In this paper, we generally formulate the dynamics prediction problem of various network systems (e.g., the prediction of mobility, traffic and topology) as the temporal link prediction task. Different from conventional techniques of temporal link prediction that ignore the potential non-linear characteristics and the informative link weights in the dynamic network, we introduce a novel non-linear model GCN-GAN to tackle the challenging temporal link prediction task of weighted dynamic networks. The proposed model leverages the benefits of the graph convolutional network (GCN), long short-term memory (LSTM) as well as the generative adversarial network (GAN). Thus, the dynamics, topology structure and evolutionary patterns of weighted dynamic networks can be fully exploited to improve the temporal link prediction performance. Concretely, we first utilize GCN to explore the local topological characteristics of each single snapshot and then employ LSTM to characterize the evolving features of the dynamic networks. Moreover, GAN is used to enhance the ability of the model to generate the next weighted network snapshot, which can effectively tackle the sparsity and the wide-value-range problem of edge weights in real-life dynamic networks. To verify the model's effectiveness, we conduct extensive experiments on four datasets of different network systems and application scenarios. The experimental results demonstrate that our model achieves impressive results compared to the state-of-the-art competitors.
However, the aforementioned approaches still have limited room for the improvement of prediction accuracy, because they are almost based on the traditional linear model, ignoring the potential non-linear characteristic of the dynamic network. Although several non-linear methods based on the restricted Boltzmann machine (RBM) @cite_27 and graph embedding @cite_4 are proposed, most of them can only be applied to the prediction of unweighted networks but cannot deal with the challenging case of weighted networks.
@cite_27 @cite_4
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Restricted Boltzmann Machine (RBM) is an important generative model modeling vectorial data. While applying an RBM in practice to images, the data have to be vectorized. This results in high-dimensional data and valuable spatial information has got lost in vectorization. In this paper, a Matrix-Variate Restricted Boltzmann Machine (MVRBM) model is proposed by generalizing the classic RBM to explicitly model matrix data. In the new RBM model, both input and hidden variables are in matrix forms which are connected by bilinear transforms. The MVRBM has much less model parameters while retaining comparable performance as the classic RBM. The advantages of the MVRBM have been demonstrated on three real-world applications: handwritten digit denoising, reconstruction and recognition. Restricted Boltzmann Machines (RBMs) are widely used as building blocks for deep learning models. Learning typically proceeds by using stochastic gradient descent, and the gradients are estimated with sampling methods. However, the gradient estimation is a computational bottleneck, so better use of the gradients will speed up the descent algorithm. To this end, we rst derive upper bounds on the RBM cost function, then show that descent methods can have natural advantages by operating in the‘1 and Shatten1 norm. We introduce a new method called Spectral Descent" that updates parameters in the normed space. Empirical results show dramatic improvements over stochastic gradient descent, and have only have a fractional increase on the per-iteration cost. Recent developments have demonstrated the capacity of restricted Boltzmann machines (RBM) to be powerful generative models, able to extract useful features from input data or construct deep artificial neural networks. In such settings, the RBM only yields a preprocessing or an initialization for some other model, instead of acting as a complete supervised model in its own right. In this paper, we argue that RBMs can provide a self-contained framework for developing competitive classifiers. We study the Classification RBM (ClassRBM), a variant on the RBM adapted to the classification setting. We study different strategies for training the ClassRBM and show that competitive classification performances can be reached when appropriately combining discriminative and generative training objectives. Since training according to the generative objective requires the computation of a generally intractable gradient, we also compare different approaches to estimating this gradient and address the issue of obtaining such a gradient for problems with very high dimensional inputs. Finally, we describe how to adapt the ClassRBM to two special cases of classification problems, namely semi-supervised and multitask learning. Time varying problems usually have complex underlying structures represented as dynamic networks where entities and relationships appear and disappear over time. The problem of efficiently performing dynamic link inference is extremely challenging due to the dynamic nature in massive evolving networks especially when there exist sparse connectivities and nonlinear transitional patterns. In this paper, we propose a novel deep learning framework, i.e., Conditional Temporal Restricted Boltzmann Machine (ctRBM), which predicts links based on individual transition variance as well as influence introduced by local neighbors. The proposed model is robust to noise and have the exponential capability to capture nonlinear variance. We tackle the computational challenges by developing an efficient algorithm for learning and inference of the proposed model. To improve the efficiency of the approach, we give a faster approximated implementation based on a proposed Neighbor Influence Clustering algorithm. Extensive experiments on simulated as well as real-world dynamic networks show that the proposed method outperforms existing algorithms in link inference on dynamic networks.