k-HyperEdge Medoids for Clustering Ensemble

Clustering ensemble has been a popular research topic in data science due to its ability to improve the robustness of the single clustering method. Many clustering ensemble methods have been proposed, most of which can be categorized into clustering-view and sample-view methods. The clustering-view method is generally efficient, but it could be affected by the unreliability that existed in base clustering results. The sample-view method shows good performance, while the construction of the pairwise sample relation is time-consuming. In this paper, the clustering ensemble is formulated as a k-HyperEdge Medoids discovery problem and a clustering ensemble method based on k-HyperEdge Medoids that considers the characteristics of the above two types of clustering ensemble methods is proposed. In the method, a set of hyperedges is selected from the clustering view efficiently, then the hyperedges are diffused and adjusted from the sample view guided by a hyperedge loss function to construct an effective k-HyperEdge Medoid set. The loss function is mainly reduced by assigning samples to the hyperedge with the highest degree of belonging. Theoretical analyses show that the solution can approximate the optimal, the assignment method can gradually reduce the loss function, and the estimation of the belonging degree is statistically reasonable. Experiments on artificial data show the working mechanism of the proposed method. The convergence of the method is verified by experimental analysis of twenty data sets. The effectiveness and efficiency of the proposed method are also verified on these data, with nine representative clustering ensemble algorithms as reference.

Clustering ensemble algorithm with high-order consistency learning

Most of the research on clustering ensemble focuses on designing practical consistency learning algorithms.To solve the problems that the quality of base clusters varies and the low-quality base clusters have an impact on the performance of the clustering ensemble, from the perspective of data mining, the intrinsic connections of data were mined based on the base clusters, and a high-order information fusion algorithm was proposed to represent the connections between data from different dimensions, namely Clustering Ensemble with High-order Consensus learning (HCLCE). Firstly, each high-order information was fused into a new structured consistency matrix. Then, the obtained multiple consistency matrices were fused together. Finally, multiple information was fused into a consistent result. Experimental results show that LCLCE algorithm has the clustering accuracy improved by an average of 7.22%, and the Normalized Mutual Information (NMI) improved by an average of 9.19% compared with the suboptimal Locally Weighted Evidence Accumulation (LWEA) algorithm. It can be seen that the proposed algorithm can obtain better clustering results compared with clustering ensemble algorithms and using one information alone.

Hierarchical Multiple Kernel K-Means Algorithm Based on Sparse Connectivity

Multiple kernel learning (MKL) aims to find an optimal, consistent kernel function. In the hierarchical multiple kernel clustering (HMKC) algorithm, sample features are extracted layer by layer from a high-dimensional space to maximize the retention of effective information. However, information interaction between layers is often ignored. In this model, only corresponding nodes in adjacent layers exchange information; other nodes remain isolated, and if full connectivity is adopted, the diversity of the final consistency matrix is reduced. Therefore, this paper proposes a hierarchical multiple kernel K-Means (SCHMKKM) algorithm based on sparse connectivity, which controls the assignment matrix to achieve sparse connections through a sparsity rate, thereby locally fusing the features obtained by distilling information between layers. Finally, we conduct cluster analysis on multiple datasets and compare it with the fully connected hierarchical multiple kernel K-Means (FCHMKKM) algorithm in experiments. It is shown that more discriminative information fusion is beneficial for learning a better consistent partition matrix, and the fusion strategy based on sparse connection outperforms the full connection strategy.

Multiple kernel concept factorization algorithm based on global fusion

Non-negative Matrix Factorization(NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization(CF) algorithm extends matrix factorization to single non-linear kernel space, improving learning ability and adaptability of matrix factorization. In unsupervised environment, to design or select proper kernel function for specific dataset, a new algorithm called Globalized Multiple Kernel CF(GMKCF)was proposed. Multiple candidate kernel functions were input in the same time and learned in the CF framework based on global linear fusion, obtaining a clustering result with high quality and stability and solving the problem of kernel function selection that the CF faced. The convergence of the proposed algorithm was verified by solving the model with alternate iteration. The experimental results on several real databases show that the proposed algorithm outperforms comparison algorithms in data clustering, such as Kernel K-Means(KKM), Spectral Clustering(SC), Kernel CF(KCF), Co-regularized multi-view spectral clustering(Coreg), and Robust Multiple KKM(RMKKM).

Multiple Kernel Clustering via Local Regression Integration

Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple candidate kernels. This paper first presents the clustering method via kernelized local regression (CKLR). It captures the local structure of kernel data and employs kernel regression on the local region to predict the clustering results. Moreover, this paper further extends it to perform clustering via the multiple kernel local regression (CMKLR). We construct the kernel level local regression sparse coefficient matrix for each candidate kernel, which well characterizes the kernel level manifold structure. We then aggregate all the kernel level local regression coefficients via linear weights and generate the consensus sparse local regression coefficient, which largely reduces the number of candidate variables and becomes more robust against noises and outliers within multiple kernel data. Thus, the proposed method CMKLR avoids the above two limitations. It only contains one additional hyperparameter for tuning. Extensive experimental results show that the clustering performance of the proposed method on benchmark datasets is better than that of 10 state-of-the-art multiple kernel clustering methods.

Unsupervised feature selection algorithm framework based on neighborhood interval disturbance fusion

Feature selection technology is a key technology of data dimensionality reduction. Becauseof the lack of label information of collected data samples, unsupervised feature selection has attracted more attention. The universality and stability of many unsupervised feature selection algorithms are very low and greatly affected by the dataset structure. For this reason, many researchers have been keen to improve the stability of the algorithm. This paper attempts to preprocess the data set and use an interval method to approximate the data set, experimentally verifying the advantages and disadvantages of the new interval data set. This paper deals with these data sets from the global perspective and proposes a new algorithm-unsupervised feature selection algorithm based on neighborhood interval disturbance fusion(NIDF). This method can realize the joint learning of the final score of the feature and the approximate data interval. By comparing with the original unsupervised feature selection methods and several existing feature selection frameworks, the superiority of the proposed model is verified.

Symmetry Nonnegative Matrix Factorization Algorithm Based on Self-paced Learning

A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an error-driven way. A weight variable that could measure the degree of difficulty to all samples was assigned in this method, and the variable was constrained by adopting both hard-weighting and soft-weighting strategies to ensure the rationality of the model. Cluster analysis was carried out on multiple data sets such as images and texts, and the experimental results showed the effectiveness of the proposed algorithm.

SLIM: Let LLM Learn More and Forget Less with Soft LoRA and Identity Mixture

Although many efforts have been made, it is still a challenge to balance the training budget, downstream performance, and the general capabilities of the LLMs in many applications. Training the whole model for downstream tasks is expensive, and could easily result in catastrophic forgetting. By introducing parameter-efficient fine-tuning (PEFT), the training cost could be reduced, but it still suffers from forgetting, and limits the learning on the downstream tasks. To efficiently fine-tune the LLMs with less limitation to their downstream performance while mitigating the forgetting of general capabilities, we propose a novel mixture of expert (MoE) framework based on Soft LoRA and Identity Mixture (SLIM), that allows dynamic routing between LoRA adapters and skipping connection, enables the suppression of forgetting. We adopt weight-yielding with sliding clustering for better out-of-domain distinguish to enhance the routing. We also propose to convert the mixture of low-rank adapters to the model merging formulation and introduce fast dynamic merging of LoRA adapters to keep the general capabilities of the base model. Extensive experiments demonstrate that the proposed SLIM is comparable to the state-of-the-art PEFT approaches on the downstream tasks while achieving the leading performance in mitigating catastrophic forgetting.

Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphs

Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.

Stable Heterogeneous Treatment Effect Estimation across Out-of-Distribution Populations

Heterogeneous treatment effect (HTE) estimation is vital for understanding the change of treatment effect across individuals or subgroups. Most existing HTE estimation methods focus on addressing selection bias induced by imbalanced distributions of confounders between treated and control units, but ignore distribution shifts across populations. Thereby, their applicability has been limited to the in-distribution (ID) population, which shares a similar distribution with the training dataset. In real-world applications, where population distributions are subject to continuous changes, there is an urgent need for stable HTE estimation across out-of-distribution (OOD) populations, which, however, remains an open problem. As pioneers in resolving this problem, we propose a novel Stable Balanced Representation Learning with Hierarchical-Attention Paradigm (SBRL-HAP) framework, which consists of 1) Balancing Regularizer for eliminating selection bias, 2) Independence Regularizer for addressing the distribution shift issue, 3) Hierarchical-Attention Paradigm for coordination between balance and independence. In this way, SBRL-HAP regresses counterfactual outcomes using ID data, while ensuring the resulting HTE estimation can be successfully generalized to out-of-distribution scenarios, thereby enhancing the model's applicability in real-world settings. Extensive experiments conducted on synthetic and real-world datasets demonstrate the effectiveness of our SBRL-HAP in achieving stable HTE estimation across OOD populations, with an average 10% reduction in the error metric PEHE and 11% decrease in the ATE bias, compared to the SOTA methods.