Early identification and removal of polyps can reduce the risk of developing colorectal cancer. However, the diverse morphologies, complex backgrounds and often concealed nature of polyps make polyp segmentation in colonoscopy images highly challenging. Despite the promising performance of existing deep learning-based polyp segmentation methods, their perceptual capabilities remain biased toward local regions, mainly because of the strong spatial correlations between neighboring pixels in the spatial domain. This limitation makes it difficult to capture the complete polyp structures, ultimately leading to sub-optimal segmentation results. In this paper, we propose a novel adaptive spectrum guidance network, called ASGNet, which addresses the limitations of spatial perception by integrating spectral features with global attributes. Specifically, we first design a spectrum-guided non-local perception module that jointly aggregates local and global information, therefore enhancing the discriminability of polyp structures, and refining their boundaries. Moreover, we introduce a multi-source semantic extractor that integrates rich high-level semantic information to assist in the preliminary localization of polyps. Furthermore, we construct a dense cross-layer interaction decoder that effectively integrates diverse information from different layers and strengthens it to generate high-quality representations for accurate polyp segmentation. Extensive quantitative and qualitative results demonstrate the superiority of our ASGNet approach over 21 state-of-the-art methods across five widely-used polyp segmentation benchmarks. The code will be publicly available at: https://github.com/CSYSI/ASGNet.

Deep neural networks (DNNs) are potent in LiDAR-based 3D object detection (LiDAR-3DOD), yet their deployment remains daunting due to their cumbersome parameters and computations. Knowledge distillation (KD) is promising for compressing DNNs in LiDAR-3DOD. However, most existing KD methods transfer inadequate knowledge between homogeneous detectors, and do not thoroughly explore optimal student architectures, resulting in insufficient gains for compact student detectors. To this end, we propose a category knowledge-driven compression framework to achieve efficient LiDAR-based 3D detectors. Firstly, we distill knowledge from two-stage teacher detectors to one-stage student detectors, overcoming the limitations of homogeneous pairs. To conduct KD in these heterogeneous pairs, we explore the gap between heterogeneous detectors, and introduce category knowledge-driven KD (CaKD), which includes both student-oriented distillation and two-stage-oriented label assignment distillation. Secondly, to search for the optimal architecture of compact student detectors, we introduce a masked category knowledge-driven structured pruning scheme. This scheme evaluates filter importance by analyzing the changes in category predictions related to foreground regions before and after filter removal, and prunes the less important filters accordingly. Finally, we propose a modified IoU-aware redundancy elimination module to remove redundant false positive samples, thereby further improving the accuracy of detectors. Experiments on various point cloud datasets demonstrate that our method delivers impressive results. For example, on KITTI, several compressed one-stage detectors outperform two-stage detectors in both efficiency and accuracy. Besides, on WOD-mini, our framework reduces the memory footprint of CenterPoint by 5.2× and improves the L2 mAPH by 0.55$\%$%.

In this work, we focus on studying the differentiable relaxations of several linear regression problems, where the original formulations are usually both nonsmooth with one nonconvex term. Unfortunately, in most cases, the standard alternating direction method of multipliers (ADMM) cannot guarantee global convergence when addressing these kinds of problems. To address this issue, by smoothing the convex term and applying a linearization technique before designing the iteration procedures, we employ nonconvex ADMM to optimize challenging nonconvex-convex composite problems. In our theoretical analysis, we prove the boundedness of the generated variable sequence and then guarantee that it converges to a stationary point. Meanwhile, a potential function is derived from the augmented Lagrange function, and we further verify that the objective function is monotonically nonincreasing. Under the Kurdyka-Łojasiewicz (KŁ) property, the global convergence is analyzed step by step. Finally, experiments on face reconstruction, image classification, and subspace clustering tasks are conducted to show the superiority of our algorithms over several state-of-the-art ones.

Low-rank matrix recovery is a major challenge in machine learning and computer vision, particularly for large-scale data matrices, as popular methods involving nuclear norm and singular value decomposition (SVD) are associated with high computational costs and biased estimators. To overcome this challenge, we propose a novel approach to learning low-rank matrices based on the matrix volume and a nonconvex logarithmic function. The matrix volume is the product of all the nonzero singular values of a matrix and has unique geometric properties and connections with other convex and nonconvex functions. We establish a generalized nonconvex regularization problem using the penalty function strategy and introduce an accelerated proximal alternating linearized minimization (AccPALM) algorithm with double acceleration, which combines Nesterov’s acceleration and power strategy. The algorithm reduces computational costs and has provable convergence results under the Kurdyka-Łojasiewicz (KŁ) inequality with mild conditions. Our approach shows superior accuracy, efficiency, and convergence behavior compared to other low-rank matrix learning methods on robust matrix completion (RMC) and low-rank representation (LRR) tasks. We analyze the impact of algorithm parameters on convergence and performance and present visually appealing results to further demonstrate the effectiveness of our approach. The proposed methodology represents a promising advance in the field of low-rank matrix recovery, and its effectiveness has been validated via extensive numerical experiments. The source code for the proposed algorithms is accessible at https://github.com/ZhangHengMin/AccPALMcodes.

In real-world applications involving sparse coding and low-rank matrix recovery problems, linear regression methods usually struggle to effectively capture the structured correlations present in data matrices. This limitation arises from representation approaches that treat images as vectors and handle testing samples individually, overlooking these correlations. To address these challenges, we propose a novel approach that leverages the low-rank property to capture the global and intrinsic structure of residual and coefficient matrices, departing from the assumption of independent and identically distributed (I.I.D) data. Our method introduces nonconvex and nonsmooth low-rank matrix regression models guided by the extended matrix variate power exponential distribution (M.P.E.D). By incorporating factorization strategies into the regression coefficient matrix and utilizing the Schatten-$p$norm with three distinct values of$p$, we enhance computational efficiency. Our formulation enables efficient subproblem solving through the introduction of auxiliary variables and the use of singular value threshold operators. We achieve closed-form solutions using the proposed multi-variable alternating direction method of multipliers (ADMM). Theoretical analysis establishes the local convergence properties and computational complexity of our optimization algorithm. Furthermore, we conduct numerical experiments on various image datasets, including face, object, and digital, to demonstrate the superior performance and computational efficiency of our methods compared to several related regression approaches. The source codes for our method are available athttps://github.com/ZhangHengMin/TIFS_SLRMFR.

To enhance the effectiveness and efficiency of subspace clustering in visual tasks, this work introduces a novel approach that automatically eliminates the optimal mean, which is embedded in the subspace clustering framework of low-rank representation (LRR) methods, along with the computationally factored formulation of Schatten p -norm. By addressing the issues related to meaningful computations involved in some LRR methods and overcoming biased estimation of the low-rank solver, we propose faster nonconvex subspace clustering methods through joint Schatten p -norm factorization with optimal mean (JS p NFOM), forming a unified framework for enhancing performance while reducing time consumption. The proposed approach employs tractable and scalable factor techniques, which effectively address the disadvantages of higher computational complexity, particularly when dealing with large-scale coefficient matrices. The resulting nonconvex minimization problems are reformulated and further iteratively optimized by multivariate weighting algorithms, eliminating the need for singular value decomposition (SVD) computations in the developed iteration procedures. Moreover, each subproblem can be guaranteed to obtain the closed-form solver, respectively. The theoretical analyses of convergence properties and computational complexity further support the applicability of the proposed methods in real-world scenarios. Finally, comprehensive experimental results demonstrate the effectiveness and efficiency of the proposed nonconvex clustering approaches compared to existing state-of-the-art methods on several publicly available databases. The demonstrated improvements highlight the practical significance of our work in subspace clustering tasks for visual data analysis. The source code for the proposed algorithms is publicly accessible at https://github.com/ZhangHengMin/TRANSUFFC.

With the growing interest in convex and nonconvex low-rank matrix learning problems, the widely used singular value thresholding (SVT) operators associated with rank relaxation functions often face higher computational complexity, particularly for large-scale data matrices. To improve the efficacy of low-rank subspace clustering and overcome the issue of high computational complexity, this work proposes an efficient and effective method that avoids the need for singular value decomposition (SVD) computations in the iteration scheme. This can be achieved through the use of a computationally efficient and compact formulation, as well as automatic removal of the optimal mean, which reduces time consumption and enhances evaluation performance. A unified clustering framework based on Schatten-$p$norm regularized by$\ell _{2,q}$-norm can be formulated using this processing way, where inner element suppression can be achieved by choosing appropriate$p$,$q \in (0,1)$. Additionally, calculating the optimal mean enhances the robustness of the proposed method in the presence of outliers. Unlike the general iteration scheme of the alternating direction method of multiplier (ADMM) algorithms that introduce auxiliary splitting variables, the proposed alternating re-weighted least square (ARwLS) algorithm uses matrix inverse and multiplication computations to obtain analytic solutions, resulting in faster processing speeds for each sub-problem. To further investigate, we provide the computational complexity of each iteration and the theoretical analysis of the convergence property, where the derived solution is a stationary point. Experimental results on synthetic data and several benchmark datasets demonstrate the promising efficiency and efficacy of the proposed clustering method compared to classical and competing algorithms.

Accompanied with the increasing popularity of linear regression approaches, most of the existing minimization problems are related with several convex measurements, e.g.,$\ell_1$/$\ell_2$/$\ell_{2,1}$-norm of a vector and$L_1$/$L_{2,1}$/Frobenius/nuclear norm of a matrix, where the regularized function and the loss function are usually studied for two objective terms case by case, respectively. To address this issue, this work combines these linear regression problems into a unified expression framework by employing an adaptive and flexible function, in which we need to choose different variable elements and adjust an inner parameter, properly. Besides this, they are equipped with some corresponding relationships and their interesting properties. Intuitively speaking, the proposed framework can generalize several traditional linear regression formulations and even more complex ones into an extended representation. For further optimizations, an iteratively re-weighted penalty solution (IRwPS) is devised without any inner loops, making the iteration programming easy to perform. Meanwhile, the theoretical results are provided for guaranteeing that the mathematical convergence analysis is solid and meaningful. Finally, by performing real-world applications in supervised, unsupervised, and semi-supervised tasks, numerical experiments are conducted to validate the theoretical properties and the superiority over some of the state-of-the-art.

Decomposing data matrix into low-rank plus additive matrices is a commonly used strategy in pattern recognition and machine learning. This article mainly studies the alternating direction method of multiplier (ADMM) with two dual variables, which is used to optimize the generalized nonconvex nonsmooth low-rank matrix recovery problems. Furthermore, the minimization framework with a feasible optimization procedure is designed along with the theoretical analysis, where the variable sequences generated by the proposed ADMM can be proved to be bounded. Most importantly, it can be concluded from the Bolzano-Weierstrass theorem that there must exist a subsequence converging to a critical point, which satisfies the Karush-Kuhn-Tucher (KKT) conditions. Meanwhile, we further ensure the local and global convergence properties of the generated sequence relying on constructing the potential objective function. Particularly, the detailed convergence analysis would be regarded as one of the core contributions besides the algorithm designs and the model generality. Finally, the numerical simulations and the real-world applications are both provided to verify the consistence of the theoretical results, and we also validate the superiority in performance over several mostly related solvers to the tasks of image inpainting and subspace clustering.

The critical step of learning the robust regression model from high-dimensional visual data is how to characterize the error term. The existing methods mainly employ the nuclear norm to describe the error term, which are robust against structure noises (e.g., illumination changes and occlusions). Although the nuclear norm can describe the structure property of the error term, global distribution information is ignored in most of these methods. It is known that optimal transport (OT) is a robust distribution metric scheme due to that it can handle correspondences between different elements in the two distributions. Leveraging this property, this article presents a novel robust regression scheme by integrating OT with convex regularization. The OT-based regression with$L_{2} $norm regularization (OTR) is first proposed to perform image classification. The alternating direction method of multipliers is developed to handle the model. To further address the occlusion problem in image classification, the extended OTR (EOTR) model is then presented by integrating the nuclear norm error term with an OTR model. In addition, we apply the alternating direction method of multipliers with Gaussian back substitution to solve EOTR and also provide the complexity and convergence analysis of our algorithms. Experiments were conducted on five benchmark datasets, including illumination changes and various occlusions. The experimental results demonstrate the performance of our robust regression model on biometric image classification against several state-of-the-art regression-based classification methods.

In recent years, most of the studies have shown that the generalized iterated shrinkage thresholdings (GISTs) have become the commonly used first-order optimization algorithms in sparse learning problems. The nonconvex relaxations of the$\ell _{0}$-norm usually achieve better performance than the convex case (e.g.,$\ell _{1}$-norm) since the former can achieve a nearly unbiased solver. To increase the calculation efficiency, this work further provides an accelerated GIST version, that is, AGIST, through the extrapolation-based acceleration technique, which can contribute to reduce the number of iterations when solving a family of nonconvex sparse learning problems. Besides, we present the algorithmic analysis, including both local and global convergence guarantees, as well as other intermediate results for the GIST and AGIST, denoted as (A)GIST, by virtue of the Kurdyka-Łojasiewica (KŁ) property and some milder assumptions. Numerical experiments on both synthetic data and real-world databases can demonstrate that the convergence results of objective function accord to the theoretical properties and nonconvex sparse learning methods can achieve superior performance over some convex ones.

Conventional multiobjective optimization algorithms (MOEAs) with or without preferences are successful in solving multi- and many-objective optimization problems. However, a strong hypothesis underlying their performance is that MOEAs are able to find a representative solution set to cover the entire Pareto-optimal front (PF) and decision makers are able to conveniently and precisely articulate their preference, which is not always easy to fulfill in practice. Accordingly, it is suggested that representative solutions in the naturally interesting regions of the PF rather than the whole PF should be targeted. A large body of research has been proposed to search or identify the knees or knee regions over the past decades. Therefore, this article aims to provide a comprehensive survey of the research on knee-oriented optimization. We start with a discussion of the importance and basic concepts of the knees, followed by a summary of knee-oriented benchmarks and indicators. After that, knee-oriented frameworks and techniques, and real-world applications are presented. Finally, potential challenges are pointed out and a few promising future lines of research are suggested. The survey offers a new perspective to develop MOEAs for solving multi- and many-objective optimization problems.

We aim to provide a computationally cheap yet effective approach for fine-grained image classification (FGIC) in this letter. Unlike previous methods that rely on complex part localization modules, our approach learns fine-grained features by enhancing the semantics of sub-features of a global feature. Specifically, we first achieve the sub-feature semantic by arranging feature channels of a CNN into different groups through channel permutation. Meanwhile, to enhance the discriminability of sub-features, the groups are guided to be activated on object parts with strong discriminability by a weighted combination regularization. Our approach is parameter parsimonious and can be easily integrated into the backbone model as a plug-and-play module for end-to-end training with only image-level supervision. Experiments verified the effectiveness of our approach and validated its comparable performance to the state-of-the-art methods. Code is available at https://github.com/cswluo/SEF.

In recent years, low-rank matrix recovery problems have attracted much attention in computer vision and machine learning. The corresponding rank minimization problems are both combinational and NP-hard in general, which are mainly solved by both nuclear norm and Schatten-p (0<p<1) norm based optimization algorithms. However, inspired by weighted nuclear norm and Schatten-p norm as the relaxations of rank function, the main merits of this work firstly provide a modified Schatten-p norm in the affine matrix rank minimization problem, denoted as the modified Schatten-p norm minimization (MSpNM). Secondly, its surrogate function is constructed and the equivalence relationship with the MSpNM is further achieved. Thirdly, the iterative singular value thresholding algorithm (ISVTA) is devised to optimize it, and its accelerated version, i.e., AISVTA, is also obtained to reduce the number of iterations through the well-known Nesterov's acceleration strategy. Most importantly, the convergence guarantees and their relationship with objective function, stationary point and variable sequence generated by the proposed algorithms are established under some specific assumptions, e.g., Kurdyka-Łojasiewicz (KŁ) property. Finally, numerical experiments demonstrate the effectiveness of the proposed algorithms in the matrix completion problem for image inpainting and recommender systems. It should be noted that the accelerated algorithm has a much faster convergence speed and a very close recovery precision when comparing with the proposed non-accelerated one.

Recently, nuclear norm-based low rank representation (LRR) methods have been popular in several applications, such as subspace segmentation. However, there exist two limitations: one is that nuclear norm as the relaxation of rank function will lead to the suboptimal solution since nuclear norm-based minimization subproblem tends to the over-relaxations of singular value elements and treats each of them equally; the other is that solving LRR problems may cause more time consumption due to involving singular value decomposition of the large scale matrix at each iteration. To overcome both disadvantages, this paper mainly considers two tractable variants of LRR: one is Schatten-p norm minimization-based LRR (i.e., SpNM_LRR) and the other is Schatten-p norm factorization-based LRR (i.e., SpNFLRR) for p=1, 2/3 and 1/2. By introducing two or more auxiliary variables in the constraints, the alternating direction method of multiplier (ADMM) with multiple updating variables can be devised to solve these variants of LRR. Furthermore, both computational complexity and convergence property are given to evaluate nonconvex multiblocks ADMM algorithms. Several experiments finally validate the efficacy and efficiency of our methods on both synthetic data and real world data.

Recently, there is a rapidly increasing attraction for the efficient recovery of low-rank matrix in computer vision and machine learning. The popular convex solution of rank minimization is nuclear norm-based minimization (NNM), which usually leads to a biased solution since NNM tends to overshrink the rank components and treats each rank component equally. To address this issue, some nonconvex nonsmooth rank (NNR) relaxations have been exploited widely. Different from these convex and nonconvex rank substitutes, this paper first introduces a general and flexible rank relaxation function named weighted NNR relaxation function, which is actually derived from the initial double NNR (DNNR) relaxations, i.e., DNNR relaxation function acts on the nonconvex singular values function (SVF). An iteratively reweighted SVF optimization algorithm with continuation technology through computing the supergradient values to define the weighting vector is devised to solve the DNNR minimization problem, and the closed-form solution of the subproblem can be efficiently obtained by a general proximal operator, in which each element of the desired weighting vector usually satisfies the nondecreasing order. We next prove that the objective function values decrease monotonically, and any limit point of the generated subsequence is a critical point. Combining the Kurdyka-Łojasiewicz property with some milder assumptions, we further give its global convergence guarantee. As an application in the matrix completion problem, experimental results on both synthetic data and real-world data can show that our methods are competitive with several state-of-the-art convex and nonconvex matrix completion methods.

-norm and rank function minimization problems. However, due to the absence of convexity in these nonconvex problems, developing efficient algorithms with convergence guarantee becomes very challenging. Inspired by the basic ideas of both the Jacobian alternating direction method of multipliers (JADMMs) for solving linearly constrained problems with separable objectives and the proximal gradient methods (PGMs) for optimizing the unconstrained problems with one variable, this paper focuses on extending the PGMs to the proximal Jacobian iteration methods (PJIMs) for handling with a family of nonconvex composite optimization problems with two splitting variables. To reduce the total computational complexity by decreasing the number of iterations, we devise the accelerated version of PJIMs through the well-known Nesterov's acceleration strategy and further extend both to solve the multivariable cases. Most importantly, we provide a rigorous convergence analysis, in theory, to show that the generated variable sequence globally converges to a critical point by exploiting the Kurdyka-Łojasiewica (KŁ) property for a broad class of functions. Furthermore, we also establish the linear and sublinear convergence rates of the obtained variable sequence in the objective function. As the specific application to the nonconvex sparse and low-rank recovery problems, several numerical experiments can verify that the newly proposed algorithms not only keep fast convergence speed but also have high precision.

Practically, we are often in the dilemma that the labeled data at hand are inadequate to train a reliable classifier, and more seriously, some of these labeled data may be mistakenly labeled due to the various human factors. Therefore, this paper proposes a novel semi-supervised learning paradigm that can handle both label insufficiency and label inaccuracy. To address label insufficiency, we use a graph to bridge the data points so that the label information can be propagated from the scarce labeled examples to unlabeled examples along the graph edges. To address label inaccuracy, Graph Trend Filtering (GTF) and Smooth Eigenbase Pursuit (SEP) are adopted to filter out the initial noisy labels. GTF penalizes the l_0 norm of label difference between connected examples in the graph and exhibits better local adaptivity than the traditional l_2 norm-based Laplacian smoother. SEP reconstructs the correct labels by emphasizing the leading eigenvectors of Laplacian matrix associated with small eigenvalues, as these eigenvectors reflect real label smoothness and carry rich class separation cues. We term our algorithm as "Semi-supervised learning under Inadequate and Incorrect Supervision" (SIIS). Thorough experimental results on image classification, text categorization, and speech recognition demonstrate that our SIIS is effective in label error correction, leading to superior performance to the state-of-the-art methods in the presence of label noise and label scarcity.

Face recognition (FR) via regression analysis-based classification has been widely studied in the past several years. Most existing regression analysis methods characterize the pixelwise representation error via l1-norm or l2-norm, which overlook the 2D structure of the error image. Recently, the nuclear norm-based matrix regression model is proposed to characterize low-rank structure of the error image. However, the nuclear norm cannot accurately describe the low-rank structural noise when the incoherence assumptions on the singular values does not hold, since it overpenalizes several much larger singular values. To address this problem, this paper presents the robust nuclear norm to characterize the structural error image and then extends it to deal with the mixed noise. The majorization-minimization (MM) method is applied to derive a iterative scheme for minimization of the robust nuclear norm optimization problem. Then, an efficiently alternating direction method of multipliers (ADMM) method is used to solve the proposed models. We use weighted nuclear norm as classification criterion to obtain the final recognition results. Experiments on several public face databases demonstrate the effectiveness of our models in handling with variations of structural noise (occlusion, illumination, and so on) and mixed noise.