Continual learning (CL) aims to enable networks to learn continuously from sequentially arriving task streams while avoiding catastrophic forgetting (CF) of previously learned tasks. In recent years, Orthogonal gradient projection (OGP)-based CL methods have garnered significant attention from the research community due to their remarkable performance. However, existing OGP approaches overlook two critical issues: (1) representation matrices are typically constructed via random sampling, which introduces misclassified and class-imbalanced samples into the projection basis, contaminating important gradient directions and degrading stability; and (2) task-specific output scale variations induce domain drift, resulting in projection bias that weakens orthogonal constraints across tasks. To address these limitations, we propose Stable Gradient Projection for Continual Learning (STEP), a plug-and-play enhancement framework for OGP-based CL that integrates Correctness-aware Balanced Sampling (CBS) to construct purified and class-balanced projection subspaces using only correctly classified samples, and Sigmoid Attention Constraint (SAC) to enforce consistent output scaling via a sigmoid-based gating mechanism, thereby mitigating scale-induced projection bias. Extensive experiments on Split CIFAR-100, CIFAR-100 Superclass, and 5-Datasets demonstrate that STEP consistently improves state-of-the-art OGP methods, achieving up to +1.4% average accuracy (ACC) gains on Split CIFAR-100, improving backward transfer (BWT) from − 0.37 to − 0.09 for GPM and from − 1.06 to − 0.73 for SGP, and attaining 93.28% ACC with positive BWT (0.17) on 5-Datasets. These results validate STEP as a simple yet effective strategy for enhancing stability–plasticity balance in OGP-based CL.

Medical image segmentation is crucial for clinical decision-making, treatment planning, and disease tracking. Nonetheless, it confronts two significant challenges: the presence of ''soft boundaries'' between the foreground and background exacerbated by poor illumination and low contrast, and the misleading co-occurrence of salient and non-salient objects during the training phase, which complicates the model's accuracy in distinguishing relevant features. To overcome these challenges, we introduce RoDeCon-Net, a novel framework engineered to enhance medical image segmentation. RoDeCon-Net incorporates a Feature Decoupling Unit (FDU) that dynamically separates encoded features into foreground, background, and uncertain regions, using advanced attention mechanisms to refine feature distinction and reduce uncertainty. Additionally, our Contrast-driven Feature Alignment Unit (CFAU) and Cross-layer Feature Cascade Unit (CFCU) synergize to reinforce feature contrasts and promote effective multi-level feature fusion, thus improving the detection of salient objects amidst complex backgrounds and handling various object scales within images. Comprehensive evaluations of RoDeCon-Net on five diverse medical image datasets validate its superior performance and versatility, showcasing its potential to set new benchmarks in medical image segmentation. Our code is available on https://github.com/ILoveACM-MM/RoDeCon-Net.

Existing RGB-D salient object detection (SOD) models are primarily trained on general-purpose datasets, which may lead to domain shift issues when applied directly to new, specific scenes, such as stereo traffic datasets. Though “large-scale datasets (COME15K and ReDweb-S)” have been released, they only partially address the domain shift problem. From the perspective of data augmentation, this paper presents a novel solution, which follows a weakly-supervised way to adapt generic RGB-D SOD models for specific scenarios, with a focus on traffic scene imagery. Our key idea is to equip plain videos (specific scenarios, i.e., traffic scenes) with newly estimated saliency informative depth maps and pseudo-SOD GTs, enabling them to support the retraining of existing RGB-D SOD models for meeting the requirements of these specific scenes. To achieve this, we offer a fresh perspective on how depth information can be leveraged in the SOD task and introduce a new paradigm for extracting intrinsic information from optical flows derived from videos to refine RGB-D SOD models. Our method achieves a 1.2% improvement in F-measure on RGB-D datasets and a 27% enhancement on real-world street view datasets compared to baseline models. These results demonstrate the effectiveness of our approach in enhancing model adaptability for traffic scene imagery, even with limited target domain data. Codes, datasets, and results are available at https://github.com/MengkeSong/AGSS.

With the Mamba framework widely applied, the state-space model has yielded outstanding results in the field of computer vision. Nevertheless, the superiority of the model to its counterparts, namely, CNN-based or Transformer-based models, is limited, because it faces large challenges in local region feature extraction resulting from the deficient positional awareness and the disproportional emphasis on posterior tokens in its pre-defined scanning schedules. Besides, a majority of the current Mamba-based models usually fail to take into account the advantages of the integration of multi-visual encoding strategies. Against this background, we propose a novel DoubleU-Net framework with multiple visual encoding strategies and a local-based scanning mechanism. The comparative & ablation experiments with the current SOTA methods verify the superiority or competitiveness of the DUMFNet. For reproduction, the implementation codes can be checked out at https://github.com/Panpz202006/DUMFNet.

In this paper, we propose a novel concept factorization method that seeks factor matrices using a cross-order positive semi-definite neighbor graph, which provides comprehensive and complementary neighbor information of the data. The factor matrices are learned with bipartite graph partitioning, which exploits explicit cluster structure of the data and is more geared towards clustering application. We develop an effective and efficient optimization algorithm for our method, and provide elegant theoretical results about the convergence. Extensive experimental results confirm the effectiveness of the proposed method.

Multi-view clustering has attracted extensive attention in recent years, which aims at integrating data from different views to improve the clustering performance. In this letter, we propose a novel approach for multi-view clustering. We propose to leverage high-order stranger information of the samples with the aid of Markov random walks to enhance inter-class separability of representation matrix in each view. Then, we seek a direct and intuitive clustering interpretation through view-specific spectral embeddings and cross-view spectral rotation fusion with auto-adjusted weights. Extensive experimental results confirm the effectiveness of our method.

Multi-view subspace clustering (MVSC) has drawn significant attention in recent study. In this paper, we propose a novel approach to MVSC. First, the new method is capable of preserving high-order neighbor information of the data, which provides essential and complicated underlying relationships of the data that is not straightforwardly preserved by the first-order neighbors. Second, we design log-based nonconvex approximations to both tensor rank and tensor sparsity, which are effective and more accurate than the convex approximations. For the associated shrinkage problems, we provide elegant theoretical results for the closed-form solutions, for which the convergence is guaranteed by theoretical analysis. Moreover, the new approximations have some interesting properties of shrinkage effects, which are guaranteed by elegant theoretical results. Extensive experimental results confirm the effectiveness of the proposed method.

Multi-view subspace clustering has drawn significant attentions in recent years, which significantly improves learning performance of the single-view methods. In this letter, we propose a novel multi-view subspace clustering method, which learns a consensus representation with auto-weighted local neighboring transition probability matrix fusion and preserves cross-view diversity with a matrix-induced term. The new model is convex and thus admits efficient optimization. The effectiveness is confirmed by extensive experiments.

In this letter, we proposea novel subspace clustering method, named Es$^{3}$SC, that learns essential samples for low-dimensional representation construction. The essential samples are expected to retain key features and better estimate the example-wise similarities, which are more geared to seeking the representation matrix (RM). Moreover, the RM is enforced to have block-diagonal structural property, which directly reveals grouping structure of the data and is essentially desired by clustering application. Experimental results show that the Es$^{3}$SC is effective in both clustering and essential feature recovery.

Previous video salient object detection (VSOD) approaches have mainly focused on the perspective of network design for achieving performance improvements. However, with the recent slowdown in the development of deep learning techniques, it might become increasingly difficult to anticipate another breakthrough solely via complex networks. Therefore, this paper proposes a universal learning scheme to obtain a further 3% performance improvement for all state-of-the-art (SOTA) VSOD models. The major highlight of our method is that we propose the ‘motion quality’, a new concept for mining video frames from the ‘buffered’ testing video stream for constructing a fine-tuning set. By using our approach, all frames in this set can all well-detect their salient object by the ‘target SOTA model’ — the one we want to improve. Thus, the VSOD results of the mined set, which were previously derived by the target SOTA model, can be directly applied as pseudolearning objectives to fine-tune a completely new spatial model that has been pretrained on the widely used DAVIS-TR set. Since some spatial scenes in the buffered testing video stream are shown, the fine-tuned spatial model can perform very well for the remaining unseen testing frames, outperforming the target SOTA model significantly. Although offline model fine tuning requires additional time costs, the performance gain can still benefit scenarios without speed requirements. Moreover, its semisupervised methodology might have considerable potential to inspire the VSOD community in the future.

The existing state-of-the-art (SOTA) video salient object detection (VSOD) models have widely followed short-term methodology, which dynamically determines the balance between spatial and temporal saliency fusion by solely considering the current consecutive limited frames. However, the short-term methodology has one critical limitation, which conflicts with the real mechanism of our visual system — a typical long-term methodology. As a result, failure cases keep showing up in the results of the current SOTA models, and the short-term methodology becomes the major technical bottleneck. To solve this problem, this paper proposes a novel VSOD approach, which performs VSOD in a complete long-term way. Our approach converts the sequential VSOD, a sequential task, to a data mining problem, i.e., decomposing the input video sequence to object proposals in advance and then mining salient object proposals as much as possible in an easy-to-hard way. Since all object proposals are simultaneously available, the proposed approach is a complete long-term approach, which can alleviate some difficulties rooted in conventional short-term approaches. In addition, we devised an online updating scheme that can grasp the most representative and trustworthy pattern profile of the salient objects, outputting framewise saliency maps with rich details and smoothing both spatially and temporally. The proposed approach outperforms almost all SOTA models on five widely used benchmark datasets.

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.

In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novell2,lognorm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For thel2,log-regularized shrinkage problem, we develop an efficient, closed-form solution, which is namedl2,log-shrinkage operator. The new regularization and the corresponding operator can be generally used in other problems that require column-wise sparsity. Moreover, we impose the spatial-spectral total variation regularization in the log-based nonconvex RPCA model, which enhances the global piece-wise smoothness and spectral consistency from the spatial and spectral views in the recovered HSI. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.

Two-dimensional PCA (2DPCA) is an effective approach to reduce dimension and extract features in the image domain. Most recently developed techniques use different error measures to improve their robustness to outliers. When certain data points are overly contaminated, the existing methods are frequently incapable of filtering out and eliminating the excessively polluted ones. Moreover, natural systems have smooth dynamics, an opportunity is lost if an unsupervised objective function remains static. Unlike previous studies, we explicitly differentiate the samples to alleviate the impact of outliers and propose a novel method called Self-Paced 2DPCA (SP2DPCA)algorithm, which progresses from `easy’ to `complex’ samples. By using an alternative optimization strategy, SP2DPCA looks for optimal projection matrix and filters out outliers iteratively. Theoretical analysis demonstrates the robustness nature of our method. Extensive experiments on image reconstruction and clustering verify the superiority of our approach.

It is a challenging task to remove heavy and mixed types of noise from Hyperspectral images (HSIs). In this paper, we propose a novel nonconvex approach to RPCA for HSI denoising, which adopts the log-determinant rank approximation and a novel $\ell_{2,\text{l}\text{o}\text{g}}$ norm, to restrict the low-rank or column-wise sparse properties for the component matrices, respectively. For the $\ell_{2,\text{l}\text{o}\text{g}}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which is named $\ell_{2,\text{l}\text{o}\text{g}}$-shrinkage operator, which can be generally used in other problems. Extensive experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method in denoising HSIs.

Multi-view clustering and multi-view dimension reduction explore ubiquitous and complementary information between multiple features to enhance the clustering, recognition performance. However, multi-view clustering and multi-view dimension reduction are treated independently, ignoring the underlying correlations between them. In addition, previous methods mainly focus on using the tensor nuclear norm for low-rank representation to explore the high correlation of multi-view features, which often causes the estimation bias of the tensor rank. To overcome these limitations, we propose the partial tubal nuclear norm regularized multi-view learning (PTN2ML) method, in which the partial tubal nuclear norm as a non-convex surrogate of the tensor tubal multi-rank, only minimizes the partial sum of the smaller tubal singular values to preserve the low-rank property of the self-representation tensor. PTN2ML pursues the latent representation from the projection space rather than from the input space to reveal the structural consensus and suppress the disturbance of noisy data. The proposed method can be efficiently optimized by the alternating direction method of multipliers. Extensive experiments, including multi-view clustering and multi-view dimension reduction substantiate the superiority of the proposed methods beyond state-of-the-arts.

We have witnessed a growing interest in video salient object detection (VSOD) techniques in today's computer vision applications. In contrast with temporal information (which is still considered a rather unstable source thus far), the spatial information is more stable and ubiquitous, thus it could influence our vision system more. As a result, the current main-stream VSOD approaches have inferred and obtained their saliency primarily from the spatial perspective, still treating temporal information as subordinate. Although the aforementioned methodology of focusing on the spatial aspect is effective in achieving a numeric performance gain, it still has two critical limitations. First, to ensure the dominance by the spatial information, its temporal counterpart remains inadequately used, though in some complex video scenes, the temporal information may represent the only reliable data source, which is critical to derive the correct VSOD. Second, both spatial and temporal saliency cues are often computed independently in advance and then integrated later on, while the interactions between them are omitted completely, resulting in saliency cues with limited quality. To combat these challenges, this paper advocates a novel spatiotemporal network, where the key innovation is the design of its temporal unit. Compared with other existing competitors (e.g., convLSTM), the proposed temporal unit exhibits an extremely lightweight design that does not degrade its strong ability to sense temporal information. Furthermore, it fully enables the computation of temporal saliency cues that interact with their spatial counterparts, ultimately boosting the overall VSOD performance and realizing its full potential towards mutual performance improvement for each. The proposed method is easy to implement yet still effective, achieving high-quality VSOD at 50 FPS in real-time applications.

The low-rank tensor representation (LRTR) has become an emerging research direction to boost the multi-view clustering performance. This is because LRTR utilizes not only the pairwise relation between data points, but also the view relation of multiple views. However, there is one significant challenge: LRTR uses the tensor nuclear norm as the convex approximation but provides a biased estimation of the tensor rank function. To address this limitation, we propose the generalized nonconvex low-rank tensor approximation (GNLTA) for multi-view subspace clustering. Instead of the pairwise correlation, GNLTA adopts the low-rank tensor approximation to capture the high-order correlation among multiple views and proposes the generalized nonconvex low-rank tensor norm to well consider the physical meanings of different singular values. We develop a unified solver to solve the GNLTA model and prove that under mild conditions, any accumulation point is a stationary point of GNLTA. Extensive experiments on seven commonly used benchmark databases have demonstrated that the proposed GNLTA achieves better clustering performance over state-of-the-art methods.

The existing fusion-based RGB-D salient object detection methods usually adopt the bistream structure to strike a balance in the fusion trade-off between RGB and depth (D). While the D quality usually varies among the scenes, the state-of-the-art bistream approaches are depth-quality-unaware, resulting in substantial difficulties in achieving complementary fusion status between RGB and D and leading to poor fusion results for low-quality D. Thus, this paper attempts to integrate a novel depth-quality-aware subnet into the classic bistream structure in order to assess the depth quality prior to conducting the selective RGB-D fusion. Compared to the SOTA bistream methods, the major advantage of our method is its ability to lessen the importance of the low-quality, no-contribution, or even negative-contribution D regions during RGB-D fusion, achieving a much improved complementary status between RGB and D. Our source code and data are available online at https://github.com/qdu1995/DQSD.

In this article, we introduce a discriminative ridge regression approach to supervised classification. It estimates a representation model while accounting for discriminativeness between classes, thereby enabling accurate derivation of categorical information. This new type of regression model extends the existing models, such as ridge, lasso, and group lasso, by explicitly incorporating discriminative information. As a special case, we focus on a quadratic model that admits a closed-form analytical solution. The corresponding classifier is called the discriminative ridge machine (DRM). Three iterative algorithms are further established for the DRM to enhance the efficiency and scalability for real applications. Our approach and the algorithms are applicable to general types of data including images, high-dimensional data, and imbalanced data. We compare the DRM with current state-of-the-art classifiers. Our extensive experimental results show the superior performance of the DRM and confirm the effectiveness of the proposed approach.

Screen content images (SCIs) usually comprise various content types with sharp edges, in which artifacts or distortions can be effectively sensed by a vanilla structure similarity measurement in a full-reference manner. Nonetheless, almost all of the current state-of-the-art (SOTA) structure similarity metrics are “locally” formulated in a single-level manner, while the true human visual system (HVS) follows the multilevel manner; such mismatch could eventually prevent these metrics from achieving reliable quality assessment. To ameliorate this issue, this article advocates a novel solution to measure structure similarity “globally” from the perspective of sparse representation. To perform multilevel quality assessment in accordance with the real HVS, the abovementioned global metric will be integrated with the conventional local ones by resorting to the newly devised selective deep fusion network. To validate its efficacy and effectiveness, we have compared our method with 12 SOTA methods over two widely used large-scale public SCI datasets, and the quantitative results indicate that our method yields significantly higher consistency with subjective quality scores than the current leading works. Both the source code and data are also publicly available to gain widespread acceptance and facilitate new advancement and validation.

This paper proposes to utilize supervised deep convolutional neural networks to take full advantage of the long-term spatial-temporal information in order to improve the video saliency detection performance. The conventional methods, which use the temporally neighbored frames solely, could easily encounter transient failure cases when the spatial-temporal saliency clues are less-trustworthy for a long period. To tackle the aforementioned limitation, we plan to identify those beyond-scope frames with trustworthy long-term saliency clues first and then align it with the current problem domain for an improved video saliency detection.

To solve the saliency detection problem in RGB-D images, the depth information plays a critical role in distinguishing salient objects or foregrounds from cluttered backgrounds. As the complementary component to color information, the depth quality directly dictates the subsequent saliency detection performance. However, due to artifacts and the limitation of depth acquisition devices, the quality of the obtained depth varies tremendously across different scenarios. Consequently, conventional selective fusion-based RGB-D saliency detection methods may result in a degraded detection performance in cases containing salient objects with low color contrast coupled with a low depth quality. To solve this problem, we make our initial attempt to estimate additional high-quality depth information, which is denoted by Depth+. Serving as a complement to the original depth, Depth+ will be fed into our newly designed selective fusion network to boost the detection performance. To achieve this aim, we first retrieve a small group of images that are similar to the given input, and then the inter-image, nonlocal correspondences are built accordingly. Thus, by using these inter-image correspondences, the overall depth can be coarsely estimated by utilizing our newly designed depth-transferring strategy. Next, we build fine-grained, object-level correspondences coupled with a saliency prior to further improve the depth quality of the previous estimation. Compared to the original depth, our newly estimated Depth+ is potentially more informative for detection improvement. Finally, we feed both the original depth and the newly estimated Depth+ into our selective deep fusion network, whose key novelty is to achieve an optimal complementary balance to make better decisions toward improving saliency boundaries.

In recent years deep neural networks have been widely applied to visual saliency detection tasks with remarkable detection performance improvements. As for the salient object detection in single image, the automatically computed convolutional features frequently demonstrate high discriminative power to distinguish salient foregrounds from its non-salient surroundings in most cases. Yet, the obstinate feature conflicts still persist, which naturally gives rise to the learning ambiguity, arriving at massive failure detections. To solve such problem, we propose to jointly re-learn common consistency of inter-image saliency and then use it to boost the detection performance. Its core rationale is to utilize the easy-to-detect cases to re-boost much harder ones. Compared with the conventional methods, which focus on their problem domain within the single image scope, our method attempts to utilize those beyond-scope information to facilitate the current salient object detection. To validate our new approach, we have conducted a comprehensive quantitative comparisons between our approach and 13 state-of-the-art methods over 5 publicly available benchmarks, and all the results suggest the advantage of our approach in terms of accuracy, reliability, and versatility.

Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art algorithms usually need to solve singular value decomposition of large matrices, which generally has at least a quadratic or even cubic complexity. This drawback has limited the application of RPCA in solving real world problems. To combat this drawback, in this paper we propose a new type of RPCA method, RES-PCA, which is linearly efficient and scalable in both data size and dimension. For comparison purpose, AltProj, an existing scalable approach to RPCA requires the precise knowlwdge of the true rank; otherwise, it may fail to recover low-rank matrices. By contrast, our method works with or without knowing the true rank; even when both methods work, our method is faster. Extensive experiments have been performed and testified to the effectiveness of proposed method quantitatively and in visual quality, which suggests that our method is suitable to be employed as a light-weight, scalable component for RPCA in any application pipelines.

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means clustering. Such common practice has two potential flaws, which may lead to severe information loss and performance degradation. First, predefined similarity graph might not be optimal for subsequent clustering. It is well-accepted that similarity graph highly affects the clustering results. To this end, we propose to automatically learn similarity information from data and simultaneously consider the constraint that the similarity matrix has exact c connected components if there are c clusters. Second, the discrete solution may deviate from the spectral solution since k-means method is well-known as sensitive to the initialization of cluster centers. In this work, we transform the candidate solution into a new one that better approximates the discrete one. Finally, those three subtasks are integrated into a unified framework, with each subtask iteratively boosted by using the results of the others towards an overall optimal solution. It is known that the performance of a kernel method is largely determined by the choice of kernels. To tackle this practical problem of how to select the most suitable kernel for a particular data set, we further extend our model to incorporate multiple kernel learning ability. Extensive experiments demonstrate the superiority of our proposed method as compared to existing clustering approaches.

In this article, we introduce a novel, general methodology, called integrate and conquer, for simultaneously accomplishing the tasks of feature extraction, manifold construction, and clustering, which is taken to be superior to building a clustering method as a single task. When the proposed novel methodology is used on two-dimensional (2D) data, it naturally induces a new clustering method highly effective on 2D data. Existing clustering algorithms usually need to convert 2D data to vectors in a preprocessing step, which, unfortunately, severely damages 2D spatial information and omits inherent structures and correlations in the original data. The induced new clustering method can overcome the matrix-vectorization-related issues to enhance the clustering performance on 2D matrices. More specifically, the proposed methodology mutually enhances three tasks of finding subspaces, learning manifolds, and constructing data representation in a seamlessly integrated fashion. When used on 2D data, we seek two projection matrices with optimal numbers of directions to project the data into low-rank, noise-mitigated, and the most expressive subspaces, in which manifolds are adaptively updated according to the projections, and new data representation is built with respect to the projected data by accounting for nonlinearity via adaptive manifolds. Consequently, the learned subspaces and manifolds are clean and intrinsic, and the new data representation is discriminative and robust. Extensive experiments have been conducted and the results confirm the effectiveness of the proposed methodology and algorithm.

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.

Spectral clustering based subspace clustering methods have emerged recently. When the inputs are 2-dimensional (2D) data, most existing clustering methods convert such data to vectors as preprocessing, which severely damages spatial information of the data. In this paper, we propose a novel subspace clustering method for 2D data with enhanced capability of retaining spatial information for clustering. It seeks two projection matrices and simultaneously constructs a linear representation of the projected data, such that the sought projections help construct the most expressive representation with the most variational information. We regularize our method based on covariance matrices directly obtained from 2D data, which have much smaller size and are more computationally amiable. Moreover, to exploit nonlinear structures of the data, a nonlinear version is proposed, which constructs an adaptive manifold according to updated projections. The learning processes of projections, representation, and manifold thus mutually enhance each other, leading to a powerful data representation. Efficient optimization procedures are proposed, which generate non-increasing objective value sequence with theoretical convergence guarantee. Extensive experimental results confirm the effectiveness of proposed method.

Construction of a reliable similarity matrix is fundamental for graph-based clustering methods. However, most of the current work is built upon some simple manifold structure, whereas limited work has been conducted on nonlinear data sets where data reside in a union of manifolds rather than a union of subspaces. Therefore, we construct a similarity graph to capture both global and local manifold structures of the input data set. The global structure is exploited based on the self-expressive property of data in an implicit feature space using kernel methods. Since the similarity graph computation is independent of the subsequent clustering, the final results may be far from optimal. To overcome this limitation, we simultaneously learn similarity graph and clustering structure in a principled way. Experimental studies demonstrate that our proposed algorithms deliver consistently superior results to other state-of-the-art algorithms.

Restoration of hyperspectral images (HSIs) is a challenging task, owing to the reason that images are inevitably contaminated by a mixture of noise, including Gaussian noise, impulse noise, dead lines, and stripes, during their acquisition process. Recently, HSI denoising approaches based on low-rank matrix approximation have become an active research field in remote sensing and have achieved state-of-the-art performance. These approaches, however, unavoidably require to calculate full or partial singular value decomposition of large matrices, leading to the relatively high computational cost and limiting their flexibility. To address this issue, this letter proposes a method exploiting a low-rank matrix factorization scheme, in which the associated robust principal component analysis is solved by the matrix factorization of the low-rank component. Our method needs only an upper bound of the rank of the underlying low-rank matrix rather than the precise value. The experimental results on the simulated and real data sets demonstrate the performance of our method by removing the mixed noise and recovering the severely contaminated images.

Subspace clustering methods have been widely studied recently. When the inputs are two-dimensional (2-D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships from original data. In this letter, we propose a novel subspace clustering method for 2-D data. It directly uses 2-D data as inputs such that the learning of representations benefits from inherent structures and relationships of the data. It simultaneously seeks image projection and representation coefficients such that they mutually enhance each other and lead to powerful data representations. An efficient algorithm is developed to solve the proposed objective function with provable decreasing and convergence property. Extensive experimental results verify the effectiveness of the new method.

Hyperspectral image (HSI) denoising is challenging not only because of the difficulty in preserving both spectral and spatial structures simultaneously, but also due to the requirement of removing various noises, which are often mixed together. In this paper, we present a nonconvex low rank matrix approximation (NonLRMA) model and the corresponding HSI denoising method by reformulating the approximation problem using nonconvex regularizer instead of the traditional nuclear norm, resulting in a tighter approximation of the original sparsity-regularised rank function. NonLRMA aims to decompose the degraded HSI, represented in the form of a matrix, into a low rank component and a sparse term with a more robust and less biased formulation. In addition, we develop an iterative algorithm based on the augmented Lagrangian multipliers method and derive the closed-form solution of the resulting subproblems benefiting from the special property of the nonconvex surrogate function. We prove that our iterative optimization converges easily. Extensive experiments on both simulated and real HSIs indicate that our approach can not only suppress noise in both severely and slightly noised bands but also preserve large-scale image structures and small-scale details well. Comparisons against state-of-the-art LRMA-based HSI denoising approaches show our superior performance.

We introduce a new supervised learning model using a discriminative regression approach. This new model estimates a regression vector to represent the similarity between a test example and training examples while seamlessly integrating the class information in the similarity estimation. This distinguishes our model from usual regression models and locally linear embedding approaches, rendering our method suitable for supervised learning problems in high-dimensional settings. Our model is easily extensible to account for nonlinear relationship and applicable to general data, including both high- and low-dimensional data. The objective function of the model is convex, for which two optimization algorithms are provided. These two optimization approaches induce two scalable solvers that are of mathematically provable, linear time complexity. Experimental results verify the effectiveness of the proposed method on various kinds of data. For example, our method shows comparable performance on low-dimensional data and superior performance on high-dimensional data to several widely used classifiers; also, the linear solvers obtain promising performance on large-scale classification.

Matrix factorization is a useful technique for data representation in many data mining and machine learning tasks. Particularly, for data sets with all nonnegative entries, matrix factorization often requires that factor matrices be nonnegative, leading to nonnegative matrix factorization (NMF). One important application of NMF is for clustering with reduced dimensions of the data represented in the new feature space. In this paper, we propose a new graph regularized NMF method capable of feature learning and apply it to clustering. Unlike existing NMF methods that treat all features in the original feature space equally, our method distinguishes features by incorporating a feature-wise sparse approximation error matrix in the formulation. It enables important features to be more closely approximated by the factor matrices. Meanwhile, the graph of the data is constructed using cleaner features in the feature learning process, which integrates feature learning and manifold learning procedures into a unified NMF model. This distinctly differs from applying the existing graph-based NMF models after feature selection in that, when these two procedures are independently used, they often fail to align themselves toward obtaining a compact and most expressive data representation. Comprehensive experimental results demonstrate the effectiveness of the proposed method, which outperforms state-of-the-art algorithms when applied to clustering.

Matrix factorization is often used for data representation in many data mining and machine-learning problems. In particular, for a dataset without any negative entries, nonnegative matrix factorization (NMF) is often used to find a low-rank approximation by the product of two nonnegative matrices. With reduced dimensions, these matrices can be effectively used for many applications such as clustering. The existing methods of NMF are often afflicted with their sensitivity to outliers and noise in the data. To mitigate this drawback, in this paper, we consider integrating NMF into a robust principal component model, and design a robust formulation that effectively captures noise and outliers in the approximation while incorporating essential nonlinear structures. A set of comprehensive empirical evaluations in clustering applications demonstrates that the proposed method has strong robustness to gross errors and superior performance to current state-of-the-art methods.

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relaxation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strategy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level.

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

Recovering low-rank matrices is a problem common in many applications of data mining and machine learning, such as matrix completion and image denoising. Robust Principal Component Analysis (RPCA) has emerged for handling such kinds of problems; however, the existing RPCA approaches are usually computationally expensive, due to the fact that they need to obtain the singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA approach that eliminates the need for SVD of large matrices. Scalable algorithms are designed for several variants of our approach, which are crucial for real world applications on large scale data. Extensive experimental results confirm the effectiveness of our approach both quantitatively and visually.

Robust principal component analysis (RPCA) has been widely used for recovering low-rank matrices in many data mining and machine learning problems. It separates a data matrix into a low-rank part and a sparse part. The convex approach has been well studied in the literature. However, state-of-the-art algorithms for the convex approach usually have relatively high complexity due to the need of solving (partial) singular value decompositions of large matrices. A non-convex approach, AltProj, has also been proposed with lighter complexity and better scalability. Given the true rank r of the underlying low rank matrix, AltProj has a complexity of O(r2dn), where d × n is the size of data matrix. In this paper, we propose a novel factorization-based model of RPCA, which has a complexity of O(kdn), where k is an upper bound of the true rank. Our method does not need the precise value of the true rank. From extensive experiments, we observe that AltProj can work only when r is precisely known in advance, however, when the needed rank parameter r is specified to a value different from the true rank, AltProj cannot fully separate the two parts while our method succeeds. Even when both work, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank.

We propose a new subspace clustering method that integrates feature selection into subspace clustering. Rather than using all features to construct a low-rank representation of the data, we find such a representation using only relevant features, which helps in revealing more accurate data relationships. Two variants are proposed by using both convex and nonconvex rank approximations. Extensive experimental results confirm the effectiveness of the proposed method and models.

Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation error may depend heavily on the magnitudes of singular values. This might restrict its capability in dealing with many practical problems. In this paper, an arctangent function is used as a tighter approximation to the rank function. We use it on the challenging subspace clustering problem. For this nonconvex minimization problem, we develop an effective optimization procedure based on a type of augmented Lagrange multipliers (ALM) method. Extensive experiments on face clustering and motion segmentation show that the proposed method is effective for rank approximation.

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate of the rank function in RPCA is widely investigated. Under certain assumptions, it can recover the underlying true low rank matrix with high probability. However, those assumptions may not hold in real-world applications. Since the nuclear norm approximates the rank by adding all singular values together, which is essentially a l1-norm of the singular values, the resulting approximation erroris not trivial and thus the resulting matrix estimator can be significantly biased. To seek a closer approximation and to alleviate the above-mentioned limitations of the nuclear norm, we propose a nonconvex rank approximation. This approximation to the matrix rank is tighter than the nuclear norm. To solve the associated nonconvex minimization problem, we develop an efficient augmented Lagrange multiplier based optimization algorithm. Experimental results demonstrate that our method outperforms current state-of-the-art algorithms in both accuracy and efficiency.

A number of machine learning and computer vision problems, such as matrix completion and subspace clustering, require a matrix to be of low-rank. To meet this requirement, most existing methods use the nuclear norm as a convex proxy of the rank function and minimize it. However, the nuclear norm simply adds all nonzero singular values together instead of treating them equally as the rank function does, which may not be a good rank approximation when some singular values are very large. To reduce this undesirable weighting effect, we use a log-determinant function as a non-convex rank approximation which reduces the contributions of large singular values while keeping those of small singular values close to zero. We apply the method of augmented Lagrangian multipliers to optimize this non-convex rank approximation-based objective function and obtain closed-form solutions for all subproblems of minimizing different variables alternatively. The log-determinant low-rank optimization method is used to solve subspace clustering problem, for which we construct an affinity matrix based on the angular information of the low-rank representation to enhance its separability property. Extensive experimental results on face clustering and motion segmentation data demonstrate the effectiveness of the proposed method.

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world applications, nuclear norm approximation to the rank function can only produce a result far from the optimum. To seek a solution of higher accuracy than the nuclear norm, in this letter, we propose a rank approximation based on Logarithm-Determinant. We consider using this rank approximation for subspace clustering application. Our framework can model different kinds of errors and noise. Effective optimization strategy is developed with theoretical guarantee to converge to a stationary point. The proposed method gives promising results on face clustering and motion segmentation tasks compared to the state-of-the-art subspace clustering algorithms.