Existing meta-path-based recommendation systems suffer from noise interference and intent fusion, which distort high-order semantic relationships and consequently degrade recommendation performance. To tackle these challenges, we propose meta-path Diffusion Denoising and Multi-view Contrastive Learning for recommendation (DDMCL), which enhances representation learning from three perspectives: (1) Dual-graph diffusion denoising: we employ diffusion model to simultaneously reconstruct the latent semantic distributions of two meta-path graphs on the user (item) side, achieving joint optimization through a shared-parameter network with graph-specific identifiers to enhance denoising performance while preserving semantic consistency. (2) Intent attention fusion: we extract path semantic representations based on graph convolutional networks, design an attention mechanism to dynamically aggregate intent features, and use the embedding of the user-item graph as a structural guide to capture the multi-dimensional preferences of users and items. (3) Multi-view contrastive optimization: we perform intent-aware contrastive learning in the meta-path semantic space and structure-enhanced contrastive learning in the user-item interaction space, jointly optimized with the main recommendation objective to improve robustness and generalization. Extensive experiments on six benchmark recommendation datasets demonstrate that DDMCL outperforms state-of-the-art baselines, improving the NDCG@20 on the Amazon and Yelp datasets by 3.27% and 3.70%, respectively.
Federated Domain Generalization (FDG) aims to train models on multiple heterogeneous source domains that generalize to unseen domains without access to target data. Existing methods mainly rely on learning domain-invariant representations while overlooking the transferability of prototypes from source domains to target domains. To address this limitation, we propose FedPRC, a prototype region calibration framework that models cross-domain transformations instead of enforcing strict invariance. FedPRC first uses a fixed prototype classifier to establish a globally shared geometric structure, which maintains consistent class-level representations across clients. Then, we introduce a pseudo-target domain generation module, which constructs virtual features to represent unseen domains and capture cross-domain variability, enabling semantic calibration. Finally, we design a prototype region calibration (PRC) module, which promotes a uniform distribution of intra-class features while preserving semantic consistency and reduces decision ambiguity on unseen domains, achieving distribution calibration. Extensive experiments on four benchmark datasets (PACS, OfficeCaltech10, Office31, and OfficeHome) involving heterogeneous multi-client settings demonstrate that FedPRC consistently outperformed nine state-of-the-art methods, achieving up to 4.56% improvement in FDG accuracy and 5.02% gain under domain-shift evaluation, while incurring only marginal computational overhead. These results validate the effectiveness and practical scalability of the proposed approach. https://github.com/qqh0618/FedPRC
In many real-world systems, interactions among nodes are not limited to pairwise connections but often emerge as group coordination, shared resources, or collaborative tasks, which are referred to as higher-order interactions. In such systems, the failure of a single node can simultaneously affect all other nodes within the higher-order interaction unit it participates in, potentially triggering large-scale cascading failures. Notably, some nodes, despite having a high degree and structurally central, may participate in only a single higher-order interaction. We define such nodes, whose hyperdegree equals one, as hyperleaf nodes, which form localized structural vulnerabilities. By iteratively removing hyperleaf nodes from the hypergraph and assuming that the hyperedges they participate in fail accordingly, the hyperdegrees of neighboring nodes are reduced, potentially turning them into new hyperleaf nodes and further triggering cascading failures. We propose a mathematical framework to analyze the cascading failure process and the impact of key parameters on system robustness. Furthermore, we investigate the critical threshold for the formation of the hypercore in hypergraphs and derive its number of nodes and hyperedges, where the hypercore is defined as the giant connected component obtained by iteratively removing all hyperleaf nodes. We found that the cardinality distribution of hyperedges significantly influenced the formation of the hypercore: the higher the heterogeneity, the lower the critical threshold required for its emergence. These findings provide theoretical guidance for fault-tolerant design in higher-order systems and practical value for critical infrastructure networks: protecting hyperleaf nodes can prevent large-scale collapse and enhance the robustness of such networks.
The separation of multicomponent signals with crossing instantaneous frequency (IF) curves remains a fundamental challenge in time-frequency analysis. Although the synchrosqueezed wavelet-chirplet transform (SWCT) enhances time-frequency readability by introducing a chirprate variable, its effectiveness is constrained by the underlying assumption of local linear chirp. Consequently, this method does not perform well when analyzing signals characterized by strong frequency modulation. This paper extends the SWCT framework by relaxing the linear chirp assumption. We model signal components as having polynomial phase behavior over short intervals and derive compact expressions for high-order IF and chirprate reassignment operators. The proposed high-order synchrosqueezed wavelet-chirplet transform (HSWCT) enables accurate estimation of both IF and chirprate, and supports robust mode retrieval even with intersecting IF curves. Another key contribution is a rigorous mathematical analysis of the approximation errors of arbitrary-order reassignment operators for IF and chirprate estimation. When the chirprate vanishes, HSWCT simplifies to the traditional high-order synchrosqueezed wavelet transform. To the best of our knowledge, no theoretical analysis exists in the literature on the approximation of arbitrary-order SST IF reassignment operators to the IF. As a by-product of this work, our established theorem provides such an analysis, thereby filling a gap in the theoretical framework of high-order SSTs.
Cancer subtype classification plays a crucial role in precision medicine and individualized therapy. With the continuous advancement of multi-omics profiling technologies, multi-view clustering has emerged as an effective framework for cancer subtype identification. However, practical multi-omics data are frequently challenged by missing views, noise in high-dimensional settings, and complex redundancy across views. In the context of these problems, we propose a tensorized incomplete multi-view subspace clustering framework for cancer subtyping. Specifically, the Hilbert–Schmidt Independence Criterion (HSIC) captures potential nonlinear statistical dependence among representation matrices from different views in a reproducing kernel Hilbert space, thereby strengthening cross-view consistency and complementary information exchange. In addition, the latent shared high-order low-rank structure in multi-view observations can be effectively characterized by an exponential nonconvex tensor nuclear norm. Meanwhile, an ℓ2,log-based group-sparse regularization term is employed to flexibly and robustly model structured outliers and noise. The resulting optimization problem is solved by an ADMM-based procedure equipped with iterative reweighting. Results obtained from several cancer multi-omics cohorts indicate that the proposed method achieves strong effectiveness and robustness in incomplete multi-view cancer subtyping.
