Local2Global: Unsupervised multi-view deep graph representation learning with Nearest Neighbor Constraint
Introduction
Deep learning based on Graphs regarded as the recent popular deep learning techniques pay an important role for graph structured data (e.g. social networks, e-commerce networks, transmission route of infection, brain nervous system, and so on) [1]. It generally has made considerable achievements in both aspects of semi-supervised and unsupervised learning [2], [3], [4]. Existing graph deep learning methods have captured effective results in the synthesis and representation domains, etc. [5], [6], [7]. However, those algorithms are not suitable for processing graph-structured data of multiple views, which usually appear by different views such as images with various features, text using diverse descriptions, web page categorization, etc. In light of that, multi-view learning method is led into jointing deep learning methods, which could effectively explore the multiple views data, have been attracted much more attention recently.
Multi-view learning is a fundamental technique in machine learning, which aims to mix together multiple features and obtain consistent knowledge information from different views [8], [9], [10]. It is integrated into deep learning methods for algorithm optimization [11], [12], [13], object recognition [14], [15], [16] and so on in the lately research. Generally, these multi-view deep learning methods have achieved more successful performances for real-world multiple big data sets. Hence, they can train a deep model with more strong learning ability for multi-view data feature fusion. The aforementioned multi-view deep learning methods can effectively process multiple non graph data views, but they are not applicable to multi-view graph-structured data.
To tackle this problem, some multi-view joint deep learning methods based graphs are studied for multiple data views with graph structures. For instance, multi-view graph auto-encoders technology are developed for drug similarity integration [17] and image features learning [18]. Also, different multi-view graph convolutional networks are studied for global poverty statistics [19] and citywide crowd flows prediction [20]. Especially, a multi-view attribute graph convolution networks model is presented for solving graph-structured data with multi-view attributes, which can reduce the noise/redundancy, learn the graph embedding features, capture the geometric relationship and the consistency of probability distribution in different graph data views [21]. And multi-view joint graph representation learning is discussed for urban region embedding, which applies a graph attention mechanism in learning region representations from each view [22]. However, in those ways, the global feature information from different graph data views is fused into the final representation, which does not take into account the local characteristics in practice. Moreover, existing multi-view joint deep learning methods mainly focus on the distribution of adjacent points themselves in the learning process of global deep representation, while ignore the constraint relationship between maximal degree node and its adjacent points in graphs. Nonetheless, the more all adjacent nodes of the maximal degree node gather towards it, the better the effect of consistent representation learning is. As a result, there is a compelling need to develop an effective method to learn more deep graph representation from multi-view graph-structured data.
In this paper, we motivate by the above observations and propose a novel Multi-view Deep Graph Representation Learning (MDGRL) framework (or model) for clustering the multi-view graph-structured data. Our MDGRL is designed with two modules to capture deep feature representation information from multi-view graph data, which is an unsupervised technique. In brief, (1) it uses Graph Auto-Encoders (GAEs) [23] to learn local hidden graph representation from the initial multi-view data sets and fuses the local features of each view graph data into global features by defined multi-view syncretic function; (2) A new Nearest Neighbor Constraint (NNC) with Variational Graph Auto-Encoder (VGAE) [24] is put forward to extract more information from the global fusion features, which performs NNC between the maximal degree nodes and their adjacent nodes to enhance the deep graph representation capability from the fusion features.
Overall, the contributions of this paper can be summarized as follows:
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We utilize K-Nearest Neighbor (KNN) [25] to obtain graph-structured data from multi-view non-graphical data set. Then GAE is performed to learn local deep graph representation. All local features of each single-view graph are fused into a multi-view global graph feature with the same weight.
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To obtain the deep representation of fused global graph feature, we present a new Nearest Neighbor Constraint (NNC) Variational Graph Auto-Encoder (NNC-VGAE), which makes the adjacent nodes of the maximal degree nodes gather more together as far as possible in the training process.
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We propose a novel unsupervised Multi-view Deep Graph Representation Learning (MDGRL) framework based on our proposed NNC-VGAE. The multi-view local deep graph representation and fusion and the multi-view global graph hidden feature learning are combined into a holistic framework.
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We not only make experiments on eight non-medical multi-view data sets, but also generalize four medical multi-view data sets. The experimental results demonstrate that our MDGRL framework outperforms other benchmark methods on those twelve multi-view data sets.
The rest of this paper is organized as follows. Section 2 introduces the related work of multi-view deep graph representation learning methods. The methodology on our proposed MDGRL is presented in Section 3. Extensive experiments are conducted in Section 4. Finally, Section 5 concludes this paper and refers to future work.
Section snippets
Related work
In this section, we firstly review the deep learning methods based on graph neural networks. Then existing multi-view jointly graph deep learning representation approaches are recommended. At last, the variant techniques based GAE and VGAE are mentioned.
Methodology
In this section, we present the proposed unsupervised Multi-view Deep Graph Representation Learning (MDGRL) framework, which is shown in Fig. 1. Firstly, we define the problem and list the corresponding symbols utilized in this paper. Secondly, we recommend the two modules of our MDGRL framework in detail. Finally, the unsupervised deep representation learning algorithm of MDGRL is briefly described.
Experiments and results
In this section, we report the experimental details that have been implemented to evaluate the performance of our proposed MDGRL framework with eight real-world non-medical databases and four real-world medical data sets. We perform experiments on a Windows Server 2010 R2 with Intel Xeon processor, 30 GB RAM with TensorFlow and MATLAB development environment. We use different development environment because deep neural network methods such as MDRRL ran in TensorFlow and other comparing
Conclusions
This paper proposed a novel unsupervised Multi-view Deep Graph Representation Learning framework named MDGRL, consisting of GAEs, feature fusion module and VGAEs, to perform clustering task with our designed Nearest Neighbor Constraint. The MDGRL used GAE to obtain the local hidden representation of each view data. Then, they were fused into a global feature of multi-view data. To obtain more excellent deep global hidden features from the fusion features, a new NNC-VGAE was presented in MDGRL,
CRediT authorship contribution statement
Xiaobo Zhang: Writing - original draft, Methodology. Yan Yang: Writing - review & editing, Investigation. Donghai Zhai: Supervision, Visualization, Writing - review & editing. Tianrui Li: Writing - review & editing. Jielei Chu: Methodology, Validation. Hao Wang: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors would like thank the authors of the comparing baselines for their codes and the providers of the data sources for their benchmark data sets used in experiments. They are also especially grateful to the anonymous reviewers for their helpful comments and suggestions. This work was partially supported by the National Natural Science Foundation of China (No. 61976247), and the Key Research and Development Programme in Sichuan Province of China under Grant 20ZDYF2837. Hao Wang would like
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The code (and data) in this article has been certified as Reproducible by Code Ocean: (https://codeocean.com/). More information on the Reproducibility Badge Initiative is available at https://www.elsevier.com/physical-sciences-and-engineering/computer-science/journals.