Abstract
The proliferation of networked data in various disciplines motivates a surge of research interests on network or graph mining. Among them, node classification is a typical learning task that focuses on exploiting the node interactions to infer the missing labels of unlabeled nodes in the network. A vast majority of existing node classification algorithms overwhelmingly focus on static networks and they assume the whole network structure is readily available before performing learning algorithms. However, it is not the case in many real-world scenarios where new nodes and new links are continuously being added in the network. Considering the streaming nature of networks, we study how to perform online node classification on this kind of streaming networks (a.k.a. online learning on streaming networks). As the existence of noisy links may negatively affect the node classification performance, we first present an online network embedding algorithm to alleviate this problem by obtaining the embedding representation of new nodes on the fly. Then we feed the learned embedding representation into a novel online soft margin kernel learning algorithm to predict the node labels in a sequential manner. Theoretical analysis is presented to show the superiority of the proposed framework of online learning on streaming networks (OLSN). Extensive experiments on real-world networks further demonstrate the effectiveness and efficiency of the proposed OLSN framework.
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Notes
It should be mentioned that for the convenience of presentation, we assume only one new node is added at time stamp \(t+1\). But it can be naturally extended to the case when a new set of m (\(m\ge 1\)) nodes are added to the existing network.
Definition RKHS Given a nonempty set \(\mathcal X\) and a Hilbert space \({{\mathcal H}}\) of functions \(f:\mathcal X\mapsto \mathcal R\), \(\mathcal H\) is a RKHS (Schölkopf and Smola 2002) endowed with kernel function \(k:\mathcal X \times \mathcal X\mapsto \mathcal R\) if k has the reproducing property:
$$\begin{aligned} \langle f(\cdot ),k(\mathbf{x},\cdot )\rangle _{\mathcal H}=f(\mathbf{x}),\forall f\in \mathcal H,\forall \mathbf{x}\in \mathcal X, \end{aligned}$$in particular, \(\langle k(\mathbf{x},\cdot ),k(\mathbf z ,\cdot )\rangle _{\mathcal H}=k(\mathbf{x},\mathbf z ), \forall \mathbf{x},\mathbf z \in \mathcal X\), and k is called the reproducing kernel for \(\mathcal H\).
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Acknowledgements
The authors would like to thank Liangyue Li for helpful discussions. Ling Jian is supported by the National Natural Science Foundation of China under Grant Nos. 61403419, 61503412, 11671418, Natural Science Foundation of Shandong Province under Grant Nos. ZR2013FQ034, ZR2014AP004, and Fundamental Research Funds for the Central Universities under Grant No. 16CX02048A. He also would like to thank the support of China Scholarship Council of visiting the Data Mining and Machine Learning Laboratory of Arizona State University during the year 2015 to 2016. Jundong Li and Huan Liu are supported by the National Science Foundation under Grant 1614576.
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Responsible editor: Charu Aggarwal.
Appendix
Appendix
In this section, we conduct experiments to see if Perceptron, Pegasos, and OSLG are sensitive to the model parameters involved. We only present the results on DBLP and Citeseer datasets as we have similar observations on the other datasets. In the experiments, we specify the embedding dimension as 30 and the percentage of training as 50%. We vary the parameter of learning rate \(\eta \) in Perceptron and the regularization parameter \(\mu \) in OLSG among \(\{0.1, 0.2, 0.5, 1, 2, 5\}\). For Pegasos, we vary the regularization parameter \(\lambda \) among \(\{10^{-6}, 10^{-5}, 10^{-4}, 10^{-3}, 10^{-2}, 10^{-1}\}\).
The performance variance w.r.t these parameters are listed in Tables 5 and 6. As can be observed, the changes of the parameter \(\eta \) in Perceptron do not affect the classification accuracy at all. For Pegasos and OSLG, different parameter settings (i.e., regularization parameters \(\lambda \) and \(\mu \)) slightly affect the end classification accuracy. However, in Pegasos and OSLG, the default parameter setting is good enough when prior knowledge is not available.
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Jian, L., Li, J. & Liu, H. Toward online node classification on streaming networks. Data Min Knowl Disc 32, 231–257 (2018). https://doi.org/10.1007/s10618-017-0533-y
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DOI: https://doi.org/10.1007/s10618-017-0533-y