CDW-CoT: Clustered Distance-Weighted Chain-of-Thoughts Reasoning

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).

OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems

In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. 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 Contrastive Multi-View Clustering with High-Confidence Guiding

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.

Disentangling Multi-view Representations Beyond Inductive Bias

Multi-view (or -modality) representation learning aims to understand the relationships between different view representations. Existing methods disentangle multi-view representations into consistent and view-specific representations by introducing strong inductive biases, which can limit their generalization ability. In this paper, we propose a novel multi-view representation disentangling method that aims to go beyond inductive biases, ensuring both interpretability and generalizability of the resulting representations. Our method is based on the observation that discovering multi-view consistency in advance can determine the disentangling information boundary, leading to a decoupled learning objective. We also found that the consistency can be easily extracted by maximizing the transformation invariance and clustering consistency between views. These observations drive us to propose a two-stage framework. In the first stage, we obtain multi-view consistency by training a consistent encoder to produce semantically-consistent representations across views as well as their corresponding pseudo-labels. In the second stage, we disentangle specificity from comprehensive representations by minimizing the upper bound of mutual information between consistent and comprehensive representations. Finally, we reconstruct the original data by concatenating pseudo-labels and view-specific representations. Our experiments on four multi-view datasets demonstrate that our proposed method outperforms 12 comparison methods in terms of clustering and classification performance. The visualization results also show that the extracted consistency and specificity are compact and interpretable. Our code can be found at \url{https://github.com/Guanzhou-Ke/DMRIB}.

A Clustering-guided Contrastive Fusion for Multi-view Representation Learning

The past two decades have seen increasingly rapid advances in the field of multi-view representation learning due to it extracting useful information from diverse domains to facilitate the development of multi-view applications. However, the community faces two challenges: i) how to learn robust representations from a large amount of unlabeled data to against noise or incomplete views setting, and ii) how to balance view consistency and complementary for various downstream tasks. To this end, we utilize a deep fusion network to fuse view-specific representations into the view-common representation, extracting high-level semantics for obtaining robust representation. In addition, we employ a clustering task to guide the fusion network to prevent it from leading to trivial solutions. For balancing consistency and complementary, then, we design an asymmetrical contrastive strategy that aligns the view-common representation and each view-specific representation. These modules are incorporated into a unified method known as CLustering-guided cOntrastiVE fusioN (CLOVEN). We quantitatively and qualitatively evaluate the proposed method on five datasets, demonstrating that CLOVEN outperforms 11 competitive multi-view learning methods in clustering and classification. In the incomplete view scenario, our proposed method resists noise interference better than those of our competitors. Furthermore, the visualization analysis shows that CLOVEN can preserve the intrinsic structure of view-specific representation while also improving the compactness of view-commom representation. Our source code will be available soon at https://github.com/guanzhou-ke/cloven.

Supervised Nonnegative Matrix Factorization to Predict ICU Mortality Risk

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.

A Survey on Multi-View Clustering

With advances in information acquisition technologies, multi-view data become ubiquitous. Multi-view learning has thus become more and more popular in machine learning and data mining fields. Multi-view unsupervised or semi-supervised learning, such as co-training, co-regularization has gained considerable attention. Although recently, multi-view clustering (MVC) methods have been developed rapidly, there has not been a survey to summarize and analyze the current progress. Therefore, this paper reviews the common strategies for combining multiple views of data and based on this summary we propose a novel taxonomy of the MVC approaches. We further discuss the relationships between MVC and multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated. To promote future development of MVC, we envision several open problems that may require further investigation and thorough examination.