programming method for labelling. The experimental results on two datasets demonstrate the effectiveness of the proposed algorithm.

Representation-based classification have received much attention in the field of face recognition. Collaborative representation-based classification (CRC) has shown the robustness and high performance. In this paper, we proposed a new feature extraction method-based collaborative representation. Firstly, we get the coefficients of all face samples by collaborative representation. Then we define the inter-class reconstructive errors and intra-class reconstructive errors for each sample. After that, Fisher criterion is used to get the discriminative feature. At last, CRC is executed to get the identification results in the new feature space. Different from other feature extraction methods, the proposed method integrates the classification criterion into the feature extraction. So the feature space we get fits the classifier better. Experiment results on several face databases show that the proposed method is more effective than other state-of-the-art face recognition methods.

A novel self-adaptive chaotic artificial bee colony algorithm based on Tent map (STOC-ABC) is proposed to enhance the global convergence and the population diversity. In the STOC-ABC, Tent chaotic opposition-based learning initialization method is presented to diversify the initial individuals and obtain good initial solutions. Furthermore, the self-adaptive Tent chaotic searching is implemented at the zones nearby individual optimum solution to help the artificial bee colony (ABC) algorithm to escape from the local optimum effectively. Moreover, the tournament selection strategy in onlooker bee phase is employed to increase the ability of the algorithm and avoid premature convergence. Experiments on six complex benchmark functions with high-dimension, the results further demonstrate that, the STOC-ABC not only accelerates the convergence rate and improves solution precision, but also provides excellent performance in dealing with complex high-dimensional functions.

Feature extraction plays an important role in analyzing data with multivariate features. Linear discriminant analysis based on L1-norm (LDA-L1) is a recently developed technique for enhancing the robustness of the classic LDA against outliers. However, LDA-L1 employs a greedy strategy to find all the discriminant vectors, which may lead to suboptimal solution. To address this issue, we develop a novel algorithm termed as ILDA-L1 in this paper, which can optimize all the discriminant vectors simultaneously in a unified framework. Specifically, we introduce an orthonormal constraint on the discriminant vectors and convert the objective function of LDA-L1 into a difference formula. To solve the resulting nonconvex and nonsmooth problem, we first construct a successive concave approximation to the objective function at current solution and then use projected sub gradient method, thus leading to a convergent iterative algorithm. The experimental results on several benchmark datasets confirm the effectiveness of ILDA-L1 in extracting robust features.

Recent research has demonstrated that sparse coding (or sparse representation) is a powerful tool for pattern classification. This paper presents a new unsupervised feature selection method, termed Sparse Representation Preserving Feature Selection (SRPFS), which aims at minimizing reconstruction residual based on sparse representation in the subspace of the selected features. A greedy algorithm and a joint selection algorithm are devised to efficiently solve the proposed combinatorial optimization formulation. In particular, the latter algorithm incorporates both l2,1-norm and l1-norm minimization within unsupervised feature selection framework. The experimental results on four real-world datasets demonstrate the improvements brought by our proposed SRPFS with joint selection algorithm.

In this study, a novel saliency detection algorithm based on linear neighbourhood propagation is proposed. The proposed algorithm is divided into three steps. First, the authors segment an input image into superpixels which are represented as the nodes in a graph. The weight matrix of the graph, which indicates the similarities between the nodes, is calculated by linear neighbourhood reconstruction. Second, the nodes, which are located at top, bottom, left and right of image boundary, are labelled as boundary priors. Then, based on weight matrix, label propagation is used to propagate the labels to unlabelled nodes. They rank the nodes according to the label information and select the nodes with minor information as saliency priors. Last, based on saliency priors, saliency detection is carried out by label propagation again. The nodes with more information are considered as saliency regions. Experimental results on three benchmark databases demonstrate the proposed method performs well when it is against the state‐of‐the‐art methods in terms of accuracy and robustness.

As an important biometric feature, human gait has great potential in video-surveillance-based applications. In this paper, we focus on the matrix representation-based human gait recognition and propose a novel discriminant subspace learning method called sparse bilinear discriminant analysis (SBDA). SBDA extends the recently proposed matrix-representation-based discriminant analysis methods to sparse cases. By introducing the L1and L2norms into the objective function of SBDA, two interrelated sparse discriminant subspaces can be obtained for gait feature extraction. Since the optimization problem has no closed-form solutions, an iterative method is designed to compute the optimal sparse subspace using the L1and L2norms sparse regression. Theoretical analyses reveal the close relationship between SBDA and previous matrix-representation-based discriminant analysis methods. Since each nonzero element in each subspace is selected from the most important variables/factors, SBDA is potential to perform equivalent to or even better than the state-of-the-art subspace learning methods in gait recognition. Moreover, using the strategy of SBDA plus linear discriminant analysis (LDA), we can further improve the performance. A set of experiments on the standard USF HumanID and CASIA gait databases demonstrate that the proposed SBDA and SBDA + LDA can obtain competitive performance.

Non‐negative matrix factorisation (NMF) has been widely used in pattern recognition problems. For the tasks of classification, however, most of the existing variants of NMF ignore both the discriminative information and the local geometry of data into the factorisation. The actual conditions of the problems will be affected by the change of the environmental factors to affect the recognition accuracy. In order to overcome these drawbacks, the authors regularised NMF by intra‐class and inter‐class fuzzy K nearest neighbour graphs, leading to NMF‐F K ‐NN in this study. By introducing two novel fuzzy K nearest neighbour graphs, NMF‐F K ‐NN can contract the intra‐class neighbourhoods and expand the inter‐class neighbourhoods in the decomposition. This method not only exploits the discriminative information and uses the geometric structure in the data effectively, but also reduces the influence of the external factors to improve recognition effect. In the factorisation, the authors minimised the approximation error whilst contracting intra‐class fuzzy neighbourhoods and expanding inter‐class fuzzy neighbourhoods. The authors develop simple multiplicative updates for NMF‐F K ‐NN and present monotonic convergence results. Experiments of the text clustering on the CLUTO toolkit and face recognition on ORL and YALE datasets show the effectiveness of our proposed method.

In pattern recognition, feature extraction techniques are widely employed to dimensionality reduction. In this paper, a novel feature extraction method, fuzzy complete linear discriminant analysis (Fuzzy-CLDA), is proposed by combining the complete linear discriminant analysis (CLDA) and the membership degrees of samples. Furthermore, we calculate the sample membership degrees with different distance metrics and compare the effectiveness of the distance metrics. In addition, experiments are provided for analyzing and illustrating our results.

In this paper, we propose a new multiscale saliency detection algorithm based on principal component analysis. To measure saliency of pixels in a given image, we first segment the image into patches and then use the principal component analysis to reduce the dimensions, in which it throw out dimensions that are noises with respect to the saliency calculation. The saliency of a patch is computed as the dissimilarities of colors and the spatial distance between it and other patches. Finally, we implement our algorithm through multiple scales so it can further decrease the saliency of background. Our method was compared with other saliency detection approaches using two public image datasets. Experimental results show that our method outperforms current state-of-the-art methods on predicting human fixations and salient object segmentation.

Two-dimensional (2-D) image-matrix-based projection methods for feature extraction are widely used in many fields of computer vision and pattern recognition. In this paper, we propose a novel framework called sparse 2-D projections (S2DP) for image feature extraction. Different from the existing 2-D feature extraction methods, S2DP iteratively learns the sparse projection matrix by using elastic net regression and singular value decomposition. Theoretical analysis shows that the optimal sparse subspace approximates the eigensubspace obtained by solving the corresponding generalized eigenequation. With the S2DP framework, many 2-D projection methods can be easily extended to sparse cases. Moreover, when each row/column of the image matrix is regarded as an independent high-dimensional vector (1-D vector), it is proven that the vector-based eigensubspace is also approximated by the sparse subspace obtained by the same method used in this paper. Theoretical analysis shows that, when compared with the vector-based sparse projection learning methods, S2DP greatly saves both computation and memory costs. This property makes S2DP more tractable for real-world applications. Experiments on well-known face databases indicate the competitive performance of the proposed S2DP over some 2-D projection methods when facial expressions, lighting conditions, and time vary.

A new fuzzy clustering algorithm using multi-prototype representation of clusters is proposed in this paper to discover clusters with arbitrary shapes and sizes. Intra-cluster non-consistency and inter-cluster overlap are proposed as two mistake measurements to guide the splitting and merging step of the algorithm. In the splitting step, clusters with the largest intra-cluster non-consistency are iteratively split such that the resulting subclusters only contain data from the same class. In the following merging step, subclusters with the largest inter-cluster overlap are iteratively merged until a pre-determined cluster number is achieved. A multi-prototype representation of clusters is used in the merging step to handle the clusters with different size and shapes. Experimental results on synthetic and real datasets demonstrate the effectiveness and robustness of the proposed algorithm.

In this paper, a novel method called tangent space discriminant analysis is proposed for dimensionality reduction and feature extraction. Differing from the recently proposed manifold learning methods completely operating on raw feature space, TSDA completely uses the local tangent space to represent the local within-class geometry and local between-class geometry. Assume that the face images of different people reside on different intrinsically low-dimensional sub-manifolds, TSDA is developed to preserve the locality of each sub-manifold and simultaneously maximize the local separability of different sub-manifolds by using local tangent space alignment. Experimental results show that TSDA achieves higher recognition rates than a few the state-of-the-art techniques.

Null space linear discriminant analysis (NLDA) and linear discriminant analysis based on generalized singular value decomposition (LDA/GSVD) are two popular linear discriminant analysis (LDA) methods that can solve Small Sample Size (SSS) problem. In this paper we present the relation between NLDA and LDA/GSVD under a mild condition, and propose a modified NLDA (MNLDA) algorithm. By both theoretical analysis and experimental results on ORL and FERET face databases, the proposed MNLDA has been proved to have the same discriminating power as LDA/GSVD and to be more efficient than LDA/GSVD.

In this paper, we develops a new approach, called fuzzy maximal marginal embedding (FMME), combining LMME (local maximal marginal embedding) with fuzzy set theory, in which the fuzzy k-nearest neighbor (FKNN) is implemented to achieve the nature distribution information of original samples, and this information is utilized to redefine the affinity weights of neighborhood graph (intraclass and interclass ) instead of the weights of the binary pattern. We can reduce sensitivity of the method to substantial variations between samples caused by varying illumination and shape, viewing conditions. That makes FMME more powerful and robust than other method. The proposed algorithm is examined using Yale and ORL face image databases. The experimental results show FMME outperforms PCA, LDA, LPP and LMME.

One of the major disadvantages of the linear dimensionality reduction algorithms, such as Principle Component Analysis (PCA) and Linear Discriminant Analysis (LDA), are that the projections are linear combination of all the original features or variables and all weights in the linear combination known as loadings are typically non-zero. Thus, they lack physical interpretation in many applications. In this paper, we propose a novel supervised learning method called Sparse Local Discriminant Projections (SLDP) for linear dimensionality reduction. SLDP introduces a sparse constraint into the objective function and obtains a set of sparse projective axes with directly physical interpretation. The sparse projections can be efficiently computed by the Elastic Net combining with spectral analysis. The experimental results show that SLDP give the explicit interpretation on its projections and achieves competitive performance compared with some dimensionality reduction techniques.

The variation of facial appearance due to the illumination degrades face recognition systems considerably, which is well known as one of the bottlenecks in face recognition. However, the variations of each subject which are due to the changes of illumination are extremely similar to each other. We offline collect many face classes each of which has many images under different lighting conditions, a common within-class scatter matrix describing the within-class illumination variations of all the face classes can be gotten. Based on this, illumination adaptive linear discriminant analysis (IALDA) is proposed to solve illumination variation problems in face recognition when each face class has only one training sample under the standard lighting conditions. In the IALDA method, the illumination direction of an input face image is firstly estimated. Then the corresponding LDA feature, which is robust to the variations between the images under the estimated lighting conditions and the standard lighting conditions, is extracted. Experiments on the face databases demonstrate the effectiveness of the proposed method.

Recently, local discriminant embedding (LDE) was proposed to manifold learning and pattern classification. In LDE framework, the neighbor and class of data points were used to construct the graph embedding for classification problems. From a high dimensional to a low dimensional subspace, data points of the same class maintain their intrinsic neighbor relations, whereas neighboring data points of different classes no longer stick to one another. But, neighboring data points of different classes are not deemphasized efficiently by LDE and it may degrade the performance of classification. In this paper, we investigated its extension, called class mean embedding (CME), using class mean of data points to enhance its discriminant power in their mapping into a low dimensional space. Experimental results on ORL and FERET face databases show the effectiveness of the proposed method.

This paper introduces the minimal local reconstruction error (MLRE) as a similarity measure and presents a MLRE-based classier. From the geometric meaning of the minimal local reconstruction error, we derive that the MLRE-based classifier is a generalization of the conventional nearest neighbor classier and the nearest neighbor line and plane classifiers. We further apply the MLRE measure to characterize the within-class and between-class local scatters and then develop a MLRE measure based discriminant feature extraction method. The proposed MLRE-based feature extraction method is in line with the MLRE-based classification method in spirit, thus the two methods can be seamlessly combined in applications. The experimental results on the CENPARMI handwritten numeral database and the FERET face image database show effectiveness of the proposed MLRE-based feature extraction and classification method.

In this paper, the integrated probability function (IPF) on local mean distance for image recognition was proposed to combine features for the best performance. Experiments were performed on CENPAMI handwriting digit database. The IPF on local mean distance was shown to be a good combination method for image recognition.

This paper examines the theory of kernel Fisher discriminant analysis (KFD) in a Hilbert space and develops a two-phase KFD framework, i.e., kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). This framework provides novel insights into the nature of KFD. Based on this framework, the authors propose a complete kernel Fisher discriminant analysis (CKFD) algorithm. CKFD can be used to carry out discriminant analysis in "double discriminant subspaces." The fact that, it can make full use of two kinds of discriminant information, regular and irregular, makes CKFD a more powerful discriminator. The proposed algorithm was tested and evaluated using the FERET face database and the CENPARMI handwritten numeral database. The experimental results show that CKFD outperforms other KFD algorithms.

Firstly, this paper answered one interesting question: what is orthogonal in ICA? We discussed the non-orthogonality of ICA transformation and claimed that the independent components (ICs) by the FastICA algorithm are orthogonal. Based on this orthogonality, an orthogonal ICA representation (OICA) of images was proposed. Experiments on ORL database, Yale database and CMU database with OICA were performed. More work is needed to discover any advantage of OICA.