Search Results (107)

Unsupervised learning often relies on non-negative matrix factorization (NMF) for extracting low-dimensional features. Standard deep NMF models, however, tend to miss complex hierarchical patterns and may warp the intrinsic geometry of high-dimensional data, resulting in solutions that are neither smooth nor stable. To counter these issues, we introduce DGLpSNMF—a deep graph-regularized $L_p$ smooth semi-NMF—that explicitly incorporates the data’s geometric structure via graph Laplacian regularization and $L_p$ smoothing. The optimization problem is tackled with a forward-backward splitting scheme, and we establish convergence of the generated sequence to a critical point. Experiments on four image benchmarks (JAFFE, Yale, ORL, PIE) demonstrate that DGLpSNMF consistently surpasses several state-of-the-art NMF variants in both accuracy and normalized mutual information. Full article

In sparse representation learning-based linear k-nearest neighbors methods, the linear representation assumption frequently fails when applied to nonlinear distributed data, leading to degraded generalization and a loss of physical interpretability. To address this, we propose the Kernelized Manifold-Optimized Linear Nearest Neighbor (KMOLNN) method. Methodologically, KMOLNN projects the data into a high-dimensional kernel space to capture the nonlinear relationships, while introducing an adaptive manifold-preserving regularization term—via an adaptive Laplacian matrix—to dynamically preserve the local geometric structures. Theoretically, this study provides a mathematical proof of the nearest neighbor group effect for the kernel framework and reveals that its weight optimization behavior implicitly implements the Bayesian decision rule. Furthermore, we derive a rigorous generalization error bound using Rademacher complexity to validate its theoretical robustness. Empirically, we evaluate KMOLNN on 15 small-to-medium-scale benchmark datasets against eight comparative methods, including recent variants. The results demonstrate significant numeric superiority, with KMOLNN achieving an average accuracy of 90.76% and a Macro F1-score of 88.62% across the evaluated datasets. Finally, we present a comprehensive runtime analysis, explicitly acknowledging that these gains in generalization capability and theoretical interpretability present a practical trade-off, requiring increased computational runtime due to the iterative alternating optimization process. Full article

Conventional multi-mission altimetry fusion tends to attenuate short-wavelength sea surface height anomaly (SLA) signals when high-density two-dimensional SWOT observations are incorporated into a single smoothing framework. To address this limitation, this study proposes a scale-separated, scale-wise fusion framework for high-resolution SLA reconstruction that jointly exploits multi-mission nadir altimetry and SWOT wide-swath observations. Multi-mission Level-3 observations from Sentinel-3A/B, HY-2B, SARAL/Altika, and SWOT are first harmonized through quality control, spatiotemporal reference unification, and cross-calibration referenced to Jason-3; Jason-3 was not used as a fusion input; instead, it served as the cross-calibration reference and as an external validation source after excluding calibration-involved samples. The SWOT-observed SLA field is then decomposed using an 80 km Lanczos filter—chosen as a practical working scale reflecting SWOT’s effective resolution rather than a universal physical boundary—into a large-scale background component and a mesoscale–submesoscale perturbation component. The large-scale component is reconstructed using adaptive optimal interpolation with latitude-dependent covariance scales, whereas the mesoscale–submesoscale component is refined through a physically regularized Transformer-based learning branch that recovers organized sub-80 km variability as a relative enhancement with respect to the AVISO/CMEMS reference. The two components are finally recombined on a 0.08° × 0.08° grid to generate a global SLA product. Validation from August 2023 to August 2024 shows that the proposed product maintains strong large-scale consistency with AVISO/CMEMS, with a mean daily spatial correlation of approximately 0.85. Sample-independent cross-validation against concurrent Jason-3 along-track observations yields a mean daily RMSE of 4.9 cm. Regional case studies in the Kuroshio Extension and the Scotia Sea further show that, relative to a conventional unified fusion scheme, the proposed framework better preserves organized sub-80 km structures, including fronts, eddy boundaries, and filamentary features, without degrading the large-scale background. Two specific technical contributions are (i) a reproducible scale-separated workflow that decouples large-scale OI mapping from fine-scale learning-based reconstruction, and (ii) a physically regularized loss formulation that constrains spatial gradients and Laplacian smoothness to suppress nonphysical artifacts during small-scale enhancement. These results suggest that scale-separated fusion provides an effective and operationally practical strategy for next-generation high-resolution SLA products and for improved observation of dynamically significant short-wavelength ocean variability. Full article

Accurate prediction of slope displacement from high-frequency GNSS monitoring data is critical for early warning of landslides and tailings dam failures. However, existing deep learning approaches often neglect the spatial coordination imposed by geological structures and fail to decouple abrupt deformation signals from background noise, leading to non-physical oscillations and inconsistent long-term predictions. To address these limitations, this paper proposes a Symmetry-Aware Physics-Guided Spatio-Temporal Graph Network (PG-STGN). First, a geological hierarchy-aware graph is constructed by integrating geometric proximity with prior knowledge of exploration levels, where the resulting adjacency matrix is symmetric by design and reflects the physical symmetry of deformation interactions among monitoring points at the same elevation. A hierarchical masking mechanism restricts feature aggregation to physically connected neighborhoods while preserving this symmetry. Second, an improved dual-path temporal convolutional network (iTCN) decouples high-frequency abrupt variations from low-frequency evolutionary trends, enabling both sensitive detection of sudden deformation and stable tracking of long-term creep. Third, a physics-consistent loss function combining first-order temporal differencing and graph Laplacian regularization enforces kinematic smoothness and spatial coordination; the Laplacian itself is derived from the symmetric adjacency matrix, ensuring symmetric regularization across the monitoring network. Evaluated on a real-world slope GNSS dataset from a large-scale mining project, PG-STGN reduces mean squared error (MSE) by approximately 23.7% and achieves a global R² of 0.924, outperforming state-of-the-art spatio-temporal models. Ablation studies confirm that the symmetric physics-guided graph, dual-path decoupling, and consistency loss are each essential for suppressing spurious correlations and maintaining physically plausible predictions. The proposed framework provides a robust, interpretable, and symmetry-constrained solution for automated slope monitoring under complex geological conditions. Full article

Movie genre classification is a significant challenge in narrative analysis, as traditional methods often fail to capture complex structural relationships within movie stories. This study introduces the Intra-Cluster Weighted Movie Network (ICWMN), a novel framework designed to improve classification by using intra-movie relationships through Graph Neural Networks (GNNs). We constructed a large-scale dataset of 1631 movie character networks using an automated pipeline comprising web scraping, regular expressions, and fine-tuned BERT models for entity recognition. To address the computational limitations of fully connected models, we partition ICWMN into clusters and establish edges only between the k-most similar nodes using the K-Nearest Neighbor algorithm and various distance measures, such as the Laplacian and NetLSD. XGBoost is applied to optimize high-dimensional node feature vectors. Experimental results demonstrate outstanding performance, with the Graph Attention Network (GAT) emerging as the top-performing architecture, resulting in classification accuracies that peak at $95.00\%$ on our 1631-movie dataset and an exceptional $97.30\%$ on the 773-movie Moviegalaxies dataset. These findings confirm that prioritizing spectral properties and cluster-based network topologies significantly improve the precision and stability of genre classification compared to state-of-the-art methods. Full article

The averaging effect is a distinctive property possessed by fractional operators. In recent years, it has emerged as a powerful tool in the study of qualitative properties of solutions to fractional elliptic and parabolic equations. In this article, we systematically summarize and prove various forms of the averaging effects for both fractional elliptic and parabolic equations, from the simplest one to the one under very relaxed conditions, including versions for antisymmetric functions. We then present examples to illustrate how to apply these effects to obtain radial symmetry and monotonicity for solutions in a unit ball and in a half space. In addition, we derive averaging effects for fractional Monge–Ampère operators and for fractional p-Laplacians, which will be potentially applied to obtain qualitative properties for solutions to equations involving these operators. Compared with the traditional approaches, methods based on the averaging effect require substantially weaker regularity assumptions and can even accommodate unbounded solutions. Full article

In semi-supervised learning scenarios, the presence of limited labeled data and abundant unlabeled samples poses significant challenges to model robustness and generalization. Although the semi-supervised broad learning system (SSBLS) effectively exploits manifold structure through graph Laplacian regularization, its optimization is typically formulated under the mean square error (MSE) criterion, which is sensitive to noise and outliers. To address this limitation, this paper introduces the maximum mixture correntropy criterion (MMC) into the SSBLS framework and proposes a model termed M2C-SSBLS. By replacing the conventional MSE loss with a mixture correntropy-based objective, the proposed method enhances robustness against non-Gaussian noise and abnormal samples while preserving the computational efficiency and analytical solution property of the BLS. Furthermore, to improve representation diversity and reduce model variance, a multi-view ensemble extension, named EC-SSBLS, is proposed. This method constructs multiple feature views through a random feature subspace strategy, and independently trains an M2C-SSBLS base learner on each subspace. Finally, the predicted results of each view are fused through a voting mechanism. Experiments on benchmark UCI datasets under noise-free, 10% and 20% label noise settings demonstrate that the proposed M2C-SSBLS consistently outperforms conventional SSBLS and other advanced semi-supervised learning approaches. The ensemble extension EC-SSBLS further enhances performance, particularly in noisy environments, validating the effectiveness of combining MMC-based optimization with multi-view ensemble learning. Full article

One of the main tasks in the field of directional statistics is to build goodness-of-fit tests for uniformity on circles, spheres or more abstract manifolds. We discuss a goodness-of-fit test for uniformity on a distance-regular graph. Our main tool is the pseudo-inverse of the combinatorial Laplacian, for which we give explicit expressions in terms of the intersection array of the graph. Such a test can be used as a test for uniformity of data from the circle or the sphere, grouped on the tiles of a regular tessellation associated with some finite group of isometries. We describe the cases of Platonic graphs and provide examples based on real circular and spherical data, vectorial or axial. Full article

In impedance imaging, the incompatibility and nonlinearity of the inverse problem lead to problems such as blurred boundaries and severe artifacts in the reconstructed images, making it difficult to meet the requirements for precise identification of multi-layer tissue structures in the legs. To this end, this paper proposes a post-processing algorithm for leg EIT that integrates the boundary attention mechanism, with a Wasserstein generative adversarial network as the training framework, cyclic residual U-Net as the generator, and the boundary attention module embedded in the RecurrentBlock. This leads to adaptive enhancement of the ability to extract organizational boundary features through a three-path fusion of spatial attention, channel attention, and learnable Laplacian edge enhancement. A leg anatomy prior constraint loss function was designed, integrating six constraints—pixel loss, edge loss, hierarchical tissue constraint, total variation regularization, structural similarity loss, and histogram matching—to guide the reconstruction results to conform to the multi-layered tissue structure features of the leg. A simulation dataset of leg sections containing multiple tissues such as skin, fat, muscle, bone, blood vessels, and nerves was constructed, and the pre-reconstructed images were obtained using the hybrid total variation regularization algorithm as the network input. The simulation results show that, under noise-free and different signal-to-noise ratio conditions, the proposed BAM-R2UNet algorithm achieves the best performance in RMSE, SSIM and PSNR metrics compared with HTV, DnCNN and standard U-Net algorithms, can remove artifacts, accurately restore the boundary and conductivity distribution of leg tissues, and has stronger anti-noise robustness. Full article

The purpose of our paper is to provide a family of bilinear orthogonal expansions all based upon the same general pattern that is valid for a wide class of special functions. Our first family involves Jacobi, Laguerre, and Hermite polynomials. We give a discrete analogue of these bilinear expansions, the three families of classical orthogonal polynomials being replaced by zonal spherical functions associated with regular distance graphs. Such expansions playing a key role in the field of mathematical statistics, we show how our results apply to this field. We provide generalizations of the well-known Cramér–von Mises and Watson’s statistics, based upon an interpretation of their kernel in terms of the circular Laplacian. The product formula, well-known for zonal functions on Lie groups, is stated for distance-regular graphs, providing an elegant tool for proofs. Examples involving Hahn, q-Hahn, and Krawtchouk polynomials are given. Full article

In this paper, we investigate the properties of the boundedness of fractional integral operators $K_{\alpha }$ defined on general measure metric spaces. We study their action in Lebesgue spaces $L^p\left(Y\right)$, Morrey spaces $L_{\phi }^p\left(Y\right)$, and extend our analysis to fractional Sobolev spaces $W^{\alpha ,p}\left(Y\right)$. Using classical dyadic decomposition and the Hardy–Littlewood maximal operator, we establish sharp bounds for $K_{\alpha }$ in terms of kernel parameters and the geometric structure of the space. A significant contribution of this work is the proof that $K_{\alpha }$ is bounded from $W^{\alpha ,p}\left(Y\right)$ to $L^q\left(Y\right)$, where thus linking our operator-theoretic framework with the theory of nonlocal and fractional partial differential equations. These results provide valuable tools for studying regularity, a priori estimates, and solution mappings in nonlocal problems involving the fractional Laplacian and related operators on irregular or non- Euclidean domains. Full article

The second immanantal polynomial is one of the important directions in algebraic theory. Let $M=\left[m_{ij}\right]$ be an $n\times n$ matrix. The second immanant of matrix M is defined as $d_2\left(M\right)={\sum }_{\sigma \in S_n}\chi \left(\sigma \right){\prod }_{i=1}^n{m}_{i\sigma \left(i\right)}$, where $\chi$ is the irreducible character of the symmetric group $S_n$ of degree n, corresponding to the partition $(2^1,1^{n-2})$. Let G be a graph with n vertices. Denote by $Q\left(G\right)$ the signless Laplacian matrix of G. The second signless Laplacian immanantal polynomial of G is defined as $d_2(xI-Q\left(G\right))={\sum }_{k=0}^n{(-1)}^k{c}_k\left(G\right)x^{n-k}$, where $c_k\left(G\right)$ is the coefficient of this polynomial. This paper investigates fundamental properties of this polynomial. First, we give combinatorial expressions for the first few coefficients of the second signless Laplacian immanantal polynomial. Next, we prove that the polynomial has no zero or negative real roots for connected graphs. Furthermore, we show that there is an equivalence relation among three polynomials for regular graphs, which implies that if two regular graphs share the same characteristic polynomial, then they also share the same second signless Laplacian immanantal polynomial. Finally, we prove that paths and almost complete graphs are determined by their second signless Laplacian immanantal polynomials. Full article

Emission tomography, including single-photon emission computed tomography (SPECT), requires image reconstruction from noisy and incomplete projection data. The maximum-likelihood expectation maximization (MLEM) algorithm is widely used due to its statistical foundation and non-negativity preservation, but it is highly sensitive to noise, particularly in low-count conditions. Although total variation (TV) regularization can reduce noise, it often oversmooths structural details and requires careful parameter tuning. We propose a Graph-Enhanced Expectation Maximization (GREM) algorithm that incorporates graph-based neighborhood information into an MLEM-type multiplicative reconstruction scheme. The method is motivated by a penalized formulation combining a Kullback–Leibler divergence term with a graph Laplacian regularization term, promoting local structural consistency while preserving edges. The resulting update retains the multiplicative structure of MLEM and preserves the non-negativity of the image estimates. Numerical experiments using synthetic phantoms under multiple noise levels, as well as clinical ^99mTc-GSA liver SPECT data, demonstrate that GREM consistently outperforms conventional MLEM and TV-regularized MLEM in terms of PSNR and MS-SSIM. These results indicate that GREM provides an effective and practical approach for edge-preserving noise suppression in emission tomography without relying on external training data. Full article

Software maintenance and release management demand proper identification of bug dependencies since priority violations or unresolved dependent issues can often lead to a chain of failures. However, dependency annotations in bug reports are extremely sparse and imbalanced. These dependencies are often expressed implicitly through natural language descriptions rather than explicit metadata. This creates challenges for automated multilabel dependency classification systems. To tackle these drawbacks, we introduce a meta-contrastive optimization framework (MCOF). This framework integrates established learning paradigms to enhance transformer-based classification through two key mechanisms: (1) a meta-contrastive objective adapted for enhancing discriminative representation learning under few-shot supervision, particularly for rare dependency types, and (2) dependency-aware Laplacian regularization that captures relational structures among different dependency types, reducing confusion between semantically related labels. Experimental evaluation on a real-world dataset demonstrates that MCOF achieves significant improvement over strong baselines, including BM25-based clustering and standard BERT fine-tuning. The framework attains a micro-F1 score of 0.76 and macro-F1 score of 0.58, while reducing hamming loss to 0.14. Label-wise analysis shows significant performance gain on low-frequency dependency types, with improvements of up to 16% in F1 score. Runtime analysis exhibits only modest inference overhead at 15%, confirming that MCOF remains practical for deployment in CI/AT pipelines. These results demonstrate that integrating meta-contrastive learning and structural regularization is an effective approach for robust bug dependency discovery. The framework provides both practical and accurate solutions for supporting real-world software engineering workflows. Full article

Point cloud semantic segmentation remains challenging under extremely low annotation budgets due to inefficient utilization of sparse labels and sensitivity to data augmentation noise. To address this, we propose a dual-branch consistency learning (DBCL) framework featuring an EMA teacher for semi-supervised point cloud segmentation. Our core innovation lies in a unified consistency regularization scheme that enforces prediction-level alignment via JS divergence and feature-level contrastive learning, while a geometry-aware Laplacian smoothing term preserves local structural consistency. Extensive experiments demonstrate that DBCL achieves 68.56% mIoU on S3DIS with only 0.1% labels, outperforming existing semi-supervised methods and even matching some fully supervised baselines. Full article