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.

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.

Abstract A strict graph-matching mechanism brings normativeness to graph grammar but leads to graph grammar insufficiency when processing fuzzy grammatical structures. To address this issue, the current paper proposes an improved formal framework for graph grammar that enables it to effectively specify the ambiguity of graph models while maintaining normativeness and intuition. First, the improved framework defines the connection probability for edges and classifies the edges based on the connection probability, which is used as the quantitative and qualitative description of the graph grammar structure’s ambiguity. Second, the concepts of credibility threshold, credible subgraphs and candidate subgraphs are defined, and the constraints on the redex are adjusted to increase the fault tolerance of the graph-matching process. Finally, the grammatical operation is redesigned, with a matching weight defined for each redex based on the connection probability and the credibility threshold, thereby providing a theoretical basis and practical guidance for the selection of multiple redexes.

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.