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Register a new userTemporal Network Embedding via Tensor Factorization
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Added by
Jing Ma
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Representation learning on static graph-structured data has shown a significant impact on many real-world applications. However, less attention has been paid to the evolving nature of temporal networks, in which the edges are often changing over time. The embeddings of such temporal networks should encode both graph-structured information and the temporally evolving pattern. Existing approaches in learning temporally evolving network representations fail to capture the temporal interdependence. In this paper, we propose Toffee, a novel approach for temporal network representation learning based on tensor decomposition. Our method exploits the tensor-tensor product operator to encode the cross-time information, so that the periodic changes in the evolving networks can be captured. Experimental results demonstrate that Toffee outperforms existing methods on multiple real-world temporal networks in generating effective embeddings for the link prediction tasks.
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Network embedding aims to embed nodes into a low-dimensional space, while capturing the network structures and properties. Although quite a few promising network embedding methods have been proposed, most of them focus on static networks. In fact, temporal networks, which usually evolve over time in terms of microscopic and macroscopic dynamics, are ubiquitous. The micro-dynamics describe the formation process of network structures in a detailed manner, while the macro-dynamics refer to the evolution pattern of the network scale. Both micro- and macro-dynamics are the key factors to network evolution; however, how to elegantly capture both of them for temporal network embedding, especially macro-dynamics, has not yet been well studied. In this paper, we propose a novel temporal network embedding method with micro- and macro-dynamics, named $rm{M^2DNE}$. Specifically, for micro-dynamics, we regard the establishments of edges as the occurrences of chronological events and propose a temporal attention point process to capture the formation process of network structures in a fine-grained manner. For macro-dynamics, we define a general dynamics equation parameterized with network embeddings to capture the inherent evolution pattern and impose constraints in a higher structural level on network embeddings. Mutual evolutions of micro- and macro-dynamics in a temporal network alternately affect the process of learning node embeddings. Extensive experiments on three real-world temporal networks demonstrate that $rm{M^2DNE}$ significantly outperforms the state-of-the-arts not only in traditional tasks, e.g., network reconstruction, but also in temporal tendency-related tasks, e.g., scale prediction.
Many tasks in graph machine learning, such as link prediction and node classification, are typically solved by using representation learning, in which each node or edge in the network is encoded via an embedding. Though there exists a lot of network embeddings for static graphs, the task becomes much more complicated when the dynamic (i.e. temporal) network is analyzed. In this paper, we propose a novel approach for dynamic network representation learning based on Temporal Graph Network by using a highly custom message generating function by extracting Causal Anonymous Walks. For evaluation, we provide a benchmark pipeline for the evaluation of temporal network embeddings. This work provides the first comprehensive comparison framework for temporal network representation learning in every available setting for graph machine learning problems involving node classification and link prediction. The proposed model outperforms state-of-the-art baseline models. The work also justifies the difference between them based on evaluation in various transductive/inductive edge/node classification tasks. In addition, we show the applicability and superior performance of our model in the real-world downstream graph machine learning task provided by one of the top European banks, involving credit scoring based on transaction data.
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single and coupled tensor factorization models. Our method can be run even for very large models and is easily implemented. It exhibits better prediction performance than existing approaches based on maximum likelihood on several real-world datasets for missing link prediction problem.
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over fitting and the performance decreases significantly. To address this problem, the completion method for a tensor based on a Biased Deep Tensor Factorization Network (BDTFN) is proposed. This method can not only overcome the shortcomings of traditional tensor factorization, but also deal with complex non-linear data. Firstly, the horizontal and lateral tensors corresponding to the observed values of the input tensors are used as inputs and projected to obtain their horizontal (lateral) potential feature tensors. Secondly, the horizontal (lateral) potential feature tensors are respectively constructed into a multilayer perceptron network. Finally, the horizontal and lateral output tensors are fused by constructing a bilinear pooling layer. Tensor forward-propagation is composed of those three step, and its parameters are updated by tensor back-propagation using the multivariable chain rule. In this paper, we consider the large-scale 5-minute traffic speed data set and use it to address the missing data imputation problem for large-scale spatiotemporal traffic data. In addition, we compare the numerical performance of the proposed algorithm with those for state-of-the-art approaches on video recovery and color image recovery. Numerical experimental results illustrate that our approach is not only much more accurate than those state-of-the-art methods, but it also has high speed.
Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large graph. Most existing methods focus on learning the structural representations of vertices in a static network, but cannot guarantee an accurate and efficient embedding in a dynamic network scenario. To address this issue, we present an efficient incremental skip-gram algorithm with negative sampling for dynamic network embedding, and provide a set of theoretical analyses to characterize the performance guarantee. Specifically, we first partition a dynamic network into the updated, including addition/deletion of links and vertices, and the retained networks over time. Then we factorize the objective function of network embedding into the added, vanished and retained parts of the network. Next we provide a new stochastic gradient-based method, guided by the partitions of the network, to update the nodes and the parameter vectors. The proposed algorithm is proven to yield an objective function value with a bounded difference to that of the original objective function. Experimental results show that our proposal can significantly reduce the training time while preserving the comparable performance. We also demonstrate the correctness of the theoretical analysis and the practical usefulness of the dynamic network embedding. We perform extensive experiments on multiple real-world large network datasets over multi-label classification and link prediction tasks to evaluate the effectiveness and efficiency of the proposed framework, and up to 22 times speedup has been achieved.
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