Traditional partition-based fuzzy clustering algorithms are widely used for revealing possible hidden structures in data. However, high computational cost limits their applications in large-scale and high-dimensional data. Moreover, most fuzzy clustering algorithms are sensitive to noise. To tackle these issues, a robust jointly sparse fast fuzzy clustering algorithm via anchor graph (RSFCAG) is proposed and analyzed in this paper. Specifically, we first propose a fast k-means method integrated shadowed set and balanced ternary tree, which serves as a fast hierarchical clustering approach by partitioning every cluster into three subclusters at each layer (3KHK). 3KHK can quickly obtain the anchor set and its optimization is solved fast by the simplex method, which also captures the ambiguity and uncertainty between clusters in large-scale clustering tasks. Second, a similarity matrix learning approach based on possibilistic neighbors is further proposed to get a robust similarity graph, which strengthens the ability of fuzzy clustering to handle large-scale data. Furthermore, the orthogonal projection matrix is integrated into the RSFCAG framework to transform the original high-dimensional space into low-dimensional space. Finally, the$L_{2,1}$-norm loss and regularization are integrated into the joint algorithm RSFCAG, which is solved optimally by block coordinate technique, to enhance the robustness and interpretability of the fuzzy clustering process. The experimental results demonstrate the effectiveness and efficiency of our proposed method in most of benchmark datasets.

On the road to 6G, the growing number of antennas and mobility-related applications emphasize the urgency of addressing the channel aging issue. Traditional channel prediction methods are no longer valid due to simplified assumptions. Deep learning (DL)-based predictors, even with attractive performance improvements, generally lack the utilization of extra correlations and flexible inference with accuracy-efficiency trade-off. In this paper, by representing the topology structure of nearby users (UEs) as a graph, a multi-user channel prediction algorithm is proposed for learnable UE correlation extraction, called LUCE, to improve prediction performance. Instead of simple summation-based fusion, LUCE introduces a predefined geographic embedding and a learnable embedding to offset the position information of the cross-attention (CA) to learn and interact UE features on the graph automatically. Furthermore, a lightweight LUCE is proposed to leverage the homogeneity of CSIs by sharing sub-networks. In addition, a variable-depth learning architecture is proposed, called adaptive LUCE (AdaLUCE), and its number of blocks can be dynamically adjusted for each input by tuning a desired threshold. In particular, AdaLUCE utilizes a hierarchical triple residual architecture to promote its training efficacy and produce predictions at its internal blocks without increasing complexity, and adopts a fitting inspired criterion (FIC) to make real-time decisions for adaptive inference. In total, AdaLUCE is optimized by the weighted sum of multiple loss functions, and a multi-step training scheme is presented. We show that AdaLUCE preserves and releases computing resources for various speeds in sample-wise, improving both prediction accuracy and inference efficiency.

Abstract. Recently, the CTV-RPCA model proposed the first recoverable theory for separating low-rank and local-smooth matrices and sparse matrices based on the correlated total variation (CTV) regularizer. However, the CTV-RPCA model ignores the influence of noise, which makes the model unable to effectively extract low-rank and local-smooth principal components under noisy circumstances. To alleviate this issue, this article extends the CTV-RPCA model by considering the influence of noise and proposes two robust models with parameter adaptive adjustment, i.e., Stable Principal Component Pursuit based on CTV (CTV-SPCP) and Square Root Principal Component Pursuit based on CTV (CTV-[Formula: see text]). Furthermore, we present a statistical recoverable error bound for the proposed models, which allows us to know the relationship between the solution of the proposed models and the ground-truth. It is worth mentioning that, in the absence of noise, our theory degenerates back to the exact recoverable theory of the CTV-RPCA model. Finally, we develop the effective algorithms with the strict convergence guarantees. Extensive experiments adequately validate the theoretical assertions and also demonstrate the superiority of the proposed models over many state-of-the-art methods on various typical applications, including video foreground extraction, multispectral image denoising, and hyperspectral image denoising. The source code is released at https://github.com/andrew-pengjj/CTV-SPCP .

Fully characterizing the spatial-spectral priors of hyperspectral images (HSI) is crucial for HSI denoising tasks. Recently, HSI denoising models based on representative coefficient images (RCIs) under the spectral low-rank decomposition framework have garnered significant attention due to their clever utilization of spatial-spectral information in HSI at a low cost. However, current methods either employ handcrafted classical denoisers or off-the-shelf deep denoisers to denoise RCIs, failing to fully capture the structural information of RCIs. In this paper, we propose a specific optimization framework for learning an RCI denoiser under the low-rank decomposition framework for the first time. Since low-rank decomposition can characterize the global low-rank property of HSI, our RCI denoiser only needs to learn the spatial prior of RCIs. Consequently, our optimization framework is inclined to learn a more powerful RCI denoiser. However, learning an RCI denoiser is not an easy task, primarily due to the lack of paired clean-noisy RCI data. To address this issue, we employ parametric techniques to represent the to-be-restored HSI as a function of RCI denoiser network parameters. In this way, the parameters of the RCI denoiser can thus be updated using noisy-clean HSI pairs. Furthermore, we adopt residual learning and Gaussian whitening techniques to enhance the RCI denoiser’s denoising ability for HSIs with various noise levels and different rank settings. Extensive experiments demonstrate that our method can achieve significant improvements in both denoising effectiveness and speed compared to state-of-the-art methods. The code of our algorithm is released at https://github.com/andrew-pengjj/RCILD.git.

It is known that the decomposition in low-rank and sparse matrices (L+S for short) can be achieved by several Robust PCA techniques. Besides the low rankness, the local smoothness (LSS) is a vitally essential prior for many real-world matrix data such as hyperspectral images and surveillance videos, which makes such matrices have low-rankness and local smoothness property at the same time. This poses an interesting question: Can we make a matrix decomposition in terms of L&LSS +S form exactly? To address this issue, we propose in this paper a new RPCA model based on three-dimensional correlated total variation regularization (3DCTV-RPCA for short) by fully exploiting and encoding the prior expression underlying such joint low-rank and local smoothness matrices. Specifically, using a modification of Golfing scheme, we prove that under some mild assumptions, the proposed 3DCTV-RPCA model can decompose both components exactly, which should be the first theoretical guarantee among all such related methods combining low rankness and local smoothness. In addition, by utilizing Fast Fourier Transform (FFT), we propose an efficient ADMM algorithm with a solid convergence guarantee for solving the resulting optimization problem. Finally, a series of experiments on both simulations and real applications are carried out to demonstrate the general validity of the proposed 3DCTV-RPCA model.

Dominance relations exist extensively in decision-making problems. Dominance-based neighborhood rough sets (DNRS) using fuzzy preference relations (FPRs) are presented in this article to deal with attribute reduction in the large-scale decision-making problems. In this model, FPR is elicited to quantify the dominance-based rough set model, which can efficiently deal with the under-fitting problem of classical dominance-based rough sets. First, by formulating a quantified dominance-based neighborhood relation which satisfies reflexivity, the propositions of the quantified DNRSs are analyzed. Second, we propose approaches to attribute reduction based on upper-approximate and lower-approximate discernibility matrices, respectively. Furthermore, we evaluate that the novel model performs efficiently and effectively in time consumption and space storage by experimental analysis. Finally, combining with parallel computing, we demonstrate that the new model can be used to deal with attribute reduction of large-scale datasets effectively.