Benefiting from the powerful tensor techniques, the tensor low-rank representation has been proposed to construct sophisticated subspace clustering models. Existing tensor low-rank representation methods predominantly rely on a single low-rank prior to reconstruct the row space, which is instrumental in determining the subspace membership of samples by the row space information. However, this strategy neglects the column space and would lead to a subspace information loss. To address this issue, we propose a Dual Tensor Low-Rank Representation method (DTLRR), the first subspace clustering framework to theoretically recover both row and column subspaces simultaneously. Particularly, not simply formulating a dual self-representation model, we instead prove the recovery of both row and column spaces via a unified theoretical framework. Then, we impose low-rank constraints on the two corresponding affinity tensors to effectively capture high-order correlations. Meanwhile, we theoretically demonstrate the existence of compact dictionary tensors within the dual self-representation framework, which effectively eliminates the null spaces of the affinity tensors and significantly reduces computational complexity. Furthermore, an efficient Alternating Direction Method of Multipliers (ADMM) algorithm is designed to solve the proposed DTLRR model with guaranteed convergence. Extensive experiments validate the superior performance of the proposed DTLRR in data clustering, hyperspectral image denoising, and hyperspectral anomaly detection.

Local Interpretable Model-Agnostic Explanations (LIME) is a widely adopted framework for interpreting opaque models due to its simplicity and intuitiveness. However, LIME suffers from unreliability rooted in two core issues: (i) low fidelity, where the surrogate model fails to accurately approximate the target model's behavior, and (ii) instability, where the generated explanations vary significantly across runs. While prior work has proposed techniques to enhance LIME, they remain fundamentally limited by the expressiveness of linear surrogate models, which cannot adequately capture complex decision boundaries. In this work, we introduce Tilia, a novel method that employs shallow decision tree regressors as the surrogate model, leveraging its structured and deterministic nature to improve both fidelity and stability. Tilia also provides insight into the interplay between surrogate models and sampling strategies, revealing new directions for enhancing explanation reliability. Across extensive experiments on tabular and textual datasets, Tilia outperforms LIME and recent variants on both fidelity and stability, achieving up to 100% approximation of the opaque model and entirely consistent explanations (i.e., 0 Jacard distance). Tilia maintains practical efficiency, completing explanations in seconds even for datasets with over 100 features. These results position Tilia as a robust alternative for model-agnostic explanations. The code is available at https://github.com/neur1n/tilia.

Recently, deep unfolding methods have achieved remarkable success in the realm of Snapshot Compressive Imaging (SCI) reconstruction. However, the existing methods all follow the iterative framework of a single image prior, which limits the efficiency of the unfolding methods and makes it a problem to use other priors simply and effectively. To break out of the box, we derive an effective Dual Prior Unfolding (DPU), which achieves the joint utilization of multiple deep priors and greatly improves iteration efficiency. Our unfolding method is implemented through two parts, i.e., Dual Prior Framework (DPF) and Focused Attention (FA). In brief, in addition to the normal image prior, DPF introduces a residual into the iteration formula and constructs a degraded prior for the residual by considering various degradations to establish the unfolding framework. To improve the effectiveness of the image prior based on self-attention, FA adopts a novel mechanism inspired by PCA denoising to scale and filter attention, which lets the attention focus more on effective features with little computation cost. Besides, an asymmetric backbone is proposed to further improve the efficiency of hierarchical self-attention. Remarkably, our 5-stage DPU achieves state-of-the-art (SOTA) performance with the least FLOPs and parameters compared to previous methods, while our 9-stage DPU significantly outperforms other unfolding methods with less computational requirement. https: / /gi thub. com/ZhangJC-2k/DPU

How to effectively utilize the spectral and spatial char-acteristics of Hyperspectral Image (HSI) is always a key problem in spectral snapshot reconstruction. Recently, the spectra-wise transformer has shown great potential in capturing inter-spectra similarities of HSI, but the classic design of the transformer, i.e., multi-head division in the spectral (channel) dimension hinders the modeling of global spectral information and results in mean effect. In addition, previous methods adopt the normal spatial priors without taking imaging processes into account and fail to address the unique spatial degradation in snapshot spectral reconstruction. In this paper, we analyze the influence of multi-head division and propose a novel Spectral-Spatial Recti-fication (SSR) method to enhance the utilization of spectral information and improve spatial degradation. Specifically, SSR includes two core parts: Window-based Spectra-wise Self-Attention (WSSA) and spAtial Rectification Block (ARB). WSSA is proposed to capture global spectral in-formation and account for local differences, whereas ARB aims to mitigate the spatial degradation using a spatial alignment strategy. The experimental results on simulation and real scenes demonstrate the effectiveness of the proposed modules, and we also provide models at multiple scales to demonstrate the superiority of our approach. https://github.com/ZhangJC-2k/SSR

In this article, a unified multiview subspace learning model, called partial tubal nuclear norm-regularized multiview subspace learning (PTN2MSL), was proposed for unsupervised multiview subspace clustering (MVSC), semisupervised MVSC, and multiview dimension reduction. Unlike most of the existing methods which treat the above three related tasks independently, PTN2MSL integrates the projection learning and the low-rank tensor representation to promote each other and mine their underlying correlations. Moreover, instead of minimizing the tensor nuclear norm which treats all singular values equally and neglects their differences, PTN2MSL develops the partial tubal nuclear norm (PTNN) as a better alternative solution by minimizing the partial sum of tubal singular values. The PTN2MSL method was applied to the above three multiview subspace learning tasks. It demonstrated that these tasks organically benefited from each other and PTN2MSL has achieved better performance in comparison to state-of-the-art methods.

Low-rank tensor representation with the tensor nuclear norm has been rising in popularity in multi-view subspace clustering (MVSC), in which the tensor nuclear norm is commonly implemented using discrete Fourier transform (DFT). Unfortunately, existing DFT-oriented MVSC methods may provide unsatisfactory results since (1) DFT exploits complex arithmetic in the Fourier domain, usually resulting in high tubal tensor rank, and (2) local structural information is rarely considered. To solve these problems, in this paper, we propose a novel double discrete cosine transform (DCT)-oriented multi-view subspace clustering (D2CTMSC) method, in which the first DCT aims to derive the tensor nuclear norm without complex arithmetic while the second DCT aims to explore the local structure of the self-representation tensor, such that the essential low-rankness and sparsity embedding in multi-view features can be thoroughly exploited. Moreover, we design an effective alternating iteration strategy to solve the proposed model. Experimental results on four types of multi-view datasets (News stories, Face images, Scene images, and Generic objects) demonstrate the superiority of the D2CTMSC method compared with DFT-based methods and other state-of-the-art clustering methods.

Deep unrolling-based snapshot compressive imaging (SCI) methods, which employ iterative formulas to construct interpretable iterative frameworks and embedded learnable modules, have achieved remarkable success in reconstructing 3-dimensional (3D) hyperspectral images (HSIs) from 2D measurement induced by coded aperture snapshot spectral imaging (CASSI). However, the existing deep unrolling-based methods are limited by the residuals associated with Taylor approximations and the poor representation ability of single hand-craft priors. To address these issues, we propose a novel HSI construction method named residual completion unrolling with mixed priors (RCUMP). RCUMP exploits a residual completion branch to solve the residual problem and incorporates mixed priors composed of a novel deep sparse prior and mask prior to enhance the representation ability. Our proposed CNN-based model can significantly reduce memory cost, which is an obvious improvement over previous CNN methods, and achieves better performance compared with the state-of-the-art transformer and RNN methods. In this work, our method is compared with the 9 most recent baselines on 10 scenes. The results show that our method consistently outperforms all the other methods while decreasing memory consumption by up to 80%.

In this paper, we study how to make unsupervised cross-modal hashing (CMH) benefit from contrastive learning (CL) by overcoming two challenges. To be exact, i) to address the performance degradation issue caused by binary optimization for hashing, we propose a novel momentum optimizer that performs hashing operation learnable in CL, thus making on-the-shelf deep cross-modal hashing possible. In other words, our method does not involve binary-continuous relaxation like most existing methods, thus enjoying better retrieval performance; ii) to alleviate the influence brought by false-negative pairs (FNPs), we propose a Cross-modal Ranking Learning loss (CRL) which utilizes the discrimination from all instead of only the hard negative pairs, where FNP refers to the within-class pairs that were wrongly treated as negative pairs. Thanks to such a global strategy, CRL endows our method with better performance because CRL will not overuse the FNPs while ignoring the true-negative pairs. To the best of our knowledge, the proposed method could be one of the first successful contrastive hashing methods. To demonstrate the effectiveness of the proposed method, we carry out experiments on five widely-used datasets compared with 13 state-of-the-art methods. The code is available at https://github.com/penghu-cs/UCCH.

Self-representation subspace clustering based on graphs has the merits of capability and efficiency. However, the graph built by the self-representation methods has two issues: (i) usually lacking conciseness and informativeness due to the negative representation coefficients. (ii) no guarantee of an overall optimal solution due to the separation of representation learning and graph construction. To alleviate these issues, we propose a novel subspace clustering via learning non-negative representation with an adaptive graph. Specifically, we explicitly impose the non-negative constraint on the self-representation learning, ensuring that each data point is approximated from a group of homogeneous samples and enhancing the distinguishability of data representation. Meanwhile, an adaptive graph is developed so that both representation and the geometric structure of data are simultaneously learned in a unified procedure. Moreover, the learned representation is less sensitive to data noise imposed by the$\ell _{2,1}$-norm, so the adaptive graph will be further improved. An efficient optimization procedure is developed to find the optimal solution. Extensive experiments on subspace clustering and the extension application to image segmentation validate the advantages of our method against state-of-the-art methods.

Categorical data are widely available in many real-world applications, and to discover valuable patterns in such data by clustering is of great importance. However, the lack of a decent quantitative relationship among categorical values makes traditional clustering approaches, which are usually developed for numerical data, perform poorly on categorical datasets. To solve this problem and boost the performance of clustering for categorical data, we propose a novel fuzzy clustering model in this article. At first, by approximating the maximum a posteriori (MAP) estimation of a discrete distribution of data partition, a new fuzzy clustering objective function is designed for categorical data. The Bayesian dissimilarity measure is formulated in this objective to tackle the subtle relationships between categorical values efficiently. Then, to further enhance the performance of clustering, a novel Kullback–Leibler divergence-based graph regularization is integrated into the clustering objective to exploit the prior knowledge on datasets, for example, the information about correlations of data points. The proposed model is solved by the alternative optimization and the experimental results on the synthetic and real-world datasets show that it outperforms the classical and relevant state-of-the-art algorithms. We also present the parameter analysis of our approach, and conduct a comprehensive study on the effectiveness of the Bayesian dissimilarity measure and the KL divergence-based graph regularization.

Hyperspectral anomaly detection (HAD), distinguishing anomalous pixels or subpixels from the background, has received increasing attention in recent years. Low-Rank Representation (LRR)-based methods have also been promoted rapidly for HAD, but they may encounter three challenges: (1) they adopted the nuclear norm as the convex approximation, yet a sub-optimal solution of the rank function; (2) they overlook the structured spatial correlation of anomalous pixels; (3) they fail to comprehensively explore the local structure details of the original background. To address these challenges, in this paper, we proposed the Structured Sparsity Plus Enhanced Low-Rank (S2ELR) method for HAD. Specifically, our S2ELR method adopts the weighted tensor Schatten-pnorm, acting as an enhanced approximation of the rank function than the tensor nuclear norm, and the structured sparse norm to characterize the low-rank properties of the background and the sparsity of the abnormal pixels, respectively. To preserve the local structural details, the position-based Laplace regularizer is accompanied. An iterative algorithm is derived from the popular alternating direction methods of multipliers. Compared to the existing state-of-the-art HAD methods, the experimental results have demonstrated the superiority of our proposed S2ELR method.

This article studies the nonsingular fixed-time control problem of multiple-input multiple-output (MIMO) nonlinear systems with unmeasured states for the first time. A state observer is designed to solve the problem that system states cannot be measured. Due to the existence of the unknown system nonlinear dynamics, neural networks (NNs) are introduced to approximate them. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive output feedback control algorithm is proposed, which introduces a filter to avoid the complicated derivation process of the virtual control function. According to the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is proven, which means that all signals of the closed-loop system remain bounded in a fixed time under the proposed algorithm. Finally, the effectiveness of the proposed algorithm is verified by the numerical simulation and practical simulation.

Tensor-based robust principal component analysis (PCA) methods are efficient to discover the low-rank part of a hyperspectral image for reducing redundant information and guarantee good classification results. However, current methods cannot remove noise adequately, and the residual noise remaining in the low-rank image limits the further improvement of classification performance. Thus, enhancing the robustness to noise is important and helpful for tensor-based robust PCA (RPCA) methods to process hyperspectral images. To this end, we propose a tensor-based RPCA method with a locality preserving graph and frontal slice sparsity (LPGTRPCA) for hyperspectral image classification. Specifically, a tensor$l_{2,2,1}$norm that requires the frontal slice sparsity of a tensor is defined to extract the noise in the hyperspectral image from the frontal direction. What is more, a position-based Laplacian graph that preserves the local structures of a tensor according to the spatial position is designed for relieving the impact of the residual noise remaining in the low-rank image. Based on the tensor nuclear norm, the tensor$l_{2,2,1}$norm, and the position-based Laplacian graph, LPGTRPCA efficiently separates the low-rank part with little noise from a raw hyperspectral image and achieves more robust classification results than current methods. LPGTRPCA is optimized by the alternative direction multiplier method (ADMM), and the convergence of solutions is experimentally demonstrated. In the experiments conducted on Indian Pines, Pavia University, and Salinas datasets, LPGTRPCA outperformed various state-of-the-art and classical tensor-based RPCA methods in terms of average class classification accuracy (AA), overall classification accuracy (OA), and kappa coefficient (KC).

Self-representation methods, such as low-rank representation (LRR), sparse subspace clustering (SSC) and their variants may generate negative coding coefficients since there is no explicit nonnegative constraint. These negative coefficients lack physical meaning. To be specific, it is unreasonable to allow a query sample encoded by heterogeneous samples to cancel each other out with subtractions. In this paper, we propose a novel model named Laplacian regularized nonnegative representation (LapNR). The new model improves its physical interpretability by ensuring that the query sample should be approximated from homogeneous samples and irrelevant to heterogeneous ones. More importantly, it captures the geometric information of input data by imposing the graph Laplacian to the nonnegative representations. As a result, the representation matrix generated by our LapNR model becomes sparse and discriminative. Based on the alternating direction method of multipliers (ADMM), an efficient optimization procedure is developed for LapNR. The extensive experiments on clustering and dimensionality reduction tasks show the effectiveness and efficiency of our LapNR.