Cancer molecular heterogeneity impedes precise subtyping and personalized therapy. Current multi-omics integration methods often overlook clinical relevance and kernel redundancy, yielding subtypes with limited prognostic utility. Here, we introduce Survival-Informed Multi-omics Kernel Fusion (SIMKF), a framework that synergizes survival-guided kernel selection with distribution-aware fusion to uncover clinically distinct subtypes. SIMKF addresses the limitations of current multi-omics integration methods by combining survival-guided kernel selection, adaptive weighting based on maximum mean discrepancy, and spectral clustering to integrate survival information with multi-omics data. This approach significantly outperforms existing techniques across five TCGA cancer datasets. Notably, in breast cancer, it successfully identifies five distinct subtypes with pronounced survival differences, revealing a nonlinear relationship between methylation levels (hypermethylation correlating with better prognosis, hypomethylation with poorer outcomes) and survival outcomes, while aligning closely with established clinical subtypes. As an automated, tuning-free tool for precision oncology, SIMKF not only uncovers prognostic biological mechanisms but also translates directly into clinically applicable subtyping models.

Microarray data classification is challenged by high dimensionality and small sample sizes, causing feature selection instability. Traditional ensemble feature selection methods struggle to balance diversity and quality effectively. We propose a novel Ensemble Feature Selection Method (EFSM) that introduces a feature mapping diversity metric to generate a robust candidate pool. EFSM first generates a diverse candidate pool of feature selectors by leveraging randomized neural networks to create multiple non-linear feature mappings (views) of the original data. Its core innovation is an ensemble pruning technique formulated as an optimization problem that jointly maximizes both the predictive accuracy of individual selectors and their pairwise diversity. We simplify this NP-hard problem by converting it into a Semi-Definite Programming (SDP) problem and deriving a novel bound for efficient solution. Finally, the rankings from the pruned ensemble are aggregated using the Borda count method. Extensive experiments on 15 biological datasets demonstrate that EFSM outperforms nine state-of-the-art feature selection methods across popular classifiers, achieving superior and stable performance for high-dimensional data analysis.

Multi-view classification aims to improve prediction performance by integrating heterogeneous data sources, leveraging the complementary and consistent information across different views. However, existing approaches predominantly focus on consistency and complementarity, often overlooking the role of diversity, which is crucial for enhancing generalization and mitigating redundancy. To address these issues, we propose a Tri-perspective Multi-view Fusion and Classification (TMFC) framework that systematically unifies consistency, complementarity, and diversity principles. TMFC consolidates multi-view data into a meta-view through feature concatenation and generates diverse latent views via random mapping, preserving structural information while reducing redundancy. These latent views are optimized through a unified formulation that balances alignment, information enrichment, and feature distinctiveness, reformulated as a semidefinite programming problem and efficiently solved using the reformulation-linearization technique with a cutting-plane algorithm. Extensive experiments on real-world datasets demonstrate TMFC’s superiority over state-of-the-art methods, achieving significant improvements in accuracy, normalized mutual information, and adjusted rand index.

Multi-view multi-label data often suffers from incomplete feature views and label noise. This paper is the first to address both challenges simultaneously, rectifying critical deficiencies in existing methodologies that inadequately extract and fuse high-order structural correlations across views while lacking robust solutions to mitigate label noise. We introduce a dynamic multiple high-order correlations fusion with noise filtering, specifically designed for incomplete multi-view noisy-label learning. By capitalizing on a dynamic multi-hypergraph neural network, inspired by the principles of ensemble learning, we adeptly capture and integrate high-order correlations among samples from different views. The model's capability is further augmented through an innovative hypergraph fusion technique based on random walk theory, which empowers it to seamlessly amalgamate both structural and feature information. Moreover, we propose sophisticated noise-filtering matrices that are tightly embedded within the hypergraph neural network, devised to counteract the detrimental impact of label noise. Recognizing that label noise perturbs the data distribution in the label space, these filtering matrices exploit the distributional disparities between feature and label spaces. The high-order structural information derived from both domains underpins the learning and efficacy of the noise-filtering matrices. Empirical evaluations on benchmark datasets unequivocally demonstrate that our method significantly outperforms contemporary state-of-the-art techniques.

Incomplete multi-view multi-label learning faces significant challenges arising from semantic heterogeneity across modalities and incomplete modality availability. Traditional fusion approaches typically emphasize superficial feature alignment, neglecting high-order semantic interactions among modalities and labels, thus resulting in redundant or conflicting information integration. To address these limitations, we propose a novel Label Semantic Guided Adaptive Fusion framework. Specifically, we leverage pretrained language models to generate semantic embeddings for both multi-view data and associated labels, facilitating unified semantic understanding. Subsequently, we construct dual-domain hypergraphs separately within the modality and label semantic spaces to explicitly model complex high-order semantic correlations. Based on these hypergraphs, we employ hypergraph neural networks to mine intrinsic semantic relationships and dynamically assess semantic consistency between each modality and the label space. Finally, an adaptive weighting strategy guided by this semantic consistency measure is introduced to fuse modalities effectively, assigning high weights to modalities with greater semantic alignment. Extensive experiments demonstrate that our LSGMM improves fusion accuracy and robustness over state-of-the-art IMvML methods, confirming the effectiveness of integrating label semantics and high-order semantic relationships into adaptive multi-view fusion.

Incomplete multi-view data, where certain views are entirely missing for some samples, poses significant challenges for traditional multi-view clustering methods. Existing deep incomplete multi-view clustering approaches often rely on static fusion strategies or two-stage pipelines, leading to suboptimal fusion results and error propagation issues. To address these limitations, this paper proposes a novel incomplete multi-view clustering framework based on Hierarchical Semantic Alignment and Cooperative Completion (HSACC). HSACC achieves robust cross-view fusion through a dual-level semantic space design. In the low-level semantic space, consistency alignment is ensured by maximizing mutual information across views. In the high-level semantic space, adaptive view weights are dynamically assigned based on the distributional affinity between individual views and an initial fused representation, followed by weighted fusion to generate a unified global representation. Additionally, HSACC implicitly recovers missing views by projecting aligned latent representations into high-dimensional semantic spaces and jointly optimizes reconstruction and clustering objectives, enabling cooperative learning of completion and clustering. Experimental results demonstrate that HSACC significantly outperforms state-of-the-art methods on five benchmark datasets. Ablation studies validate the effectiveness of the hierarchical alignment and dynamic weighting mechanisms, while parameter analysis confirms the model's robustness to hyperparameter variations. The code is available at \url{https://github.com/XiaojianDing/2025-NeurIPS-HSACC}.

Multi kernel learning (MKL) is a representative supervised multi-view learning method widely applied in multi-modal and multi-view applications. MKL aims to classify data by integrating complementary information from predefined kernels. Although existing MKL methods achieve promising performance, they fail to consider the tradeoff between diversity and classification accuracy of kernels, preventing further improvement of classification performance. In this paper, we tackle this problem by generating a number of high-quality base learning kernels and selecting a kernel subset with maximum pairwise diversity and minimum generalization errors. We first formulate this idea as a nonconvex quadratic integer programming problem. Then we transform this nonconvex problem into a convex optimization problem and prove it is equivalent to a semidefinite relaxation problem, which a semidefinite-based branch-and-bound algorithm can quickly solve. Experimental results on the real-world datasets demonstrate the superiority of the proposed method. The results also show that our method works for the support vector machine (SVM) classifier and other state-of-the-art kernel classifiers.

Insufficient labeled training samples pose a critical challenge in multi-label classification, potentially leading to overfitting of the model. This paper delineates a criterion for establishing a common domain among different datasets, whereby datasets sharing analogous object descriptions and label structures are considered part of the 'same field'. Integrating samples from disparate datasets within this shared field for training purposes effectively mitigates overfitting and enhances model accuracy. Motivated by this approach, we introduce a novel method for multi-label classification termed Non-Overlapped Multi-View Weak-Label Learning Guided by Multiple Correlations (NOMWM). Our method strategically amalgamates samples from diverse datasets within the shared field to enrich the training dataset. Furthermore, we project samples from various datasets onto a unified subspace to facilitate learning in a consistent latent space. Additionally, we address the challenge of weak labels stemming from incomplete label overlaps across datasets. Leveraging weak-label indicator matrices and label correlation mining techniques, we effectively mitigate the impact of weak labels. Extensive experimentation on multiple benchmark datasets validates the efficacy of our method, demonstrating clear improvements over existing state-of-the-art approaches.

In cross-modal retrieval, the hashing technique has sparked a great revolution because of its competitive query speed and minimal storage. However, existing approaches may have critical limitations: 1) Label Intrinsic Relations. They barely explore category information inherent in labels and only consider labels as distinct entities, losing rich latent semantic information. 2) Modality-specific and Modality-coherence Semantics. They often construct a common subspace and an affinity matrix to learn modality-specific features and modality-coherence correlations, respectively. The former will lead to considerable quantization errors because the subspaces should be approximate rather than exactly equal. The latter is not scalable due to its high computational costs. 3) Non-relaxation Optimization Strategy. To solve constraints, some approaches relax the binary constraints to continuous, rising significant quantization errors. To mitigate these problems, we propose Disperse Asymmetric Subspace Relation Hashing, termed DASRH. In particular, it first embeds modality-specific kernel features into dispersed latent spaces, which can effectively fuse heterogeneous patterns. Additionally, it exploits fine-grained categories from labels by reconstructing collective semantic representations, making discriminative binary codes. Furthermore, it constructs an asymmetric consistent relation integration, preserving both inter-modal disparities and intra-class differences. In the optimization process, an effective alternative iterative optimization scheme is established. Theoretical analysis and comprehensive experiments highlight the advantages of our DASRH against cutting-edge technology.

In feature selection research, simultaneous multi-class feature selection technologies are popular because they simultaneously select informative features for all classes. Recursive feature elimination (RFE) methods are state-of-the-art binary feature selection algorithms. However, extending existing RFE algorithms to multi-class tasks may increase the computational cost and lead to performance degradation. With this motivation, we introduce a unified multi-class feature selection (UFS) framework for randomization-based neural networks to address these challenges. First, we propose a new multi-class feature ranking criterion using the output weights of neural networks. The heuristic underlying this criterion is that "the importance of a feature should be related to the magnitude of the output weights of a neural network". Subsequently, the UFS framework utilizes the original features to construct a training model based on a randomization-based neural network, ranks these features by the criterion of the norm of the output weights, and recursively removes a feature with the lowest ranking score. Extensive experiments on 15 real-world datasets suggest that our proposed framework outperforms state-of-the-art algorithms. The code of UFS is available at https://github.com/SVMrelated/UFS.git.

Cross-modal hashing utilize the advantages of hash codes to enable flexible retrieval across different modalities, greatly improving the retrieval efficiency of heterogeneous modes. However, most existing approach do not fully take modal intrinsic semantic properties and semantic category structure into consideration during learning the latent subspace. In addition, previous theory works commonly focus on binary pairwise similarity, without investigating the rich semantic contained in the label matrix. To alleviate these problems, in this study, we present a novel cross-media retrieval approach, termed SEmantic preserving Asymmetric discrete Hashing (SEAH), which constructs an asymmetric scheme to learn the binary codes from the common representation to maintain the similarity. Specially, we incorporate label matrix and hash codes into a mutual mapping framework, the learned hash codes are more discriminative. Moreover, we introduce the Augmented Lagrange Multiplier (ALM) algorithm for optimization, which make it easier to solve the objective functions. Comprehensive systematically experiments on two benchmark datasets demonstrate that our approach achieves promising performance gain and outperforms the several state-of-the-art works.

This paper presents a recursive feature elimination (RFE) mechanism to select the most informative genes with a least square kernel extreme learning machine (LSKELM) classifier. Describing the generalization ability of LSKELM in a way that is related to small norm of weights, we propose a ranking criterion to evaluate the importance of genes by the norm of weights obtained by LSKELM. The proposed method is called LSKELM-RFE which first employs the original genes to build a LSKELM classifier, and then ranks the genes according to their importance given by the norm of output weights of LSKELM and finally removes a "least important" gene. Benefiting from the random mapping mechanism of the extreme learning machine (ELM) kernel, there are no parameter of LSKELM-RFE needs to be manually tuned. A comparative study among our proposed algorithm and other two famous RFE algorithms has shown that LSKELM-RFE outperforms other RFE algorithms in both the computational cost and generalization ability.

Due to the simplicity of their implementations, least square support vector machine (LS-SVM) and proximal support vector machine (PSVM) have been widely used in binary classification applications. The conventional LS-SVM and PSVM cannot be used in regression and multiclass classification applications directly, although variants of LS-SVM and PSVM have been proposed to handle such cases. This paper shows that both LS-SVM and PSVM can be simplified further and a unified learning framework of LS-SVM, PSVM, and other regularization algorithms referred to extreme learning machine (ELM) can be built. ELM works for the "generalized" single-hidden-layer feedforward networks (SLFNs), but the hidden layer (or called feature mapping) in ELM need not be tuned. Such SLFNs include but are not limited to SVM, polynomial network, and the conventional feedforward neural networks. This paper shows the following: 1) ELM provides a unified learning platform with a widespread type of feature mappings and can be applied in regression and multiclass classification applications directly; 2) from the optimization method point of view, ELM has milder optimization constraints compared to LS-SVM and PSVM; 3) in theory, compared to ELM, LS-SVM and PSVM achieve suboptimal solutions and require higher computational complexity; and 4) in theory, ELM can approximate any target continuous function and classify any disjoint regions. As verified by the simulation results, ELM tends to have better scalability and achieve similar (for regression and binary class cases) or much better (for multiclass cases) generalization performance at much faster learning speed (up to thousands times) than traditional SVM and LS-SVM.