Graph Neural Networks (GNNs) excel at modeling graph data but often amplify biases tied to sensitive attributes like gender and race. Existing causality-based methods use isolated interventions on graph topology or features but struggle to produce representations that balance predictive power with fairness. This leads to two issues: (1) weak predictive power, where representations miss critical task-relevant features, and (2) bias amplification, where representations encode sensitive attributes, causing unfair outcomes. To address these issues, we introduce the Probability of Necessity and Sufficiency (PNS), where necessity ensures representations capture only essential features for predictions, and sufficiency guarantees these features are adequate without relying on sensitive attributes. We propose FairSNR, a fairness-aware graph representation learning framework that introduces constraints based on the PNS. This leverages PNS to guide the learning of fair representations from graph data. In particular, FairSNR employs an encoder to learn node representations with high PNS for downstream tasks. To compute and optimize PNS, FairSNR introduces an intervenor to generate the most challenging counterfactual interventions on the representations, thereby enhancing the model’s causal stability even under worst-case scenarios. Further, a discriminator is trained to detect and mitigate sensitive information leakage in the learned representations, effectively disentangling sensitive biases from task-relevant features. Experiments on real-world graph datasets demonstrate that FairSNR outperforms existing state-of-the-art (SOTA) methods in both fairness and utility.

Although previous deep imputation methods (eg., Generative Adversarial Network (GAN) based methods) have been widely designed to impute missing data, they still suffer from the issues, ie., lack of the imputation diversity and the generalization ability. In this paper, we propose a new GAN-based imputation method, namely Meta-based Generative Adversarial Imputation Network (Meta-GAIN), to investigate a new generator for achieving diverse imputation and generalization ability. Specifically, we employ the Kullback-Leibler (KL) divergence to achieve the imputation diversity by generating a continuous embedding space of the original data. We also design a task regularizer to suppress redundant features and capture a more authentic distribution, thus enhancing the generalization ability of the imputation model. Moreover, we theoretically prove that our proposed regularizer achieves the generalization ability. In addition, we design a new meta network to efficient optimize our objective function as well as to improve imputation diversity. Experimental results on real datasets show that our method outperforms all comparison methods under different missing mechanisms in terms of imputation and classification performance.

Unsupervised multi-view feature selection involves selecting a subset of crucial features across diverse views to diminish feature dimensionality without leveraging label information. While numerous studies have delved into this area, current solutions predominantly rely on linear multi-view data or employ weakly supervised learning to aid in feature selection. These approaches may risk losing semantic information when applied to real-world multi-view datasets. In this study, we introduce a novel model, Unsupervised Kernel-based Multi-view Feature selection with Robust self-representation and Binary hashing (UKMFS), which aims to identify robust consistent graph representation across views and leverage binary hashing codes to guide feature selection. Specifically, we first explore the underlying geometry by unifying the dimension of multi-view data with non-linear kernel mapping. Then, we search the consistent graph across views by fusing unique graph representations of each view in a self-representation manner. Additionally, we impose low-rank constraints on the graph of each view to mitigate noise and unimportant parts for preserving the main structures and patterns. Furthermore, we design an unsupervised hashing feature selection model to exploit reliable binary labels across views and weighted matrices from each view. Finally, an effective optimization method is customised to solve the formulated problem iteratively. Comprehensive experiments on public multi-view datasets indicate that our proposed method achieves state-of-the-art performance compared with the representative comparison methods regarding the clustering and the feature selection task.

Multi-view feature selection across diverse views identifying a compact subset of the most informative feature across various data views without relying on labeled information. While most of the solutions are limited to linear multi-view data or utilize weakly-supervised single-label learning to assist in feature selection, leading to the loss of valuable semantic information, especially when dealing with complex real-world multi-view datasets. To overcome these limitations, we introduce a novel Resilient Kernel-based Unsupervised Multi-view Feature Selection via compact Binary Hashing (RKUMBH), which aims to search a robust and consistent graph representation across views, leveraging binary hashing codes to guide feature selection. Specifically, we first standardize the dimensionality of multi-view data by using non-linear kernel mapping. Then, we explore consistent graph structures across different views by fusing individual similarity graph of each view under a self-representation guidance. Moreover, the low-rank constraints are used to preserve the primary structures and patterns embedding within the data, and an unsupervised hashing feature selection framework is conducted to generate reliable hashing codes across views. Additionally, we design a customized iterative optimization method to solve the unified model. Extensive experiments on six public multi-view datasets demonstrate that our proposed method obtains state-of-the-art results compared to existing works for both clustering and feature selection tasks.

Graph convolutional network (GCN) outputs powerful representation by considering the structure information of the data to conduct representation learning, but its robustness is sensitive to the quality of both the feature matrix and the initial graph. In this article, we propose a novel multigraph fusion method to produce a high-quality graph and a low-dimensional space of original high-dimensional data for the GCN model. Specifically, the proposed method first extracts the common information and the complementary information among multiple local graphs to obtain a unified local graph, which is then fused with the global graph of the data to obtain the initial graph for the GCN model. As a result, the proposed method conducts the graph fusion process twice to simultaneously learn the low-dimensional space and the intrinsic graph structure of the data in a unified framework. Experimental results on real datasets demonstrated that our method outperformed the comparison methods in terms of classification tasks.

Graph neural networks (GNNs) conduct feature learning by taking into account the local structure preservation of the data to produce discriminative features, but need to address the following issues, i.e., 1) the initial graph containing faulty and missing edges often affect feature learning and 2) most GNN methods suffer from the issue of out-of-example since their training processes do not directly generate a prediction model to predict unseen data points. In this work, we propose a reverse GNN model to learn the graph from the intrinsic space of the original data points as well as to investigate a new out-of-sample extension method. As a result, the proposed method can output a high-quality graph to improve the quality of feature learning, while the new method of out-of-sample extension makes our reverse GNN method available for conducting supervised learning and semi-supervised learning. Experimental results on real-world datasets show that our method outputs competitive classification performance, compared to state-of-the-art methods, in terms of semi-supervised node classification, out-of-sample extension, random edge attack, link prediction, and image retrieval.

Both data augmentation and contrastive loss are the key components of contrastive learning. In this paper, we design a new multi-view unsupervised graph representation learning method including adaptive data augmentation and multi-view contrastive learning, to address some issues of contrastive learning ignoring the information from feature space. Specifically, the adaptive data augmentation first builds a feature graph from the feature space, and then designs a deep graph learning model on the original representation and the topology graph to update the feature graph and the new representation. As a result, the adaptive data augmentation outputs multi-view information, which is fed into two GCNs to generate multi-view embedding features. Two kinds of contrastive losses are further designed on multi-view embedding features to explore the complementary information among the topology and feature graphs. Additionally, adaptive data augmentation and contrastive learning are embedded in a unified framework to form an end-to-end model. Experimental results verify the effectiveness of our proposed method, compared to state-of-the-art methods.

The functional connectomics study on resting state functional magnetic resonance imaging (rs-fMRI) data has become a popular way for early disease diagnosis. However, previous methods did not jointly consider the global patterns, the local patterns, and the temporal information of the blood-oxygen-level-dependent (BOLD) signals, thereby restricting the model effectiveness for early disease diagnosis. In this paper, we propose a new graph convolutional network (GCN) method to capture local and global patterns for conducting dynamically functional connectivity analysis. Specifically, we first employ the sliding window method to partition the original BOLD signals into multiple segments, aiming at achieving the dynamically functional connectivity analysis, and then design a multi-view node classification and a temporal graph classification to output two kinds of representations, which capture the temporally global patterns and the temporally local patterns, respectively. We further fuse these two kinds of representation by the weighted concatenation method whose effectiveness is experimentally proved as well. Experimental results on real datasets demonstrate the effectiveness of our method, compared to comparison methods on different classification tasks.

Abstract Non-negative matrix factorization (NMF) is a powerful tool for data science researchers, and it has been successfully applied to data mining and machine learning community, due to its advantages such as simple form, good interpretability and less storage space. In this paper, we give a detailed survey on existing NMF methods, including a comprehensive analysis of their design principles, characteristics and drawbacks. In addition, we also discuss various variants of NMF methods and analyse properties and applications of these variants. Finally, we evaluate the performance of nine NMF methods through numerical experiments, and the results show that NMF methods perform well in clustering tasks.

The functional connectomic profile is one of the non-invasive imaging biomarkers in the computer-assisted diagnostic system for many neuro-diseases. However, the diagnostic power of functional connectivity is challenged by mixed frequency-specific neuronal oscillations in the brain, which makes the single Functional Connectivity Network (FCN) often underpowered to capture the disease-related functional patterns. To address this challenge, we propose a novel functional connectivity analysis framework to conduct joint feature learning and personalized disease diagnosis, in a semi-supervised manner, aiming at focusing on putative multi-band functional connectivity biomarkers from functional neuroimaging data. Specifically, we first decompose the Blood Oxygenation Level Dependent (BOLD) signals into multiple frequency bands by the discrete wavelet transform, and then cast the alignment of all fully-connected FCNs derived from multiple frequency bands into a parameter-free multi-band fusion model. The proposed fusion model fuses all fully-connected FCNs to obtain a sparsely-connected FCN (sparse FCN for short) for each individual subject, as well as lets each sparse FCN be close to its neighbored sparse FCNs and be far away from its furthest sparse FCNs. Furthermore, we employ the$\ell _{{1}}$-SVM to conduct joint brain region selection and disease diagnosis. Finally, we evaluate the effectiveness of our proposed framework on various neuro-diseases,i.e.,Fronto-Temporal Dementia (FTD), Obsessive-Compulsive Disorder (OCD), and Alzheimer’s Disease (AD), and the experimental results demonstrate that our framework shows more reasonable results, compared to state-of-the-art methods, in terms of classification performance and the selected brain regions. The source code can be visited by the urlhttps://github.com/reynard-hu/mbbna.

Brain functional connectivity analysis on fMRI data could improve the understanding of human brain function. However, due to the influence of the inter-subject variability and the heterogeneity across subjects, previous methods of functional connectivity analysis are often insufficient in capturing disease-related representation so that decreasing disease diagnosis performance. In this paper, we first propose a new multi-graph fusion framework to fine-tune the original representation derived from Pearson correlation analysis, and then employ L1-SVM on fine-tuned representations to conduct joint brain region selection and disease diagnosis for avoiding the issue of the curse of dimensionality on high-dimensional data. The multi-graph fusion framework automatically learns the connectivity number for every node (i.e., brain region) and integrates all subjects in a unified framework to output homogenous and discriminative representations of all subjects. Experimental results on two real data sets, i.e., fronto-temporal dementia (FTD) and obsessive-compulsive disorder (OCD), verified the effectiveness of our proposed framework, compared to state-of-the-art methods.

In this paper, we propose conducting Robust Graph Dimensionality Reduction (RGDR) by learning a transformation matrix to map original high-dimensional data into their low-dimensional intrinsic space without the influence of outliers. To do this, we propose simultaneously 1) adaptively learning three variables, \ie a reverse graph embedding of original data, a transformation matrix, and a graph matrix preserving the local similarity of original data in their low-dimensional intrinsic space; and 2) employing robust estimators to avoid outliers involving the processes of optimizing these three matrices. As a result, original data are cleaned by two strategies, \ie a prediction of original data based on three resulting variables and robust estimators, so that the transformation matrix can be learnt from accurately estimated intrinsic space with the helping of the reverse graph embedding and the graph matrix. Moreover, we propose a new optimization algorithm to the resulting objective function as well as theoretically prove the convergence of our optimization algorithm. Experimental results indicated that our proposed method outperformed all the comparison methods in terms of different classification tasks.