Previous successful approaches to missing modality completion rely on carefully designed fusion techniques and extensive pre-training on complete data, which can limit their generalizability in out-of-domain (OOD) scenarios. In this study, we pose a new challenge: can we develop a missing modality completion model that is both resource-efficient and robust to OOD generalization? To address this, we present a training-free framework for missing modality completion that leverages large multimodal models (LMMs). Our approach, termed the "Knowledge Bridger", is modality-agnostic and integrates generation and ranking of missing modalities. By defining domain-specific priors, our method automatically extracts structured information from available modalities to construct knowledge graphs. These extracted graphs connect the missing modality generation and ranking modules through the LMM, resulting in high-quality imputations of missing modalities. Experimental results across both general and medical domains show that our approach consistently outperforms competing methods, including in OOD generalization. Additionally, our knowledge-driven generation and ranking techniques demonstrate superiority over variants that directly employ LMMs for generation and ranking, offering insights that may be valuable for applications in other domains.

Incomplete multi-view clustering has become one of the important research problems due to the extensive missing multi-view data in the real world. Although the existing methods have made great progress, there are still some problems: 1) most methods cannot effectively mine the information hidden in the missing data; 2) most methods typically divide representation learning and clustering into two separate stages, but this may affect the clustering performance as the clustering results directly depend on the learned representation. To address these problems, we propose a novel incomplete multi-view clustering method with hierarchical information transfer. Firstly, we design the view-specific Graph Convolutional Networks (GCN) to obtain the representation encoding the graph structure, which is then fused into the consensus representation. Secondly, considering that one layer of GCN transfers one-order neighbor node information, the global graph propagation with the consensus representation is proposed to handle the missing data and learn deep representation. Finally, we design a weight-sharing pseudo-classifier with contrastive learning to obtain an end-to-end framework that combines view-specific representation learning, global graph propagation with hierarchical information transfer, and contrastive clustering for joint optimization. Extensive experiments conducted on several commonly-used datasets demonstrate the effectiveness and superiority of our method in comparison with other state-of-the-art approaches. The code is available at https://github.com/KelvinXuu/GHICMC.

Large Language Models (LLMs) have recently achieved impressive results in complex reasoning tasks through Chain of Thought (CoT) prompting. However, most existing CoT methods rely on using the same prompts, whether manually designed or automatically generated, to handle the entire dataset. This one-size-fits-all approach may fail to meet the specific needs arising from the diversities within a single dataset. To solve this problem, we propose the Clustered Distance-Weighted Chain of Thought (CDW-CoT) method, which dynamically constructs prompts tailored to the characteristics of each data instance by integrating clustering and prompt optimization techniques. Our method employs clustering algorithms to categorize the dataset into distinct groups, from which a candidate pool of prompts is selected to reflect the inherent diversity within the dataset. For each cluster, CDW-CoT trains the optimal prompt probability distribution tailored to their specific characteristics. Finally, it dynamically constructs a unique prompt probability distribution for each test instance, based on its proximity to cluster centers, from which prompts are selected for reasoning. CDW-CoT consistently outperforms traditional CoT methods across six datasets, including commonsense, symbolic, and mathematical reasoning tasks. Specifically, when compared to manual CoT, CDW-CoT achieves an average accuracy improvement of 25.34% on LLaMA2 (13B) and 15.72% on LLaMA3 (8B).

This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral imaging reconstruction, and multispectral image denoising. Existing tensor singular value decomposition (t-SVD) definitions rely on hand-designed or pre-given transforms, which lack flexibility for defining tensor nuclear norm (TNN). The TNN-regularized optimization problem is solved by the singular value thresholding (SVT) operator, which leverages the t-SVD framework to obtain the low-rank tensor. However, it is quite complicated to introduce SVT into deep neural networks due to the numerical instability problem in solving the derivatives of the eigenvectors. In this paper, we introduce a novel data-driven generative low-rank t-SVD model based on the learnable orthogonal transform, which can be naturally solved under its representation. Prompted by the linear algebra theorem of the Householder transformation, our learnable orthogonal transform is achieved by constructing an endogenously orthogonal matrix adaptable to neural networks, optimizing it as arbitrary orthogonal matrices. Additionally, we propose a low-rank solver as a generalization of SVT, which utilizes an efficient representation of generative networks to obtain low-rank structures. Extensive experiments highlight its significant restoration enhancements.

Incomplete multi-view clustering becomes an important research problem, since multi-view data with missing values are ubiquitous in real-world applications. Although great efforts have been made for incomplete multi-view clustering, there are still some challenges: 1) most existing methods didn't make full use of multi-view information to deal with missing values; 2) most methods just employ the consistent information within multi-view data but ignore the complementary information; 3) For the existing incomplete multi-view clustering methods, incomplete multi-view representation learning and clustering are treated as independent processes, which leads to performance gap. In this work, we proposed a novel Incomplete Contrastive Multi-View Clustering method with high-confidence guiding (ICMVC). Firstly, we proposed a multi-view consistency relation transfer plus graph convolutional network to tackle missing values problem. Secondly, instance-level attention fusion and high-confidence guiding are proposed to exploit the complementary information while instance-level contrastive learning for latent representation is designed to employ the consistent information. Thirdly, an end-to-end framework is proposed to integrate multi-view missing values handling, multi-view representation learning and clustering assignment for joint optimization. Experiments compared with state-of-the-art approaches demonstrated the effectiveness and superiority of our method. Our code is publicly available at https://github.com/liunian-Jay/ICMVC.

ICU mortality risk prediction is a tough yet important task. On one hand, due to the complex temporal data collected, it is difficult to identify the effective features and interpret them easily; on the other hand, good prediction can help clinicians take timely actions to prevent the mortality. These correspond to the interpretability and accuracy problems. Most existing methods lack of the interpretability, but recently Subgraph Augmented Nonnegative Matrix Factorization (SANMF) has been successfully applied to time series data to provide a path to interpret the features well. Therefore, we adopted this approach as the backbone to analyze the patient data. One limitation of the raw SANMF method is its poor prediction ability due to its unsupervised nature. To deal with this problem, we proposed a supervised SANMF algorithm by integrating the logistic regression loss function into the NMF framework and solved it with an alternating optimization procedure. We used the simulation data to verify the effectiveness of this method, and then we applied it to ICU mortality risk prediction and demonstrated its superiority over other conventional supervised NMF methods.

With the fast development of information technology, especially the popularization of internet, multi-view learning becomes more and more popular in machine learning and data mining fields. As we all know that, multi-view semi-supervised learning, such as co-training, co-regularization has gained considerable attentions. Although recently, multi-view clustering (MVC) has developed rapidly, there are not a survey or review to summarize and analyze the current progress. Therefore, this paper sums up the common strategies of combining multiple views and based on that we proposed a novel taxonomy of the MVC approaches. We also discussed the relationships between MVC and multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and multi-view semi-supervised learning. Several representative real-world applications are elaborated. To promote the further development of MVC, we pointed out several open problems that are worth exploring in the future.

Maximum entropy discrimination (MED) is a general framework for discriminative estimation based on the well known maximum entropy principle, which embodies the Bayesian integration of prior information with large margin constraints on observations. It is a successful combination of maximum entropy learning and maximum margin learning, and can subsume support vector machines (SVMs) as a special case. In this paper, we present a multi-view maximum entropy discrimination framework that is an extension of MED to the scenario of learning with multiple feature sets. Different from existing approaches to exploiting multiple views, such as co-training style algorithms and co-regularization style algorithms, we propose a new method to make use of the distinct views where classification margins from these views are required to be identical. We give the general form of the solution to the multi-view maximum entropy discrimination, and provide an instantiation under a specific prior formulation which is analogical to a multi-view version of SVMs. Experimental results on real-world data sets show the effectiveness of the proposed multi-view maximum entropy discrimination approach.